Daily Papers

Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still struggle with solving mathematical problems due to the intricate reasoning required. This paper investigates the mathematical problem-solving capabilities of LLMs using the newly developed "MathOdyssey" dataset. The dataset includes diverse mathematical problems at high school and university levels, created by experts from notable institutions to rigorously test LLMs in advanced problem-solving scenarios and cover a wider range of subject areas. By providing the MathOdyssey dataset as a resource to the AI community, we aim to contribute to the understanding and improvement of AI capabilities in complex mathematical problem-solving. We conduct benchmarking on open-source models, such as Llama-3 and DBRX-Instruct, and closed-source models from the GPT series and Gemini models. Our results indicate that while LLMs perform well on routine and moderately difficult tasks, they face significant challenges with Olympiad-level problems and complex university-level questions. Our analysis shows a narrowing performance gap between open-source and closed-source models, yet substantial challenges remain, particularly with the most demanding problems. This study highlights the ongoing need for research to enhance the mathematical reasoning of LLMs. The dataset, results, and code are publicly available.

Recently, the release of INSTRUCTEVAL has provided valuable insights into the performance of large language models (LLMs) that utilize encoder-decoder or decoder-only architecture. Interestingly, despite being introduced four years ago, T5-based LLMs, such as FLAN-T5, continue to outperform the latest decoder-based LLMs, such as LLAMA and VICUNA, on tasks that require general problem-solving skills. This performance discrepancy can be attributed to three key factors: (1) Pre-training data, (2) Backbone architecture, and (3) Instruction dataset. In this technical report, our main focus is on investigating the impact of the third factor by leveraging VICUNA, a large language model based on LLAMA, which has undergone fine-tuning on ChatGPT conversations. To achieve this objective, we fine-tuned VICUNA using a customized instruction dataset collection called FLANMINI. This collection includes a subset of the large-scale instruction dataset known as FLAN, as well as various code-related datasets and conversational datasets derived from ChatGPT/GPT-4. This dataset comprises a large number of tasks that demand problem-solving skills. Our experimental findings strongly indicate that the enhanced problem-solving abilities of our model, FLACUNA, are obtained through fine-tuning VICUNA on the FLAN dataset, leading to significant improvements across numerous benchmark datasets in INSTRUCTEVAL. FLACUNA is publicly available at https://huggingface.co/declare-lab/flacuna-13b-v1.0.

Recent advances in large language models (LLMs) have demonstrated notable progress on many mathematical benchmarks. However, most of these benchmarks only feature problems grounded in junior and senior high school subjects, contain only multiple-choice questions, and are confined to a limited scope of elementary arithmetic operations. To address these issues, this paper introduces an expansive benchmark suite SciBench that aims to systematically examine the reasoning capabilities required for complex scientific problem solving. SciBench contains two carefully curated datasets: an open set featuring a range of collegiate-level scientific problems drawn from mathematics, chemistry, and physics textbooks, and a closed set comprising problems from undergraduate-level exams in computer science and mathematics. Based on the two datasets, we conduct an in-depth benchmark study of two representative LLMs with various prompting strategies. The results reveal that current LLMs fall short of delivering satisfactory performance, with an overall score of merely 35.80%. Furthermore, through a detailed user study, we categorize the errors made by LLMs into ten problem-solving abilities. Our analysis indicates that no single prompting strategy significantly outperforms others and some strategies that demonstrate improvements in certain problem-solving skills result in declines in other skills. We envision that SciBench will catalyze further developments in the reasoning abilities of LLMs, thereby ultimately contributing to scientific research and discovery.

Multi-Agent Large Language Models (LLMs) are gaining significant attention for their ability to harness collective intelligence in complex problem-solving, decision-making, and planning tasks. This aligns with the concept of the wisdom of crowds, where diverse agents contribute collectively to generating effective solutions, making it particularly suitable for educational settings. Senior design projects, also known as capstone or final year projects, are pivotal in engineering education as they integrate theoretical knowledge with practical application, fostering critical thinking, teamwork, and real-world problem-solving skills. In this paper, we explore the use of Multi-Agent LLMs in supporting these senior design projects undertaken by engineering students, which often involve multidisciplinary considerations and conflicting objectives, such as optimizing technical performance while addressing ethical, social, and environmental concerns. We propose a framework where distinct LLM agents represent different expert perspectives, such as problem formulation agents, system complexity agents, societal and ethical agents, or project managers, thus facilitating a holistic problem-solving approach. This implementation leverages standard multi-agent system (MAS) concepts such as coordination, cooperation, and negotiation, incorporating prompt engineering to develop diverse personas for each agent. These agents engage in rich, collaborative dialogues to simulate human engineering teams, guided by principles from swarm AI to efficiently balance individual contributions towards a unified solution. We adapt these techniques to create a collaboration structure for LLM agents, encouraging interdisciplinary reasoning and negotiation similar to real-world senior design projects. To assess the efficacy of this framework, we collected six proposals of engineering and computer science of...

The development of reasoning capabilities represents a critical frontier in large language models (LLMs) research, where reinforcement learning (RL) and process reward models (PRMs) have emerged as predominant methodological frameworks. Contrary to conventional wisdom, empirical evidence from DeepSeek-R1 demonstrates that pure RL training focused on mathematical problem-solving can progressively enhance reasoning abilities without PRM integration, challenging the perceived necessity of process supervision. In this study, we conduct a systematic investigation of the relationship between RL training and PRM capabilities. Our findings demonstrate that problem-solving proficiency and process supervision capabilities represent complementary dimensions of reasoning that co-evolve synergistically during pure RL training. In particular, current PRMs underperform simple baselines like majority voting when applied to state-of-the-art models such as DeepSeek-R1 and QwQ-32B. To address this limitation, we propose Self-PRM, an introspective framework in which models autonomously evaluate and rerank their generated solutions through self-reward mechanisms. Although Self-PRM consistently improves the accuracy of the benchmark (particularly with larger sample sizes), analysis exposes persistent challenges: The approach exhibits low precision (<10\%) on difficult problems, frequently misclassifying flawed solutions as valid. These analyses underscore the need for continued RL scaling to improve reward alignment and introspective accuracy. Overall, our findings suggest that PRM may not be essential for enhancing complex reasoning, as pure RL not only improves problem-solving skills but also inherently fosters robust PRM capabilities. We hope these findings provide actionable insights for building more reliable and self-aware complex reasoning models.

Language agents have shown impressive problem-solving skills within defined settings and brief timelines. Yet, with the ever-evolving complexities of open-world simulations, there's a pressing need for agents that can flexibly adapt to complex environments and consistently maintain a long-term memory to ensure coherent actions. To bridge the gap between language agents and open-world games, we introduce Language Agent for Role-Playing (LARP), which includes a cognitive architecture that encompasses memory processing and a decision-making assistant, an environment interaction module with a feedback-driven learnable action space, and a postprocessing method that promotes the alignment of various personalities. The LARP framework refines interactions between users and agents, predefined with unique backgrounds and personalities, ultimately enhancing the gaming experience in open-world contexts. Furthermore, it highlights the diverse uses of language models in a range of areas such as entertainment, education, and various simulation scenarios. The project page is released at https://miao-ai-lab.github.io/LARP/.

Mathematical questioning is crucial for assessing students problem-solving skills. Since manually creating such questions requires substantial effort, automatic methods have been explored. Existing state-of-the-art models rely on fine-tuning strategies and struggle to generate questions that heavily involve multiple steps of logical and arithmetic reasoning. Meanwhile, large language models(LLMs) such as ChatGPT have excelled in many NLP tasks involving logical and arithmetic reasoning. Nonetheless, their applications in generating educational questions are underutilized, especially in the field of mathematics. To bridge this gap, we take the first step to conduct an in-depth analysis of ChatGPT in generating pre-university math questions. Our analysis is categorized into two main settings: context-aware and context-unaware. In the context-aware setting, we evaluate ChatGPT on existing math question-answering benchmarks covering elementary, secondary, and ternary classes. In the context-unaware setting, we evaluate ChatGPT in generating math questions for each lesson from pre-university math curriculums that we crawl. Our crawling results in TopicMath, a comprehensive and novel collection of pre-university math curriculums collected from 121 math topics and 428 lessons from elementary, secondary, and tertiary classes. Through this analysis, we aim to provide insight into the potential of ChatGPT as a math questioner.

Training large language models (LLMs) to act as autonomous agents for multi-turn, long-horizon tasks remains significant challenges in scalability and training efficiency. To address this, we introduce L-Zero (L0), a scalable, end-to-end training pipeline for general-purpose agents. Featuring a low-cost, extensible, and sandboxed concurrent agent worker pool, L0 lowers the barrier for applying reinforcement learning in complex environments. We also introduce NB-Agent, the agent scaffold within L0, which operates in a "code-as-action" fashion via a Read-Eval-Print-Loop (REPL). We evaluate L0 on factuality question-answering benchmarks. Our experiments demonstrate that a base model can develop robust problem-solving skills using solely Reinforcement Learning with Verifiable Rewards (RLVR). On the Qwen2.5-7B-Instruct model, our method boosts accuracy on SimpleQA from 30 % to 80 % and on HotpotQA from 22 % to 41 %. We have open-sourced the entire L0 system, including our L0 series models, the NB-Agent, a complete training pipeline, and the corresponding training recipes on (https://github.com/cmriat/l0).

In the field of industrial inspection, Multimodal Large Language Models (MLLMs) have a high potential to renew the paradigms in practical applications due to their robust language capabilities and generalization abilities. However, despite their impressive problem-solving skills in many domains, MLLMs' ability in industrial anomaly detection has not been systematically studied. To bridge this gap, we present MMAD, the first-ever full-spectrum MLLMs benchmark in industrial Anomaly Detection. We defined seven key subtasks of MLLMs in industrial inspection and designed a novel pipeline to generate the MMAD dataset with 39,672 questions for 8,366 industrial images. With MMAD, we have conducted a comprehensive, quantitative evaluation of various state-of-the-art MLLMs. The commercial models performed the best, with the average accuracy of GPT-4o models reaching 74.9%. However, this result falls far short of industrial requirements. Our analysis reveals that current MLLMs still have significant room for improvement in answering questions related to industrial anomalies and defects. We further explore two training-free performance enhancement strategies to help models improve in industrial scenarios, highlighting their promising potential for future research.

NLP has recently made exciting progress toward training language models (LMs) with strong scientific problem-solving skills. However, model development has not focused on real-life use-cases of LMs for science, including applications in education that require processing long scientific documents. To address this, we introduce TutorEval and TutorChat. TutorEval is a diverse question-answering benchmark consisting of questions about long chapters from STEM textbooks, written by experts. TutorEval helps measure real-life usability of LMs as scientific assistants, and it is the first benchmark combining long contexts, free-form generation, and multi-disciplinary scientific knowledge. Moreover, we show that fine-tuning base models with existing dialogue datasets leads to poor performance on TutorEval. Therefore, we create TutorChat, a dataset of 80,000 long synthetic dialogues about textbooks. We use TutorChat to fine-tune Llemma models with 7B and 34B parameters. These LM tutors specialized in math have a 32K-token context window, and they excel at TutorEval while performing strongly on GSM8K and MATH. Our datasets build on open-source materials, and we release our models, data, and evaluations.

Large language models have demonstrated impressive performance on challenging mathematical reasoning tasks, which has triggered the discussion of whether the performance is achieved by true reasoning capability or memorization. To investigate this question, prior work has constructed mathematical benchmarks when questions undergo simple perturbations -- modifications that still preserve the underlying reasoning patterns of the solutions. However, no work has explored hard perturbations, which fundamentally change the nature of the problem so that the original solution steps do not apply. To bridge the gap, we construct MATH-P-Simple and MATH-P-Hard via simple perturbation and hard perturbation, respectively. Each consists of 279 perturbed math problems derived from level-5 (hardest) problems in the MATH dataset (Hendrycksmath et. al., 2021). We observe significant performance drops on MATH-P-Hard across various models, including o1-mini (-16.49%) and gemini-2.0-flash-thinking (-12.9%). We also raise concerns about a novel form of memorization where models blindly apply learned problem-solving skills without assessing their applicability to modified contexts. This issue is amplified when using original problems for in-context learning. We call for research efforts to address this challenge, which is critical for developing more robust and reliable reasoning models.

Despite their impressive performance on complex tasks, current language models (LMs) typically operate in a vacuum: Each input query is processed separately, without retaining insights from previous attempts. Here, we present Dynamic Cheatsheet (DC), a lightweight framework that endows a black-box LM with a persistent, evolving memory. Rather than repeatedly re-discovering or re-committing the same solutions and mistakes, DC enables models to store and reuse accumulated strategies, code snippets, and general problem-solving insights at inference time. This test-time learning enhances performance substantially across a range of tasks without needing explicit ground-truth labels or human feedback. Leveraging DC, Claude 3.5 Sonnet's accuracy more than doubled on AIME math exams once it began retaining algebraic insights across questions. Similarly, GPT-4o's success rate on Game of 24 increased from 10% to 99% after the model discovered and reused a Python-based solution. In tasks prone to arithmetic mistakes, such as balancing equations, DC enabled GPT-4o and Claude to reach near-perfect accuracy by recalling previously validated code, whereas their baselines stagnated around 50%. Beyond arithmetic challenges, DC yields notable accuracy gains on knowledge-demanding tasks. Claude achieved a 9% improvement in GPQA-Diamond and an 8% boost on MMLU-Pro problems. Crucially, DC's memory is self-curated, focusing on concise, transferable snippets rather than entire transcript. Unlike finetuning or static retrieval methods, DC adapts LMs' problem-solving skills on the fly, without modifying their underlying parameters. Overall, our findings present DC as a promising approach for augmenting LMs with persistent memory, bridging the divide between isolated inference events and the cumulative, experience-driven learning characteristic of human cognition.

Recent supervised fine-tuning (SFT) approaches have significantly improved language models' performance on mathematical reasoning tasks, even when models are trained at a small scale. However, the specific capabilities enhanced through such fine-tuning remain poorly understood. In this paper, we conduct a detailed analysis of model performance on the AIME24 dataset to understand how reasoning capabilities evolve. We discover a ladder-like structure in problem difficulty, categorize questions into four tiers (Easy, Medium, Hard, and Extremely Hard (Exh)), and identify the specific requirements for advancing between tiers. We find that progression from Easy to Medium tier requires adopting an R1 reasoning style with minimal SFT (500-1K instances), while Hard-level questions suffer from frequent model's errors at each step of the reasoning chain, with accuracy plateauing at around 65% despite logarithmic scaling. Exh-level questions present a fundamentally different challenge; they require unconventional problem-solving skills that current models uniformly struggle with. Additional findings reveal that carefully curated small-scale datasets offer limited advantage-scaling dataset size proves far more effective. Our analysis provides a clearer roadmap for advancing language model capabilities in mathematical reasoning.

Large language models (LLMs) excel in high-resource languages but struggle with low-resource languages (LRLs), particularly those spoken by minority communities in China, such as Tibetan, Uyghur, Kazakh, and Mongolian. To systematically track the progress in these languages, we introduce MiLiC-Eval, a benchmark designed for minority languages in China, featuring 24K instances across 9 tasks. MiLiC-Eval focuses on underrepresented writing systems and provides a fine-grained assessment of linguistic and problem-solving skills. Our evaluation reveals that LLMs perform poorly on syntax-intensive tasks and multi-script languages. We further demonstrate how MiLiC-Eval can help advance LRL research in handling diverse writing systems and understanding the process of language adaptation.

Recent advancements have positioned AI, and particularly Large Language Models (LLMs), as transformative tools for scientific research, capable of addressing complex tasks that require reasoning, problem-solving, and decision-making. Their exceptional capabilities suggest their potential as scientific research assistants but also highlight the need for holistic, rigorous, and domain-specific evaluation to assess effectiveness in real-world scientific applications. This paper describes a multifaceted methodology for Evaluating AI models as scientific Research Assistants (EAIRA) developed at Argonne National Laboratory. This methodology incorporates four primary classes of evaluations. 1) Multiple Choice Questions to assess factual recall; 2) Open Response to evaluate advanced reasoning and problem-solving skills; 3) Lab-Style Experiments involving detailed analysis of capabilities as research assistants in controlled environments; and 4) Field-Style Experiments to capture researcher-LLM interactions at scale in a wide range of scientific domains and applications. These complementary methods enable a comprehensive analysis of LLM strengths and weaknesses with respect to their scientific knowledge, reasoning abilities, and adaptability. Recognizing the rapid pace of LLM advancements, we designed the methodology to evolve and adapt so as to ensure its continued relevance and applicability. This paper describes the methodology state at the end of February 2025. Although developed within a subset of scientific domains, the methodology is designed to be generalizable to a wide range of scientific domains.

Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This begs the question: Are these errors incidental, or do they signal more substantial limitations? In an attempt to demystify Transformers, we investigate the limits of these models across three representative compositional tasks -- multi-digit multiplication, logic grid puzzles, and a classic dynamic programming problem. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. We formulate compositional tasks as computation graphs to systematically quantify the level of complexity, and break down reasoning steps into intermediate sub-procedures. Our empirical findings suggest that Transformers solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching, without necessarily developing systematic problem-solving skills. To round off our empirical study, we provide theoretical arguments on abstract multi-step reasoning problems that highlight how Transformers' performance will rapidly decay with increased task complexity.

Recent large-scale language models (LLMs) with long Chain-of-Thought reasoning-such as DeepSeek-R1-have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA-Out-of-distribution Math Problems Evaluation with 3 Generalization Axes-a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory-applying known problem solving skills to more complex instances within the same problem domain; (2) Compositional-combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative-adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

Physics problem-solving is a challenging domain for large AI models, requiring integration of conceptual understanding, mathematical reasoning, and interpretation of physical diagrams. Current evaluation methodologies show notable limitations in capturing the breadth and complexity of undergraduate-level physics, underscoring the need for more rigorous assessments. To this end, we present PhysUniBench, a large-scale multimodal benchmark designed to evaluate and improve the reasoning capabilities of multimodal large language models (MLLMs) specifically on undergraduate-level physics problems. PhysUniBench consists of 3,304 physics questions spanning 8 major sub-disciplines of physics, each accompanied by one visual diagrams. The benchmark includes both open-ended and multiple-choice questions, systematically curated and difficulty-rated through an iterative model-in-the-loop process. The benchmark's construction involved a rigorous multi-stage process, including multiple roll-outs, expert-level evaluation, automated filtering of easily solved problems, and a nuanced difficulty grading system with five levels. Through extensive experiments, we observe that current state-of-the-art models encounter substantial challenges in physics reasoning. For example, GPT-4o mini achieves only about 34.2\% accuracy in the proposed PhysUniBench. These results highlight that current MLLMs struggle with advanced physics reasoning, especially on multi-step problems and those requiring precise diagram interpretation. By providing a broad and rigorous assessment tool, PhysUniBench aims to drive progress in AI for Science, encouraging the development of models with stronger physical reasoning, problem-solving skills, and multimodal understanding. The benchmark and evaluation scripts are available at https://prismax-team.github.io/PhysUniBenchmark/.

Programming often involves converting detailed and complex specifications into code, a process during which developers typically utilize visual aids to more effectively convey concepts. While recent developments in Large Multimodal Models have demonstrated remarkable abilities in visual reasoning and mathematical tasks, there is little work on investigating whether these models can effectively interpret visual elements for code generation. To this end, we present MMCode, the first multi-modal coding dataset for evaluating algorithmic problem-solving skills in visually rich contexts. MMCode contains 3,548 questions and 6,620 images collected from real-world programming challenges harvested from 10 code competition websites, presenting significant challenges due to the extreme demand for reasoning abilities. Our experiment results show that current state-of-the-art models struggle to solve these problems. The results highlight the lack of powerful vision-code models, and we hope MMCode can serve as an inspiration for future works in this domain. The data and code are publicly available at https://github.com/happylkx/MMCode.

In this paper, we present an investigative study on how Mental Sets influence the reasoning capabilities of LLMs. LLMs have excelled in diverse natural language processing (NLP) tasks, driven by advancements in parameter-efficient fine-tuning (PEFT) and emergent capabilities like in-context learning (ICL). For complex reasoning tasks, selecting the right model for PEFT or ICL is critical, often relying on scores on benchmarks such as MMLU, MATH, and GSM8K. However, current evaluation methods, based on metrics like F1 Score or reasoning chain assessments by larger models, overlook a key dimension: adaptability to unfamiliar situations and overcoming entrenched thinking patterns. In cognitive psychology, Mental Set refers to the tendency to persist with previously successful strategies, even when they become inefficient - a challenge for problem solving and reasoning. We compare the performance of LLM models like Llama-3.1-8B-Instruct, Llama-3.1-70B-Instruct and GPT-4o in the presence of mental sets. To the best of our knowledge, this is the first study to integrate cognitive psychology concepts into the evaluation of LLMs for complex reasoning tasks, providing deeper insights into their adaptability and problem-solving efficacy.

Cognitive textual and visual reasoning tasks, such as puzzles, series, and analogies, demand the ability to quickly reason, decipher, and evaluate patterns both textually and spatially. While LLMs and VLMs, through extensive training on large amounts of human-curated data, have attained a high level of pseudo-human intelligence in some common sense reasoning tasks, they still struggle with more complex reasoning tasks that require cognitive understanding. In this work, we introduce a new dataset, NTSEBench, designed to evaluate the cognitive multi-modal reasoning and problem-solving skills of large models. The dataset comprises 2,728 multiple-choice questions comprising of a total of 4,642 images across 26 categories sampled from the NTSE examination conducted nationwide in India, featuring both visual and textual general aptitude questions that do not rely on rote learning. We establish baselines on the dataset using state-of-the-art LLMs and VLMs. To facilitate a comparison between open source and propriety models, we propose four distinct modeling strategies to handle different modalities (text and images) in the dataset instances.

Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment of the LLMs' math capabilities. To address this gap, we introduce MathBench, a new benchmark that rigorously assesses the mathematical capabilities of large language models. MathBench spans a wide range of mathematical disciplines, offering a detailed evaluation of both theoretical understanding and practical problem-solving skills. The benchmark progresses through five distinct stages, from basic arithmetic to college mathematics, and is structured to evaluate models at various depths of knowledge. Each stage includes theoretical questions and application problems, allowing us to measure a model's mathematical proficiency and its ability to apply concepts in practical scenarios. MathBench aims to enhance the evaluation of LLMs' mathematical abilities, providing a nuanced view of their knowledge understanding levels and problem solving skills in a bilingual context. The project is released at https://github.com/open-compass/MathBench .

Large Language Models (LLMs), such as ChatGPT and Bard, have revolutionized natural language understanding and generation. They possess deep language comprehension, human-like text generation capabilities, contextual awareness, and robust problem-solving skills, making them invaluable in various domains (e.g., search engines, customer support, translation). In the meantime, LLMs have also gained traction in the security community, revealing security vulnerabilities and showcasing their potential in security-related tasks. This paper explores the intersection of LLMs with security and privacy. Specifically, we investigate how LLMs positively impact security and privacy, potential risks and threats associated with their use, and inherent vulnerabilities within LLMs. Through a comprehensive literature review, the paper categorizes the papers into "The Good" (beneficial LLM applications), "The Bad" (offensive applications), and "The Ugly" (vulnerabilities of LLMs and their defenses). We have some interesting findings. For example, LLMs have proven to enhance code security (code vulnerability detection) and data privacy (data confidentiality protection), outperforming traditional methods. However, they can also be harnessed for various attacks (particularly user-level attacks) due to their human-like reasoning abilities. We have identified areas that require further research efforts. For example, Research on model and parameter extraction attacks is limited and often theoretical, hindered by LLM parameter scale and confidentiality. Safe instruction tuning, a recent development, requires more exploration. We hope that our work can shed light on the LLMs' potential to both bolster and jeopardize cybersecurity.

This paper presents the first Arabic crossword puzzle generator driven by advanced AI technology. Leveraging cutting-edge large language models including GPT4, GPT3-Davinci, GPT3-Curie, GPT3-Babbage, GPT3-Ada, and BERT, the system generates distinctive and challenging clues. Based on a dataset comprising over 50,000 clue-answer pairs, the generator employs fine-tuning, few/zero-shot learning strategies, and rigorous quality-checking protocols to enforce the generation of high-quality clue-answer pairs. Importantly, educational crosswords contribute to enhancing memory, expanding vocabulary, and promoting problem-solving skills, thereby augmenting the learning experience through a fun and engaging approach, reshaping the landscape of traditional learning methods. The overall system can be exploited as a powerful educational tool that amalgamates AI and innovative learning techniques, heralding a transformative era for Arabic crossword puzzles and the intersection of technology and education.

Programming is a powerful and ubiquitous problem-solving tool. Developing systems that can assist programmers or even generate programs independently could make programming more productive and accessible, yet so far incorporating innovations in AI has proven challenging. Recent large-scale language models have demonstrated an impressive ability to generate code, and are now able to complete simple programming tasks. However, these models still perform poorly when evaluated on more complex, unseen problems that require problem-solving skills beyond simply translating instructions into code. For example, competitive programming problems which require an understanding of algorithms and complex natural language remain extremely challenging. To address this gap, we introduce AlphaCode, a system for code generation that can create novel solutions to these problems that require deeper reasoning. In simulated evaluations on recent programming competitions on the Codeforces platform, AlphaCode achieved on average a ranking of top 54.3% in competitions with more than 5,000 participants. We found that three key components were critical to achieve good and reliable performance: (1) an extensive and clean competitive programming dataset for training and evaluation, (2) large and efficient-to-sample transformer-based architectures, and (3) large-scale model sampling to explore the search space, followed by filtering based on program behavior to a small set of submissions.

Large Language Models (LLMs) have demonstrated proficiency in their reasoning abilities, yet their large size presents scalability challenges and limits any further customization. In contrast, compact models offer customized training but often fall short in solving complex reasoning tasks. This study focuses on distilling the LLMs' decomposition skills into compact models using offline reinforcement learning. We leverage the advancements in the LLM`s capabilities to provide feedback and generate a specialized task-specific dataset for training compact models. The development of an AI-generated dataset and the establishment of baselines constitute the primary contributions of our work, underscoring the potential of compact models in replicating complex problem-solving skills.

Large Language Models (LLMs) are transforming how people find information, and many users turn nowadays to chatbots to obtain answers to their questions. Despite the instant access to abundant information that LLMs offer, it is still important to promote critical thinking and problem-solving skills. Automatic hint generation is a new task that aims to support humans in answering questions by themselves by creating hints that guide users toward answers without directly revealing them. In this context, hint evaluation focuses on measuring the quality of hints, helping to improve the hint generation approaches. However, resources for hint research are currently spanning different formats and datasets, while the evaluation tools are missing or incompatible, making it hard for researchers to compare and test their models. To overcome these challenges, we introduce HintEval, a Python library that makes it easy to access diverse datasets and provides multiple approaches to generate and evaluate hints. HintEval aggregates the scattered resources into a single toolkit that supports a range of research goals and enables a clear, multi-faceted, and reliable evaluation. The proposed library also includes detailed online documentation, helping users quickly explore its features and get started. By reducing barriers to entry and encouraging consistent evaluation practices, HintEval offers a major step forward for facilitating hint generation and analysis research within the NLP/IR community.

This paper introduces the first Turkish crossword puzzle generator designed to leverage the capabilities of large language models (LLMs) for educational purposes. In this work, we introduced two specially created datasets: one with over 180,000 unique answer-clue pairs for generating relevant clues from the given answer, and another with over 35,000 samples containing text, answer, category, and clue data, aimed at producing clues for specific texts and keywords within certain categories. Beyond entertainment, this generator emerges as an interactive educational tool that enhances memory, vocabulary, and problem-solving skills. It's a notable step in AI-enhanced education, merging game-like engagement with learning for Turkish and setting new standards for interactive, intelligent learning tools in Turkish.

We present a design framework called Conversational Learning with Analytical Step-by-Step Strategies (CLASS) for developing high-performance Intelligent Tutoring Systems (ITS). The CLASS framework aims to empower ITS with with two critical capabilities: imparting tutor-like step-by-step guidance and enabling tutor-like conversations in natural language to effectively engage learners. To empower ITS with the aforementioned capabilities, the CLASS framework employs two carefully curated synthetic datasets. The first scaffolding dataset encompasses a variety of elements, including problems, their corresponding subproblems, hints, incorrect solutions, and tailored feedback. This dataset provides ITS with essential problem-solving strategies necessary for guiding students through each step of the conversation. The second conversational dataset contains simulated student-tutor conversations that involve the application of problem-solving strategies learned from the first dataset. In the second dataset, the tutoring system adheres to a pre-defined response template, which helps to maintain consistency and structure in ITS's responses during its interactions. This structured methodology facilitates seamless integration of user feedback and yields valuable insights into ITS's internal decision-making process, allowing for continuous refinement and improvement of the system. We also present a proof-of-concept ITS, referred to as SPOCK, trained using the CLASS framework with a focus on college level introductory biology content. A carefully constructed protocol was developed for SPOCK's preliminary evaluation, examining aspects such as the factual accuracy and relevance of its responses. Experts in the field of biology offered favorable remarks, particularly highlighting SPOCK's capability to break down questions into manageable subproblems and provide step-by-step guidance to students.

Despite the existence of various benchmarks for evaluating natural language processing models, we argue that human exams are a more suitable means of evaluating general intelligence for large language models (LLMs), as they inherently demand a much wider range of abilities such as language understanding, domain knowledge, and problem-solving skills. To this end, we introduce M3Exam, a novel benchmark sourced from real and official human exam questions for evaluating LLMs in a multilingual, multimodal, and multilevel context. M3Exam exhibits three unique characteristics: (1) multilingualism, encompassing questions from multiple countries that require strong multilingual proficiency and cultural knowledge; (2) multimodality, accounting for the multimodal nature of many exam questions to test the model's multimodal understanding capability; and (3) multilevel structure, featuring exams from three critical educational periods to comprehensively assess a model's proficiency at different levels. In total, M3Exam contains 12,317 questions in 9 diverse languages with three educational levels, where about 23\% of the questions require processing images for successful solving. We assess the performance of top-performing LLMs on M3Exam and find that current models, including GPT-4, still struggle with multilingual text, particularly in low-resource and non-Latin script languages. Multimodal LLMs also perform poorly with complex multimodal questions. We believe that M3Exam can be a valuable resource for comprehensively evaluating LLMs by examining their multilingual and multimodal abilities and tracking their development. Data and evaluation code is available at https://github.com/DAMO-NLP-SG/M3Exam.

This paper introduces the novel task of multimodal puzzle solving, framed within the context of visual question-answering. We present a new dataset, AlgoPuzzleVQA designed to challenge and evaluate the capabilities of multimodal language models in solving algorithmic puzzles that necessitate both visual understanding, language understanding, and complex algorithmic reasoning. We create the puzzles to encompass a diverse array of mathematical and algorithmic topics such as boolean logic, combinatorics, graph theory, optimization, search, etc., aiming to evaluate the gap between visual data interpretation and algorithmic problem-solving skills. The dataset is generated automatically from code authored by humans. All our puzzles have exact solutions that can be found from the algorithm without tedious human calculations. It ensures that our dataset can be scaled up arbitrarily in terms of reasoning complexity and dataset size. Our investigation reveals that large language models (LLMs) such as GPT4V and Gemini exhibit limited performance in puzzle-solving tasks. We find that their performance is near random in a multi-choice question-answering setup for a significant number of puzzles. The findings emphasize the challenges of integrating visual, language, and algorithmic knowledge for solving complex reasoning problems.

This paper introduces the "GPT-in-the-loop" approach, a novel method combining the advanced reasoning capabilities of Large Language Models (LLMs) like Generative Pre-trained Transformers (GPT) with multiagent (MAS) systems. Venturing beyond traditional adaptive approaches that generally require long training processes, our framework employs GPT-4 for enhanced problem-solving and explanation skills. Our experimental backdrop is the smart streetlight Internet of Things (IoT) application. Here, agents use sensors, actuators, and neural networks to create an energy-efficient lighting system. By integrating GPT-4, these agents achieve superior decision-making and adaptability without the need for extensive training. We compare this approach with both traditional neuroevolutionary methods and solutions provided by software engineers, underlining the potential of GPT-driven multiagent systems in IoT. Structurally, the paper outlines the incorporation of GPT into the agent-driven Framework for the Internet of Things (FIoT), introduces our proposed GPT-in-the-loop approach, presents comparative results in the IoT context, and concludes with insights and future directions.

Despite recent advancements in large language models (LLMs), their performance on complex reasoning problems requiring multi-step thinking and combining various skills is still limited. To address this, we propose a novel framework HDFlow for complex reasoning with LLMs that combines fast and slow thinking modes in an adaptive manner. Our approach consists of two key components: 1) a new approach for slow, deliberate reasoning called Dynamic Workflow, which automatically decomposes complex problems into more manageable sub-tasks and dynamically designs a workflow to assemble specialized LLM or symbolic reasoning tools to solve sub-tasks; 2) Hybrid Thinking, a general framework that dynamically combines fast and slow thinking based on problem complexity. Finally, we propose an easy-to-scale method for automatically synthesizing a large-scale dataset of 27K challenging reasoning problems for complex reasoning and a hybrid thinking tuning method that trains smaller LLMs on this dataset to internalize the fast/slow hybrid reasoning strategies. Experiments on four reasoning benchmark datasets demonstrate that our slow thinking with dynamic workflows significantly outperforms Chain-of-Thought, and hybrid thinking achieves the highest accuracy while providing an effective balance between computational efficiency and performance. Fine-tuning using our hybrid thinking approach also significantly boosts the complex reasoning capabilities of open-source language models. The results showcase the promise of slow thinking, dynamic workflows, and hybrid thinking in expanding the frontier of complex problem-solving with LLMsCode and data will be released at \url{https://github.com/wenlinyao/HDFlow.}.

Metacognitive knowledge refers to humans' intuitive knowledge of their own thinking and reasoning processes. Today's best LLMs clearly possess some reasoning processes. The paper gives evidence that they also have metacognitive knowledge, including ability to name skills and procedures to apply given a task. We explore this primarily in context of math reasoning, developing a prompt-guided interaction procedure to get a powerful LLM to assign sensible skill labels to math questions, followed by having it perform semantic clustering to obtain coarser families of skill labels. These coarse skill labels look interpretable to humans. To validate that these skill labels are meaningful and relevant to the LLM's reasoning processes we perform the following experiments. (a) We ask GPT-4 to assign skill labels to training questions in math datasets GSM8K and MATH. (b) When using an LLM to solve the test questions, we present it with the full list of skill labels and ask it to identify the skill needed. Then it is presented with randomly selected exemplar solved questions associated with that skill label. This improves accuracy on GSM8k and MATH for several strong LLMs, including code-assisted models. The methodology presented is domain-agnostic, even though this article applies it to math problems.

Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging benchmark aimed at evaluating the general cognitive reasoning abilities of MLLMs. PolyMATH comprises 5,000 manually collected high-quality images of cognitive textual and visual challenges across 10 distinct categories, including pattern recognition, spatial reasoning, and relative reasoning. We conducted a comprehensive, and quantitative evaluation of 15 MLLMs using four diverse prompting strategies, including Chain-of-Thought and Step-Back. The best scores achieved on PolyMATH are ~41%, ~36%, and ~27%, obtained by Claude-3.5 Sonnet, GPT-4o and Gemini-1.5 Pro respectively - highlighting the logical and visual complexity of these questions. A further fine-grained error analysis reveals that these models struggle to understand spatial relations and perform drawn-out, high-level reasoning. This is further strengthened by our ablation study estimating MLLM performance when given textual descriptions in place of diagrams. As evidenced by ~4% improvement over textual descriptions as opposed to actual images, we discover that models do not truly comprehend visual diagrams and the spatial information therein, and are thus prone to logical errors. Finally, we evaluate the OpenAI o1 models and find that their performance only matches the human baseline, highlighting the difficulty of the benchmark. The results on PolyMATH highlight the room for improvement in multi-modal reasoning and provide unique insights to guide the development of future MLLMs.

Few-shot learning is a challenging task that requires language models to generalize from limited examples. Large language models like GPT-3 and PaLM have made impressive progress in this area, but they still face difficulties in reasoning tasks such as GSM8K, a benchmark for arithmetic problems. To improve their reasoning skills, previous work has proposed to guide the language model with prompts that elicit a series of reasoning steps before giving the final answer, achieving a significant improvement on GSM8K from 17.9% to 58.1% in problem-solving rate. In this paper, we present DIVERSE (Diverse Verifier on Reasoning Step), a novel approach that further enhances the reasoning capability of language models. DIVERSE has three main components: first, it generates diverse prompts to explore different reasoning paths for the same question; second, it uses a verifier to filter out incorrect answers based on a weighted voting scheme; and third, it verifies each reasoning step individually instead of the whole chain. We evaluate DIVERSE on the latest language model code-davinci-002 and show that it achieves new state-of-the-art results on six of eight reasoning benchmarks (e.g., GSM8K 74.4% to 83.2%).

Large Language Models (LLMs) show great promise in complex reasoning, with Reinforcement Learning with Verifiable Rewards (RLVR) being a key enhancement strategy. However, a prevalent issue is ``superficial self-reflection'', where models fail to robustly verify their own outputs. We introduce RISE (Reinforcing Reasoning with Self-Verification), a novel online RL framework designed to tackle this. RISE explicitly and simultaneously trains an LLM to improve both its problem-solving and self-verification abilities within a single, integrated RL process. The core mechanism involves leveraging verifiable rewards from an outcome verifier to provide on-the-fly feedback for both solution generation and self-verification tasks. In each iteration, the model generates solutions, then critiques its own on-policy generated solutions, with both trajectories contributing to the policy update. Extensive experiments on diverse mathematical reasoning benchmarks show that RISE consistently improves model's problem-solving accuracy while concurrently fostering strong self-verification skills. Our analyses highlight the advantages of online verification and the benefits of increased verification compute. Additionally, RISE models exhibit more frequent and accurate self-verification behaviors during reasoning. These advantages reinforce RISE as a flexible and effective path towards developing more robust and self-aware reasoners.

Despite rapid advances in vision-language models (VLMs), current benchmarks for multimodal reasoning fall short in three key dimensions. First, they overwhelmingly rely on static images, failing to capture the temporal complexity of real-world environments. Second, they narrowly focus on mathematical problem-solving, neglecting the broader spectrum of reasoning skills -- including abstract, physical, planning, spatial, and temporal capabilities -- required for robust multimodal intelligence. Third, many benchmarks quickly saturate, offering limited headroom for diagnosing failure modes or measuring continued progress. We introduce MORSE-500 (Multimodal Reasoning Stress-test Environment), a video benchmark composed of 500 fully scripted clips with embedded questions spanning six complementary reasoning categories. Each instance is programmatically generated using deterministic Python scripts (via Manim, Matplotlib, MoviePy), generative video models, and curated real footage. This script-driven design allows fine-grained control over visual complexity, distractor density, and temporal dynamics -- enabling difficulty to be scaled systematically as models improve. Unlike static benchmarks that become obsolete once saturated, MORSE-500 is built to evolve: its controllable generation pipeline supports the creation of arbitrarily challenging new instances, making it ideally suited for stress-testing next-generation models. Initial experiments with state-of-the-art systems -- including various Gemini 2.5 Pro and OpenAI o3 which represent the strongest available at the time, alongside strong open-source models -- reveal substantial performance gaps across all categories, with particularly large deficits in abstract and planning tasks. We release the full dataset, generation scripts, and evaluation harness to support transparent, reproducible, and forward-looking multimodal reasoning research.

The research in AI-based formal mathematical reasoning has shown an unstoppable growth trend. These studies have excelled in mathematical competitions like IMO, showing significant progress. However, these studies intertwined multiple skills simultaneously, i.e., problem-solving, reasoning, and writing formal specifications, making it hard to precisely identify the LLMs' strengths and weaknesses in each task. This paper focuses on formal verification, an immediate application scenario of formal reasoning, and decomposes it into six sub-tasks. We constructed 18k high-quality instruction-response pairs across five mainstream formal specification languages (Coq, Lean4, Dafny, ACSL, and TLA+) in six formal-verification-related tasks by distilling GPT-4o. They are split into a 14k+ fine-tuning dataset FM-alpaca and a 4k benchmark FM-Bench. We found that LLMs are good at writing proof segments when given either the code, or the detailed description of proof steps. Also, the fine-tuning brought about a nearly threefold improvement at most. Interestingly, we observed that fine-tuning with formal data also enhances mathematics, reasoning, and coding abilities. We hope our findings inspire further research. Fine-tuned models are released to facilitate subsequent studies

Recent advances in large language models (LLMs), particularly those enhanced through reinforced post-training, have demonstrated impressive reasoning capabilities, as exemplified by models such as OpenAI o1 and DeepSeek-R1. However, these capabilities are predominantly benchmarked on domains like mathematical problem solving and code generation -- leaving open the question of whether such reasoning skills generalize to complex, real-world scenarios. In this paper, we introduce LocationReasoner, a benchmark designed to evaluate LLMs' reasoning abilities in the context of real-world site selection, where models must identify feasible locations by reasoning over diverse and complicated spatial, environmental, and logistical constraints. The benchmark comprises over 300 carefully crafted queries of varying difficulty levels, supported by a sandbox environment with in-house tools for constraint-based location search. Extensive evaluations reveal that state-of-the-art reasoning models offer limited improvement over their non-reasoning predecessors in real-world contexts, with even the latest OpenAI o4 model failing on 30% of site selection tasks. Moreover, agentic strategies such as ReAct and Reflexion often suffer from over-reasoning, leading to worse outcomes than direct code-generation prompting. With key limitations of LLMs in holistic and non-linear reasoning highlighted, we release LocationReasoner to foster the development of LLMs and agents capable of robust, grounded reasoning in real-world decision-making tasks. Codes and data for our benchmark are available at https://github.com/miho-koda/LocationReasoner.

Large language and multimodal models have shown remarkable successes on various benchmarks focused on specific skills such as general-purpose programming, natural language understanding, math word problem-solving, and visual question answering. However, it is unclear how well these models perform on tasks that require a combination of these skills. In this paper, we curate a novel program synthesis benchmark based on the XLogoOnline visual programming environment. The benchmark comprises 85 real-world tasks from the Mini-level of the XLogoOnline environment, each requiring a combination of different skills such as spatial planning, basic programming, and logical reasoning. Our evaluation shows that current state-of-the-art models like GPT-4V and Llama3-70B struggle to solve these tasks, achieving only 20% and 2.35% success rates. Next, we develop a fine-tuning pipeline to boost the performance of models by leveraging a large-scale synthetic training dataset with over 80000 tasks. Moreover, we showcase how emulator-driven feedback can be used to design a curriculum over training data distribution. We showcase that a fine-tuned Llama3-8B drastically outperforms GPT-4V and Llama3-70B models, and provide an in-depth analysis of the models' expertise across different skill dimensions. We will publicly release the benchmark for future research on program synthesis in visual programming.

Recent advancements of large language models (LLMs) have led to claims of AI surpassing humans in natural language processing (NLP) tasks such as textual understanding and reasoning. This work investigates these assertions by introducing CAIMIRA, a novel framework rooted in item response theory (IRT) that enables quantitative assessment and comparison of problem-solving abilities of question-answering (QA) agents: humans and AI systems. Through analysis of over 300,000 responses from ~70 AI systems and 155 humans across thousands of quiz questions, CAIMIRA uncovers distinct proficiency patterns in knowledge domains and reasoning skills. Humans outperform AI systems in knowledge-grounded abductive and conceptual reasoning, while state-of-the-art LLMs like GPT-4 and LLaMA show superior performance on targeted information retrieval and fact-based reasoning, particularly when information gaps are well-defined and addressable through pattern matching or data retrieval. These findings highlight the need for future QA tasks to focus on questions that challenge not only higher-order reasoning and scientific thinking, but also demand nuanced linguistic interpretation and cross-contextual knowledge application, helping advance AI developments that better emulate or complement human cognitive abilities in real-world problem-solving.

Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical reasoning skills. Existing approaches to address this challenge often rely on ensemble methods and suffer from the problem of data scarcity in target domains. In this work, we present a novel method to enhance LLMs' capabilities in mathematical reasoning tasks. Motivated by the need to bridge this gap, our approach incorporates a question paraphrase strategy, which aims at diversifying the linguistic forms of mathematical questions to improve generalization. Additionally, specialized training objectives are employed to guide the model's learning process, focusing on enhancing its understanding of mathematical concepts and reasoning processes. We conduct experiments on four datasets using different LLMs, and demonstrate the effectiveness of our approach in improving LLMs' performance on mathematical reasoning tasks. Our findings underscore the significance of our methodology in the advancement of large language models and its potential implications for real-world applications that require mathematical reasoning abilities.

We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally, solving geometry problems and generating diagrams have been treated as separate tasks in machine learning, with no models successfully integrating both to support problem creation. However, we believe that mastery in geometry requires frictionless integration of all of these skills, from solving problems to visualizing geometric relationships, and finally, crafting tailored problems. Our extensive experiments demonstrate that GeoUni, with only 1.5B parameters, achieves performance comparable to larger models such as DeepSeek-R1 with 671B parameters in geometric reasoning tasks. GeoUni also excels in generating precise geometric diagrams, surpassing both text-to-image models and unified models, including the GPT-4o image generation. Most importantly, GeoUni is the only model capable of successfully generating textual problems with matching diagrams based on specific knowledge points, thus offering a wider range of capabilities that extend beyond current models.

Using blockchain technology, it is possible to create contracts that offer a reward in exchange for a trained machine learning model for a particular data set. This would allow users to train machine learning models for a reward in a trustless manner. The smart contract will use the blockchain to automatically validate the solution, so there would be no debate about whether the solution was correct or not. Users who submit the solutions won't have counterparty risk that they won't get paid for their work. Contracts can be created easily by anyone with a dataset, even programmatically by software agents. This creates a market where parties who are good at solving machine learning problems can directly monetize their skillset, and where any organization or software agent that has a problem to solve with AI can solicit solutions from all over the world. This will incentivize the creation of better machine learning models, and make AI more accessible to companies and software agents.

The releases of OpenAI's o1 and o3 mark a significant paradigm shift in Large Language Models towards advanced reasoning capabilities. Notably, o3 outperformed humans in novel problem-solving and skill acquisition on the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI). However, this benchmark is limited to symbolic patterns, whereas humans often perceive and reason about multimodal scenarios involving both vision and language data. Thus, there is an urgent need to investigate advanced reasoning capabilities in multimodal tasks. To this end, we track the evolution of the GPT-[n] and o-[n] series models on challenging multimodal puzzles, requiring fine-grained visual perception with abstract or algorithmic reasoning. The superior performance of o1 comes at nearly 750 times the computational cost of GPT-4o, raising concerns about its efficiency. Our results reveal a clear upward trend in reasoning capabilities across model iterations, with notable performance jumps across GPT-series models and subsequently to o1. Nonetheless, we observe that the o1 model still struggles with simple multimodal puzzles requiring abstract reasoning. Furthermore, its performance in algorithmic puzzles remains poor. We plan to continuously track new models in the series and update our results in this paper accordingly. All resources used in this evaluation are openly available https://github.com/declare-lab/LLM-PuzzleTest.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

Code generation by Llama 3.1 models, such as Meta's Llama 3.1 405B, represents a significant advancement in the field of artificial intelligence, particularly in natural language processing and programming automation. This paper explores the capabilities and applications of Llama-driven code generation, highlighting its ability to translate natural language prompts into executable code across multiple programming languages. Key features include contextual awareness, multi-language support, and enhanced debugging and optimization functionalities. By examining these aspects, we illustrate how Llama can serve as a versatile tool for developers of all skill levels, improving productivity and efficiency in software development. The potential implications for education, industry, and the future of coding practices are also discussed, underscoring the transformative impact of AI in programming. Experimentation shows that while Llama 3.1 405B performs well with simple algorithmic and data structure based problems, it still struggles with problems on Quantum Computing, Bioinformatics, and Artificial Intelligence.

Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can be designed to improve strategies and frustration can be minimized by adapting to a student's natural way of thinking rather than trying to fit a standard strategy for all. While it may be possible for human experts to identify strategies manually in classroom settings with sufficient student interaction, it is not possible to scale this up to big data. Therefore, we leverage advances in Machine Learning and AI methods to perform scalable strategy prediction that is also fair to students at all skill levels. Specifically, we develop an embedding called MVec where we learn a representation based on the mastery of students. We then cluster these embeddings with a non-parametric clustering method where we progressively learn clusters such that we group together instances that have approximately symmetrical strategies. The strategy prediction model is trained on instances sampled from these clusters. This ensures that we train the model over diverse strategies and also that strategies from a particular group do not bias the DNN model, thus allowing it to optimize its parameters over all groups. Using real world large-scale student interaction datasets from MATHia, we implement our approach using transformers and Node2Vec for learning the mastery embeddings and LSTMs for predicting strategies. We show that our approach can scale up to achieve high accuracy by training on a small sample of a large dataset and also has predictive equality, i.e., it can predict strategies equally well for learners at diverse skill levels.

In-context learning (ICL) allows a language model to improve its problem-solving capability when provided with suitable information in context. Since the choice of in-context information can be determined based on the problem itself, in-context learning is analogous to human learning from teachers in a classroom. Recent works (Didolkar et al., 2024a; 2024b) show that ICL performance can be improved by leveraging a frontier large language model's (LLM) ability to predict required skills to solve a problem, popularly referred to as an LLM's metacognition, and using the recommended skills to construct necessary in-context examples. While this skill-based strategy boosts ICL performance in larger models, its gains on small language models (SLMs) have been minimal, highlighting a performance gap in ICL capabilities. We investigate this gap and show that skill-based prompting can hurt SLM performance on easy questions by introducing unnecessary information, akin to cognitive overload. To address this, we introduce AdaptMI, an adaptive approach to selecting skill-based in-context Math Instructions for SLMs. Inspired by cognitive load theory from human pedagogy, our method only introduces skill-based examples when the model performs poorly. We further propose AdaptMI+, which adds examples targeted to the specific skills missing from the model's responses. On 5-shot evaluations across popular math benchmarks and five SLMs (1B--7B; Qwen, Llama), AdaptMI+ improves accuracy by up to 6% over naive skill-based strategies.

Large language models (LLMs) are primarily evaluated by overall performance on various text understanding and generation tasks. However, such a paradigm fails to comprehensively differentiate the fine-grained language and cognitive skills, rendering the lack of sufficient interpretation to LLMs' capabilities. In this paper, we present FAC^2E, a framework for Fine-grAined and Cognition-grounded LLMs' Capability Evaluation. Specifically, we formulate LLMs' evaluation in a multi-dimensional and explainable manner by dissociating the language-related capabilities and the cognition-related ones. Besides, through extracting the intermediate reasoning from LLMs, we further break down the process of applying a specific capability into three sub-steps: recalling relevant knowledge, utilizing knowledge, and solving problems. Finally, FAC^2E evaluates each sub-step of each fine-grained capability, providing a two-faceted diagnosis for LLMs. Utilizing FAC^2E, we identify a common shortfall in knowledge utilization among models and propose a straightforward, knowledge-enhanced method to mitigate this issue. Our results not only showcase promising performance enhancements but also highlight a direction for future LLM advancements.

Current benchmarks for evaluating Vision Language Models (VLMs) often fall short in thoroughly assessing model abilities to understand and process complex visual and textual content. They typically focus on simple tasks that do not require deep reasoning or the integration of multiple data modalities to solve an original problem. To address this gap, we introduce the PARROT-360V Benchmark, a novel and comprehensive benchmark featuring 2487 challenging visual puzzles designed to test VLMs on complex visual reasoning tasks. We evaluated leading models: GPT-4o, Claude-3.5-Sonnet, and Gemini-1.5-Pro, using PARROT-360V to assess their capabilities in combining visual clues with language skills to solve tasks in a manner akin to human problem-solving. Our findings reveal a notable performance gap: state-of-the-art models scored between 28 to 56 percentage on our benchmark, significantly lower than their performance on popular benchmarks. This underscores the limitations of current VLMs in handling complex, multi-step reasoning tasks and highlights the need for more robust evaluation frameworks to advance the field.

Large Language Models have achieved remarkable success in natural language processing tasks, with Reinforcement Learning playing a key role in adapting them to specific applications. However, obtaining ground truth answers for training LLMs in mathematical problem-solving is often challenging, costly, and sometimes unfeasible. This research delves into the utilization of format and length as surrogate signals to train LLMs for mathematical problem-solving, bypassing the need for traditional ground truth answers.Our study shows that a reward function centered on format correctness alone can yield performance improvements comparable to the standard GRPO algorithm in early phases. Recognizing the limitations of format-only rewards in the later phases, we incorporate length-based rewards. The resulting GRPO approach, leveraging format-length surrogate signals, not only matches but surpasses the performance of the standard GRPO algorithm relying on ground truth answers in certain scenarios, achieving 40.0\% accuracy on AIME2024 with a 7B base model. Through systematic exploration and experimentation, this research not only offers a practical solution for training LLMs to solve mathematical problems and reducing the dependence on extensive ground truth data collection, but also reveals the essence of why our label-free approach succeeds: base model is like an excellent student who has already mastered mathematical and logical reasoning skills, but performs poorly on the test paper, it simply needs to develop good answering habits to achieve outstanding results in exams , in other words, to unlock the capabilities it already possesses.

Recent advances in language models have demonstrated their capability to solve mathematical reasoning problems, achieving near-perfect accuracy on grade-school level math benchmarks like GSM8K. In this paper, we formally study how language models solve these problems. We design a series of controlled experiments to address several fundamental questions: (1) Can language models truly develop reasoning skills, or do they simply memorize templates? (2) What is the model's hidden (mental) reasoning process? (3) Do models solve math questions using skills similar to or different from humans? (4) Do models trained on GSM8K-like datasets develop reasoning skills beyond those necessary for solving GSM8K problems? (5) What mental process causes models to make reasoning mistakes? (6) How large or deep must a model be to effectively solve GSM8K-level math questions? Our study uncovers many hidden mechanisms by which language models solve mathematical questions, providing insights that extend beyond current understandings of LLMs.

Recent progress in large language models (LLMs) like GPT-4 and PaLM-2 has brought significant advancements in addressing math reasoning problems. In particular, OpenAI's latest version of GPT-4, known as GPT-4 Code Interpreter, shows remarkable performance on challenging math datasets. In this paper, we explore the effect of code on enhancing LLMs' reasoning capability by introducing different constraints on the Code Usage Frequency of GPT-4 Code Interpreter. We found that its success can be largely attributed to its powerful skills in generating and executing code, evaluating the output of code execution, and rectifying its solution when receiving unreasonable outputs. Based on this insight, we propose a novel and effective prompting method, explicit code-based self-verification~(CSV), to further boost the mathematical reasoning potential of GPT-4 Code Interpreter. This method employs a zero-shot prompt on GPT-4 Code Interpreter to encourage it to use code to self-verify its answers. In instances where the verification state registers as ``False'', the model shall automatically amend its solution, analogous to our approach of rectifying errors during a mathematics examination. Furthermore, we recognize that the states of the verification result indicate the confidence of a solution, which can improve the effectiveness of majority voting. With GPT-4 Code Interpreter and CSV, we achieve an impressive zero-shot accuracy on MATH dataset (53.9\% to 84.3\%).

Intelligent instruction-following robots capable of improving from autonomously collected experience have the potential to transform robot learning: instead of collecting costly teleoperated demonstration data, large-scale deployment of fleets of robots can quickly collect larger quantities of autonomous data that can collectively improve their performance. However, autonomous improvement requires solving two key problems: (i) fully automating a scalable data collection procedure that can collect diverse and semantically meaningful robot data and (ii) learning from non-optimal, autonomous data with no human annotations. To this end, we propose a novel approach that addresses these challenges, allowing instruction-following policies to improve from autonomously collected data without human supervision. Our framework leverages vision-language models to collect and evaluate semantically meaningful experiences in new environments, and then utilizes a decomposition of instruction following tasks into (semantic) language-conditioned image generation and (non-semantic) goal reaching, which makes it significantly more practical to improve from this autonomously collected data without any human annotations. We carry out extensive experiments in the real world to demonstrate the effectiveness of our approach, and find that in a suite of unseen environments, the robot policy can be improved significantly with autonomously collected data. We open-source the code for our semantic autonomous improvement pipeline, as well as our autonomous dataset of 30.5K trajectories collected across five tabletop environments.

Large language models (LLMs) have demonstrated impressive reasoning capabilities, yet there is ongoing debate about these abilities and the potential data contamination problem recently. This paper aims to evaluate the reasoning capacities of LLMs, specifically in solving recent competition-level programming problems in Codeforces, which are expert-crafted and unique, requiring deep understanding and robust reasoning skills. We first provide a comprehensive evaluation of GPT-4's peiceived zero-shot performance on this task, considering various aspects such as problems' release time, difficulties, and types of errors encountered. Surprisingly, the peiceived performance of GPT-4 has experienced a cliff like decline in problems after September 2021 consistently across all the difficulties and types of problems, which shows the potential data contamination, as well as the challenges for any existing LLM to solve unseen complex reasoning problems. We further explore various approaches such as fine-tuning, Chain-of-Thought prompting and problem description simplification, unfortunately none of them is able to consistently mitigate the challenges. Through our work, we emphasis the importance of this excellent data source for assessing the genuine reasoning capabilities of LLMs, and foster the development of LLMs with stronger reasoning abilities and better generalization in the future.

Solving complex long-horizon robotic manipulation problems requires sophisticated high-level planning capabilities, the ability to reason about the physical world, and reactively choose appropriate motor skills. Vision-language models (VLMs) pretrained on Internet data could in principle offer a framework for tackling such problems. However, in their current form, VLMs lack both the nuanced understanding of intricate physics required for robotic manipulation and the ability to reason over long horizons to address error compounding issues. In this paper, we introduce a novel test-time computation framework that enhances VLMs' physical reasoning capabilities for multi-stage manipulation tasks. At its core, our approach iteratively improves a pretrained VLM with a "reflection" mechanism - it uses a generative model to imagine future world states, leverages these predictions to guide action selection, and critically reflects on potential suboptimalities to refine its reasoning. Experimental results demonstrate that our method significantly outperforms several state-of-the-art commercial VLMs as well as other post-training approaches such as Monte Carlo Tree Search (MCTS). Videos are available at https://reflect-vlm.github.io.

Expert problem-solving is driven by powerful languages for thinking about problems and their solutions. Acquiring expertise means learning these languages -- systems of concepts, alongside the skills to use them. We present DreamCoder, a system that learns to solve problems by writing programs. It builds expertise by creating programming languages for expressing domain concepts, together with neural networks to guide the search for programs within these languages. A ``wake-sleep'' learning algorithm alternately extends the language with new symbolic abstractions and trains the neural network on imagined and replayed problems. DreamCoder solves both classic inductive programming tasks and creative tasks such as drawing pictures and building scenes. It rediscovers the basics of modern functional programming, vector algebra and classical physics, including Newton's and Coulomb's laws. Concepts are built compositionally from those learned earlier, yielding multi-layered symbolic representations that are interpretable and transferrable to new tasks, while still growing scalably and flexibly with experience.

Recent methods have demonstrated that Large Language Models (LLMs) can solve reasoning tasks better when they are encouraged to solve subtasks of the main task first. In this paper we devise a similar strategy that breaks down reasoning tasks into a problem decomposition phase and a problem solving phase and show that the strategy is able to outperform a single stage solution. Further, we hypothesize that the decomposition should be easier to distill into a smaller model compared to the problem solving because the latter requires large amounts of domain knowledge while the former only requires learning general problem solving strategies. We propose methods to distill these two capabilities and evaluate their impact on reasoning outcomes and inference cost. We find that we can distill the problem decomposition phase and at the same time achieve good generalization across tasks, datasets, and models. However, it is harder to distill the problem solving capability without losing performance and the resulting distilled model struggles with generalization. These results indicate that by using smaller, distilled problem decomposition models in combination with problem solving LLMs we can achieve reasoning with cost-efficient inference and local adaptation.

Large Language Models (LLMs) have achieved remarkable success in reasoning tasks with the development of prompting methods. However, existing prompting approaches cannot reuse insights of solving similar problems and suffer from accumulated errors in multi-step reasoning, since they prompt LLMs to reason from scratch. To address these issues, we propose \textit{Thought Propagation (TP)}, which explores the analogous problems and leverages their solutions to enhance the complex reasoning ability of LLMs. These analogous problems are related to the input one, with reusable solutions and problem-solving strategies. Thus, it is promising to propagate insights of solving previous analogous problems to inspire new problem-solving. To achieve this, TP first prompts LLMs to propose and solve a set of analogous problems that are related to the input one. Then, TP reuses the results of analogous problems to directly yield a new solution or derive a knowledge-intensive plan for execution to amend the initial solution obtained from scratch. TP is compatible with existing prompting approaches, allowing plug-and-play generalization and enhancement in a wide range of tasks without much labor in task-specific prompt engineering. Experiments across three challenging tasks demonstrate TP enjoys a substantial improvement over the baselines by an average of 12\% absolute increase in finding the optimal solutions in Shortest-path Reasoning, 13\% improvement of human preference in Creative Writing, and 15\% enhancement in the task completion rate of LLM-Agent Planning.

Advancements in LLMs have significantly expanded their capabilities across various domains. However, mathematical reasoning remains a challenging area, prompting the development of math-specific LLMs. These models typically follow a two-stage training paradigm: pre-training with math-related corpora and post-training with problem datasets for SFT. Despite these efforts, the improvements in mathematical reasoning achieved through continued pre-training (CPT) are often less significant compared to those obtained via SFT. This study addresses this discrepancy by exploring alternative strategies during the pre-training phase, focusing on the use of problem-solving data over general mathematical corpora. We investigate three primary research questions: (1) Can problem-solving data enhance the model's mathematical reasoning capabilities more effectively than general mathematical corpora during CPT? (2) Are synthetic data from the same source equally effective, and which synthesis methods are most efficient? (3) How do the capabilities developed from the same problem-solving data differ between the CPT and SFT stages, and what factors contribute to these differences? Our findings indicate that problem-solving data significantly enhances the model's mathematical capabilities compared to general mathematical corpora. We also identify effective data synthesis methods, demonstrating that the tutorship amplification synthesis method achieves the best performance. Furthermore, while SFT facilitates instruction-following abilities, it underperforms compared to CPT with the same data, which can be partially attributed to its poor learning capacity for hard multi-step problem-solving data. These insights provide valuable guidance for optimizing the mathematical reasoning capabilities of LLMs, culminating in our development of a powerful mathematical base model called JiuZhang-8B.

The ability to solve problems is a hallmark of intelligence and has been an enduring goal in AI. AI systems that can create programs as solutions to problems or assist developers in writing programs can increase productivity and make programming more accessible. Recently, pre-trained large language models have shown impressive abilities in generating new codes from natural language descriptions, repairing buggy codes, translating codes between languages, and retrieving relevant code segments. However, the evaluation of these models has often been performed in a scattered way on only one or two specific tasks, in a few languages, at a partial granularity (e.g., function) level and in many cases without proper training data. Even more concerning is that in most cases the evaluation of generated codes has been done in terms of mere lexical overlap rather than actual execution whereas semantic similarity (or equivalence) of two code segments depends only on their ``execution similarity'', i.e., being able to get the same output for a given input.

Does RL teach LLMs genuinely new skills, or does it merely activate existing ones? This question lies at the core of ongoing debates about the role of RL in LLM post-training. On one side, strong empirical results can be achieved with RL even without preceding supervised finetuning; on the other, critics argue that RL contributes little beyond reweighting existing reasoning strategies. This work provides concrete evidence that LLMs can acquire genuinely new skills during RL by composing existing ones, mirroring one of the central mechanisms by which humans acquire new cognitive skills. To mitigate data contamination and other confounding factors, and to allow precise control over task complexity, we develop a synthetic framework for our investigation. Specifically, we define a skill as the ability to infer the output of a string transformation function f(x) given x. When an LLM has already learned f and g prior to RL, our experiments reveal that RL enables it to learn unseen compositions of them h(x)=g(f(x)). Further, this compositional ability generalizes to more difficult problems such as compositions of >2 functions unseen during RL training. Surprisingly, our experiments show that compositional skill acquired on a source task transfers to a different target task. This transfer happens even without compositional training on the target, requiring only prior knowledge of the target's atomic skills. Our qualitative analysis shows that RL fundamentally changes the reasoning behaviors of the models. In contrast, next-token training with the same data yields none of these findings. Our systematic experiments provide fresh insights into LLM learning, suggesting the value of first building base models with basic skills, then using RL to incentivize advanced, generalizable skills for complex problems.

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99% using just 14 exemplars, compared to only 16% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

Large Language Models (LLMs) have demonstrated promising capabilities in solving mathematical reasoning tasks, leveraging Chain-of-Thought (CoT) data as a vital component in guiding answer generation. Current paradigms typically generate CoT and answers directly for a given problem, diverging from human problem-solving strategies to some extent. Humans often solve problems by recalling analogous cases and leveraging their solutions to reason about the current task. Inspired by this cognitive process, we propose MetaLadder, a novel framework that explicitly prompts LLMs to recall and reflect on meta-problems, those structurally or semantically analogous problems, alongside their CoT solutions before addressing the target problem. Additionally, we introduce a problem-restating mechanism to enhance the model's comprehension of the target problem by regenerating the original question, which further improves reasoning accuracy. Therefore, the model can achieve reasoning transfer from analogical problems, mimicking human-like "learning from examples" and generalization abilities. Extensive experiments on mathematical benchmarks demonstrate that our MetaLadder significantly boosts LLMs' problem-solving accuracy, largely outperforming standard CoT-based methods (10.3\% accuracy gain) and other methods. Our code and data has been released at https://github.com/LHL3341/MetaLadder.

The impressive performance of recent language models across a wide range of tasks suggests that they possess a degree of abstract reasoning skills. Are these skills general and transferable, or specialized to specific tasks seen during pretraining? To disentangle these effects, we propose an evaluation framework based on "counterfactual" task variants that deviate from the default assumptions underlying standard tasks. Across a suite of 11 tasks, we observe nontrivial performance on the counterfactual variants, but nevertheless find that performance substantially and consistently degrades compared to the default conditions. This suggests that while current LMs may possess abstract task-solving skills to a degree, they often also rely on narrow, non-transferable procedures for task-solving. These results motivate a more careful interpretation of language model performance that teases apart these aspects of behavior.

Large Language Models (LLMs) have exhibited exceptional performance across a broad range of tasks and domains. However, they still encounter difficulties in solving mathematical problems due to the rigorous and logical nature of mathematics. Previous studies have employed techniques such as supervised fine-tuning (SFT), prompt engineering, and search-based methods to improve the mathematical problem-solving abilities of LLMs. Despite these efforts, their performance remains suboptimal and demands substantial computational resources. To address this issue, we propose a novel approach, BEATS, to enhance mathematical problem-solving abilities. Our method leverages newly designed prompts that guide the model to iteratively rewrite, advance by one step, and generate answers based on previous steps. Additionally, we introduce a new back-verification technique that uses LLMs to validate the correctness of the generated answers. Furthermore, we employ a pruning tree search to optimize search time while achieving strong performance. Notably, our method improves Qwen2-7b-Instruct's score from 36.94 to 61.52, outperforming GPT4's 42.5 on the MATH benchmark.

We study building a multi-task agent in Minecraft. Without human demonstrations, solving long-horizon tasks in this open-ended environment with reinforcement learning (RL) is extremely sample inefficient. To tackle the challenge, we decompose solving Minecraft tasks into learning basic skills and planning over the skills. We propose three types of fine-grained basic skills in Minecraft, and use RL with intrinsic rewards to accomplish basic skills with high success rates. For skill planning, we use Large Language Models to find the relationships between skills and build a skill graph in advance. When the agent is solving a task, our skill search algorithm walks on the skill graph and generates the proper skill plans for the agent. In experiments, our method accomplishes 24 diverse Minecraft tasks, where many tasks require sequentially executing for more than 10 skills. Our method outperforms baselines in most tasks by a large margin. The project's website and code can be found at https://sites.google.com/view/plan4mc.

The nature of abstract reasoning is a matter of debate. Modern artificial neural network (ANN) models, like large language models, demonstrate impressive success when tested on abstract reasoning problems. However, it has been argued that their success reflects some form of memorization of similar problems (data contamination) rather than a general-purpose abstract reasoning capability. This concern is supported by evidence of brittleness, and the requirement of extensive training. In our study, we explored whether abstract reasoning can be achieved using the toolbox of ANNs, without prior training. Specifically, we studied an ANN model in which the weights of a naive network are optimized during the solution of the problem, using the problem data itself, rather than any prior knowledge. We tested this modeling approach on visual reasoning problems and found that it performs relatively well. Crucially, this success does not rely on memorization of similar problems. We further suggest an explanation of how it works. Finally, as problem solving is performed by changing the ANN weights, we explored the connection between problem solving and the accumulation of knowledge in the ANNs.

Large language models (LLMs) are known to struggle with complicated reasoning tasks such as math word problems (MWPs). In this paper, we present how analogy from similarly structured questions can improve LLMs' problem-solving capabilities for MWPs. Specifically, we rely on the retrieval of problems with similar computational graphs to the given question to serve as exemplars in the prompt, providing the correct reasoning path for the generation model to refer to. Empirical results across six math word problem datasets demonstrate the effectiveness of our proposed method, which achieves a significant improvement of up to 6.7 percent on average in absolute value, compared to baseline methods. These results highlight our method's potential in addressing the reasoning challenges in current LLMs.

Recent large language models (LLMs) have shown indications of mathematical reasoning ability. However it has not been clear how they would fare on more challenging competition-level problems. And while self-generated verbalizations of intermediate reasoning steps (i.e., chain-of-thought prompting) have been shown to be helpful, whether LLMs can make use of helpful side information such as problem-specific hints has not been investigated before. In this paper, we propose a challenging benchmark dataset for enabling such analyses. The Concept and Hint-Annotated Math Problems (CHAMP) consists of high school math competition problems, annotated with concepts, or general math facts, and hints, or problem-specific tricks. These annotations allow us to explore the effects of additional information, such as relevant hints, misleading concepts, or related problems. This benchmark is difficult, with the best model only scoring 58.1% in standard settings. With concepts and hints, performance sometimes improves, indicating that some models can make use of such side information. We further annotate model-generated solutions for their correctness. Using this corpus, we find that models often arrive at the correct final answer through wrong reasoning steps. In addition, we test whether models are able to verify these solutions, and find that most models struggle. The dataset and code are available on the project website.

We consider the problem of eliciting compositional generalization capabilities in large language models (LLMs) with a novel type of prompting strategy. Compositional generalization empowers the LLMs to solve problems that are harder than the ones they have seen (i.e., easy-to-hard generalization), which is a critical reasoning capability of human-like intelligence. However, even the current state-of-the-art LLMs still struggle with this form of reasoning. To bridge this gap, we propose skills-in-context (SKiC) prompting, which instructs LLMs how to compose basic skills to resolve more complex problems. We find that it is crucial to demonstrate both the skills and the compositional examples within the same prompting context. With as few as two examplars, our SKiC prompting initiates strong synergies between skills and their composition capabilities. Notably, it empowers LLMs to solve unseen problems that require innovative skill compositions, achieving near-perfect generalization on a broad range of challenging compositionality tasks. Intriguingly, SKiC prompting unlocks the latent potential of LLMs, enabling them to leverage pre-existing internal skills acquired during earlier pre-training stages, even when these skills are not explicitly presented in the prompting context. This results in the capability of LLMs to solve unseen complex problems by activating and composing internal competencies. With such prominent features, SKiC prompting is able to achieve state-of-the-art performance on challenging mathematical reasoning benchmarks (e.g., MATH).

Reasoning, as an essential ability for complex problem-solving, can provide back-end support for various real-world applications, such as medical diagnosis, negotiation, etc. This paper provides a comprehensive survey of cutting-edge research on reasoning with language model prompting. We introduce research works with comparisons and summaries and provide systematic resources to help beginners. We also discuss the potential reasons for emerging such reasoning abilities and highlight future research directions. Resources are available at https://github.com/zjunlp/Prompt4ReasoningPapers (updated periodically).

Recent developments, particularly OpenAI's O1 model, have demonstrated the remarkable potential of Large Language Models (LLMs) for complex reasoning tasks. Through analysis of O1's outputs and provided sample Chain-of-Thought (CoT) demonstrations, we observe that it approaches problem-solving in a distinctly human-like manner, systematically brainstorming ideas, testing hypotheses, verifying results, and planning comprehensive solutions. These sophisticated reasoning capabilities remain notably absent in other state-of-the-art language models. In this paper, we hypothesize that this performance gap stems from the limited availability of high-quality reasoning process data in current training sets. We demonstrate that by constructing a specialized dataset focused on explicit problem-solving workflows ("worked solutions"), we can elicit substantially improved planning capabilities from existing models. Additionally, we propose the Reasoning Enhancement Loop (REL), a method for generating synthetic worked solutions.

In this paper, we present a novel approach for distilling math word problem solving capabilities from large language models (LLMs) into smaller, more efficient student models. Our approach is designed to consider the student model's weaknesses and foster a tailored learning experience by generating targeted exercises aligned with educational science principles, such as knowledge tracing and personalized learning. Concretely, we let GPT-3 be a math tutor and run two steps iteratively: 1) assessing the student model's current learning status on a GPT-generated exercise book, and 2) improving the student model by training it with tailored exercise samples generated by GPT-3. Experimental results reveal that our approach outperforms LLMs (e.g., GPT-3 and PaLM) in accuracy across three distinct benchmarks while employing significantly fewer parameters. Furthermore, we provide a comprehensive analysis of the various components within our methodology to substantiate their efficacy.

The quest for human imitative AI has been an enduring topic in AI research since its inception. The technical evolution and emerging capabilities of the latest cohort of large language models (LLMs) have reinvigorated the subject beyond academia to the cultural zeitgeist. While recent NLP evaluation benchmark tasks test some aspects of human-imitative behaviour (e.g., BIG-bench's 'human-like behavior' tasks), few, if not none, examine creative problem solving abilities. Creative problem solving in humans is a well-studied topic in cognitive neuroscience with standardized tests that predominantly use the ability to associate (heterogeneous) connections among clue words as a metric for creativity. Exposure to misleading stimuli - distractors dubbed red herrings - impede human performance in such tasks via the fixation effect and Einstellung paradigm. In cognitive neuroscience studies, such fixations are experimentally induced by pre-exposing participants to orthographically similar incorrect words to subsequent word-fragments or clues. The popular British quiz show Only Connect's Connecting Wall segment essentially mimics Mednick's Remote Associates Test (RAT) formulation with built-in, deliberate red herrings, which makes it an ideal proxy dataset to explore and study fixation effect and Einstellung paradigm from cognitive neuroscience in LLMs. In addition to presenting the novel Only Connect Wall (OCW) dataset, we also report results from our evaluation of selected pre-trained language models and LLMs (including OpenAI's GPT series) on creative problem solving tasks like grouping clue words by heterogeneous connections, and identifying correct open knowledge domain connections in respective groups. The code and link to the dataset are available at https://github.com/TaatiTeam/OCW.

While visual question-answering (VQA) benchmarks have catalyzed the development of reasoning techniques, they have focused on vertical thinking. Effective problem-solving also necessitates lateral thinking, which remains understudied in AI and has not been used to test visual perception systems. To bridge this gap, we formulate visual lateral thinking as a multiple-choice question-answering task and describe a three-step taxonomy-driven methodology for instantiating task examples. Then, we develop COLUMBUS, a synthetic benchmark that applies the task pipeline to create QA sets with text and icon rebus puzzles based on publicly available collections of compounds and common phrases. COLUMBUS comprises over 1,000 puzzles, each with four answer candidates. While the SotA vision-language models (VLMs) achieve decent performance, our evaluation demonstrates a substantial gap between humans and models. VLMs benefit from human-curated descriptions but struggle to self-generate such representations at the right level of abstraction.

Geometry problem solving is a key area of mathematical reasoning, which is widely involved in many important fields such as education, mathematical ability assessment of artificial intelligence, and multimodal ability assessment. In recent years, the rapid development of deep learning technology, especially the rise of multimodal large language models, has triggered a widespread research boom. This paper provides a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of the current challenges and future directions that can be explored. Our goal is to provide a comprehensive and practical reference of deep learning for geometry problem solving to promote further developments in this field. We create a continuously updated list of papers on GitHub: https://github.com/majianz/dl4gps.

This study presents a novel learning approach designed to enhance both mathematical reasoning and problem-solving abilities of Large Language Models (LLMs). We focus on integrating the Chain-of-Thought (CoT) and the Program-of-Thought (PoT) learning, hypothesizing that prioritizing the learning of mathematical reasoning ability is helpful for the amplification of problem-solving ability. Thus, the initial learning with CoT is essential for solving challenging mathematical problems. To this end, we propose a sequential learning approach, named SAAS (Solving Ability Amplification Strategy), which strategically transitions from CoT learning to PoT learning. Our empirical study, involving an extensive performance comparison using several benchmarks, demonstrates that our SAAS achieves state-of-the-art (SOTA) performance. The results underscore the effectiveness of our sequential learning approach, marking a significant advancement in the field of mathematical reasoning in LLMs.

Despite impressive progress on complex reasoning, current large language models (LLMs) typically operate in isolation - treating each problem as an independent attempt, without accumulating or integrating experiential knowledge. In contrast, expert problem solvers - such as Olympiad or programming contest teams - leverage a rich tapestry of experiences: absorbing mentorship from coaches, developing intuition from past problems, leveraging knowledge of tool usage and library functionality, adapting strategies based on the expertise and experiences of peers, continuously refining their reasoning through trial and error, and learning from other related problems even during competition. We introduce Xolver, a training-free multi-agent reasoning framework that equips a black-box LLM with a persistent, evolving memory of holistic experience. Xolver integrates diverse experience modalities, including external and self-retrieval, tool use, collaborative interactions, agent-driven evaluation, and iterative refinement. By learning from relevant strategies, code fragments, and abstract reasoning patterns at inference time, Xolver avoids generating solutions from scratch - marking a transition from isolated inference toward experience-aware language agents. Built on both open-weight and proprietary models, Xolver consistently outperforms specialized reasoning agents. Even with lightweight backbones (e.g., QWQ-32B), it often surpasses advanced models including Qwen3-235B, Gemini 2.5 Pro, o3, and o4-mini-high. With o3-mini-high, it achieves new best results on GSM8K (98.1%), AIME'24 (94.4%), AIME'25 (93.7%), Math-500 (99.8%), and LiveCodeBench-V5 (91.6%) - highlighting holistic experience learning as a key step toward generalist agents capable of expert-level reasoning. Code and data are available at https://kagnlp.github.io/xolver.github.io/.

We introduce a new type of programming challenge called programming puzzles, as an objective and comprehensive evaluation of program synthesis, and release an open-source dataset of Python Programming Puzzles (P3). Each puzzle is defined by a short Python program f, and the goal is to find an input which makes f return True. The puzzles are objective in that each one is specified entirely by the source code of its verifier f, so evaluating f is all that is needed to test a candidate solution. They do not require an answer key or input/output examples, nor do they depend on natural language understanding. The dataset is comprehensive in that it spans problems of a range of difficulties and domains, ranging from trivial string manipulation problems, to classic programming puzzles (e.g., Tower of Hanoi), to interview/competitive-programming problems (e.g., dynamic programming), to longstanding open problems in algorithms and mathematics (e.g., factoring). We develop baseline enumerative program synthesis, GPT-3 and Codex solvers that are capable of solving puzzles -- even without access to any reference solutions -- by learning from their own past solutions. Codex performs best, solving up to 18% of 397 test problems with a single try and 80% of the problems with 1,000 tries per problem. In a small user study, we find a positive correlation between puzzle-solving performance and coding experience, and between the puzzle difficulty for humans and AI solvers. Therefore, further improvements on P3 could have a significant impact on many program synthesis areas.

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as algorithmic prompting. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Math word problems are critical K-8 educational tools, but writing them is time-consuming and requires domain expertise. We suggest that language models can support K-8 math education by automatically generating problems at scale. To be educational, generated problems must be 1) solvable, 2) accurate, and 3) appropriate. Existing datasets are unlabeled for these criteria, making them ill-suited for training problem generators. We introduce MATHWELL, a Llama-2 (70B) model iteratively finetuned to generate K-8 math word problems using data from expert annotation. Using MATHWELL, we generate the largest English word problem dataset to date, containing 20,490 problems. 3,484 are scored by domain experts who find MATHWELL has a 40% higher share of problems that have executable solutions and meet all criteria than alternatives, with 74% of its problems with executable solutions being solvable, accurate, and appropriate.

We explore the ability of large language models to solve and generate puzzles from the NPR Sunday Puzzle game show using PUZZLEQA, a dataset comprising 15 years of on-air puzzles. We evaluate four large language models using PUZZLEQA, in both multiple choice and free response formats, and explore two prompt engineering techniques to improve free response performance: chain-of-thought reasoning and prompt summarization. We find that state-of-the-art large language models can solve many PUZZLEQA puzzles: the best model, GPT-3.5, achieves 50.2% loose accuracy. However, in our few-shot puzzle generation experiment, we find no evidence that models can generate puzzles: GPT-3.5 generates puzzles with answers that do not conform to the generated rules. Puzzle generation remains a challenging task for future work.

LLMs are typically trained to answer user questions or follow instructions similarly to how human experts respond. However, in the standard alignment framework they lack the basic ability of explicit thinking before answering. Thinking is important for complex questions that require reasoning and planning -- but can be applied to any task. We propose a training method for equipping existing LLMs with such thinking abilities for general instruction following without use of additional human data. We achieve this by an iterative search and optimization procedure that explores the space of possible thought generations, allowing the model to learn how to think without direct supervision. For each instruction, the thought candidates are scored using a judge model to evaluate their responses only, and then optimized via preference optimization. We show that this procedure leads to superior performance on AlpacaEval and Arena-Hard, and shows gains from thinking on non-reasoning categories such as marketing, health and general knowledge, in addition to more traditional reasoning & problem-solving tasks.

Large Reasoning Models (LRMs) have demonstrated remarkable problem-solving abilities in mathematics, as evaluated by existing benchmarks exclusively on well-defined problems. However, such evaluation setup constitutes a critical gap, since a genuine intelligent agent should not only solve problems (as a math quiz solver), but also be able~to ask for information when the problems lack sufficient information, enabling proactivity in responding users' requests. To bridge such gap, we proposes a new dataset consisting of two types of incomplete problems with diverse contexts. Based on the dataset, our systematical evaluation of LRMs reveals their inability in proactively asking for information. In addition, we uncover the behaviors related to overthinking and hallucination of LRMs, and highlight the potential and challenges of supervised fine-tuning in learning such ability. We hope to provide new insights in developing LRMs with genuine intelligence, rather than just solving problems.

We explore the automatic generation of interactive, scenario-based lessons designed to train novice human tutors who teach middle school mathematics online. Employing prompt engineering through a Retrieval-Augmented Generation approach with GPT-4o, we developed a system capable of creating structured tutor training lessons. Our study generated lessons in English for three key topics: Encouraging Students' Independence, Encouraging Help-Seeking Behavior, and Turning on Cameras, using a task decomposition prompting strategy that breaks lesson generation into sub-tasks. The generated lessons were evaluated by two human evaluators, who provided both quantitative and qualitative evaluations using a comprehensive rubric informed by lesson design research. Results demonstrate that the task decomposition strategy led to higher-rated lessons compared to single-step generation. Human evaluators identified several strengths in the LLM-generated lessons, including well-structured content and time-saving potential, while also noting limitations such as generic feedback and a lack of clarity in some instructional sections. These findings underscore the potential of hybrid human-AI approaches for generating effective lessons in tutor training.

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze both final answers and solution steps to identify reasoning failures. Evaluating eight state-of-the-art models - including Mixtral, Llama, Gemini, GPT-4o, and OpenAI's o1 variants - we find that while newer models (e.g., o3-mini, deepseek-r1) achieve higher accuracy, all models exhibit errors in spatial reasoning, strategic planning, and arithmetic, sometimes producing correct answers through flawed logic. Common failure modes include unwarranted assumptions, over-reliance on numerical patterns, and difficulty translating physical intuition into mathematical steps. Manual analysis reveals that models struggle with problems requiring multi-step deduction or real-world knowledge, despite possessing broad mathematical knowledge. Our results underscore the importance of evaluating reasoning processes, not just answers, and caution against overestimating LLMs' problem-solving proficiency. The study highlights persistent gaps in LLMs' generalization abilities, emphasizing the need for targeted improvements in structured reasoning and constraint handling.

Large Language Models (LLMs) have demonstrated impressive reasoning abilities through test-time computation (TTC) techniques such as chain-of-thought prompting and tree-based reasoning. However, we argue that current reasoning LLMs (RLLMs) lack the ability to systematically explore the solution space. This paper formalizes what constitutes systematic problem solving and identifies common failure modes that reveal reasoning LLMs to be wanderers rather than systematic explorers. Through qualitative and quantitative analysis across multiple state-of-the-art LLMs, we uncover persistent issues: invalid reasoning steps, redundant explorations, hallucinated or unfaithful conclusions, and so on. Our findings suggest that current models' performance can appear to be competent on simple tasks yet degrade sharply as complexity increases. Based on the findings, we advocate for new metrics and tools that evaluate not just final outputs but the structure of the reasoning process itself.

Large language models (LLMs) have demonstrated solid zero-shot reasoning capabilities, which is reflected in their performance on the current test tasks. This calls for a more challenging benchmark requiring highly advanced reasoning ability to be solved. In this paper, we introduce such a benchmark, consisting of 191 long-form (1200 words on average) mystery narratives constructed as detective puzzles. Puzzles are sourced from the "5 Minute Mystery" platform and include a multiple-choice question for evaluation. Only 47% of humans solve a puzzle successfully on average, while the best human solvers achieve over 80% success rate. We show that GPT-3 models barely outperform random on this benchmark (with 28% accuracy) while state-of-the-art GPT-4 solves only 38% of puzzles. This indicates that there is still a significant gap in the deep reasoning abilities of LLMs and humans and highlights the need for further research in this area. Our work introduces a challenging benchmark for future studies on reasoning in language models and contributes to a better understanding of the limits of LLMs' abilities.

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains challenging due to the dual demands of spatial understanding and rigorous logical reasoning. Recent advances in large models have enabled notable breakthroughs, particularly for SAT-level problems, yet the field remains fragmented across methodologies, benchmarks, and evaluation frameworks. This survey systematically synthesizes GPS advancements through three core dimensions: (1) benchmark construction, (2) textual and diagrammatic parsing, and (3) reasoning paradigms. We further propose a unified analytical paradigm, assess current limitations, and identify emerging opportunities to guide future research toward human-level geometric reasoning, including automated benchmark generation and interpretable neuro-symbolic integration.

Recent studies show evidence for emergent cognitive abilities in Large Pre-trained Language Models (PLMs). The increasing cognitive alignment of these models has made them candidates for cognitive science theories. Prior research into the emergent cognitive abilities of PLMs has largely been path-independent to model training, i.e., has focused on the final model weights and not the intermediate steps. However, building plausible models of human cognition using PLMs would benefit from considering the developmental alignment of their performance during training to the trajectories of children's thinking. Guided by psychometric tests of human intelligence, we choose four sets of tasks to investigate the alignment of ten popular families of PLMs and evaluate their available intermediate and final training steps. These tasks are Numerical ability, Linguistic abilities, Conceptual understanding, and Fluid reasoning. We find a striking regularity: regardless of model size, the developmental trajectories of PLMs consistently exhibit a window of maximal alignment to human cognitive development. Before that window, training appears to endow "blank slate" models with the requisite structure to be poised to rapidly learn from experience. After that window, training appears to serve the engineering goal of reducing loss but not the scientific goal of increasing alignment with human cognition.

Causal language modeling using the Transformer architecture has yielded remarkable capabilities in Large Language Models (LLMs) over the last few years. However, the extent to which fundamental search and reasoning capabilities emerged within LLMs remains a topic of ongoing debate. In this work, we study if causal language modeling can learn a complex task such as solving Sudoku puzzles. To solve a Sudoku, the model is first required to search over all empty cells of the puzzle to decide on a cell to fill and then apply an appropriate strategy to fill the decided cell. Sometimes, the application of a strategy only results in thinning down the possible values in a cell rather than concluding the exact value of the cell. In such cases, multiple strategies are applied one after the other to fill a single cell. We observe that Transformer models trained on this synthetic task can indeed learn to solve Sudokus (our model solves 94.21% of the puzzles fully correctly) when trained on a logical sequence of steps taken by a solver. We find that training Transformers with the logical sequence of steps is necessary and without such training, they fail to learn Sudoku. We also extend our analysis to Zebra puzzles (known as Einstein puzzles) and show that the model solves 92.04 % of the puzzles fully correctly. In addition, we study the internal representations of the trained Transformer and find that through linear probing, we can decode information about the set of possible values in any given cell from them, pointing to the presence of a strong reasoning engine implicit in the Transformer weights.

Chain of Thought prompting strategy has enhanced the performance of Large Language Models (LLMs) across various NLP tasks. However, it still has shortcomings when dealing with complex reasoning tasks, following~cot_wei, including understanding errors, calculation errors and process errors (e.g. missing-step and hallucinations). Subsequently, Our in-depth analysis of various error types has found that deeply understanding the whole problem is critical in addressing complicated reasoning tasks. In this paper, we proposed a novel prompt strategy called Deeply Understanding the Problems (DUP) prompting, inspired by how humans solve complex reasoning problems, designed to enhance the comprehensive understanding of problems by LLMs. It consists of three stages: 1) extract the core question; 2) find out problem-solving information based on the core question; 3) generate and extract answers by LLMs. We evaluate the performance of DUP prompting on ten diverse reasoning datasets. Experimental results suggest that DUP prompting significantly outperforms Zero-Shot CoT ~kojima2022large across all datasets. Notably, DUP achieves state-of-the-art on SVAMP (90.4\% to 94.2\%) and GSM8K (94.6\% to 97.1\%).

Recent Language Models (LMs) achieve breakthrough performance in code generation when trained on human-authored problems, even solving some competitive-programming problems. Self-play has proven useful in games such as Go, and thus it is natural to ask whether LMs can generate their own instructive programming problems to improve their performance. We show that it is possible for an LM to synthesize programming problems and solutions, which are filtered for correctness by a Python interpreter. The LM's performance is then seen to improve when it is fine-tuned on its own synthetic problems and verified solutions; thus the model 'improves itself' using the Python interpreter. Problems are specified formally as programming puzzles [Schuster et al., 2021], a code-based problem format where solutions can easily be verified for correctness by execution. In experiments on publicly-available LMs, test accuracy more than doubles. This work demonstrates the potential for code LMs, with an interpreter, to generate instructive problems and improve their own performance.

Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

Large language model (LLM) performance on reasoning problems typically does not generalize out of distribution. Previous work has claimed that this can be mitigated by modifying prompts to include examples with chains of thought--demonstrations of solution procedures--with the intuition that it is possible to in-context teach an LLM an algorithm for solving the problem. This paper presents a case study of chain of thought on problems from Blocksworld, a classical planning domain, and examine the performance of two state-of-the-art LLMs across two axes: generality of examples given in prompt, and complexity of problems queried with each prompt. While our problems are very simple, we only find meaningful performance improvements from chain of thought prompts when those prompts are exceedingly specific to their problem class, and that those improvements quickly deteriorate as the size n of the query-specified stack grows past the size of stacks shown in the examples. Our results hint that, contrary to previous claims in the literature, CoT's performance improvements do not stem from the model learning general algorithmic procedures via demonstrations and depend on carefully engineering highly problem specific prompts. This spotlights drawbacks of chain of thought, especially because of the sharp tradeoff between possible performance gains and the amount of human labor necessary to generate examples with correct reasoning traces.

Human intelligence thrives on the concept of cognitive synergy, where collaboration and information integration among different cognitive processes yield superior outcomes compared to individual cognitive processes in isolation. Although Large Language Models (LLMs) have demonstrated promising performance as general task-solving agents, they still struggle with tasks that require intensive domain knowledge and complex reasoning. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist refers to an intelligent agent that collaborates with multiple minds, combining their individual strengths and knowledge, to enhance problem-solving and overall performance in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. We have discovered that assigning multiple, fine-grained personas in LLMs elicits better problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, SPP effectively elicits internal knowledge acquisition abilities, reduces hallucination, and maintains strong reasoning capabilities. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.

Mathematical problem-solving is a key field in artificial intelligence (AI) and a critical benchmark for evaluating the capabilities of large language models (LLMs). While extensive research has focused on mathematical problem-solving, most existing work and datasets concentrate on computational tasks, leaving gaps in areas like mathematical analysis, which demands rigorous proofs and formal reasoning. We developed the DEMI-MathAnalysis dataset, comprising proof-based problems from mathematical analysis topics such as Sequences and Limits, Infinite Series, and Convex Functions. We also designed a guiding framework to rigorously enhance LLMs' ability to solve these problems. Through fine-tuning LLMs on this dataset and employing our framework, we observed significant improvements in their capability to generate logical, complete, and elegant proofs. This work addresses critical gaps in mathematical reasoning and contributes to advancing trustworthy AI capable of handling formalized mathematical language. The code is publicly accessible at LLMs for Mathematical Analysis.

The ability of large language models to solve complex mathematical problems has progressed significantly, particularly for tasks requiring advanced reasoning. However, the scarcity of sufficiently challenging problems, particularly at the Olympiad level, hinders further advancements. In this work, we introduce PromptCoT, a novel approach for automatically generating high-quality Olympiad-level math problems. The proposed method synthesizes complex problems based on mathematical concepts and the rationale behind problem construction, emulating the thought processes of experienced problem designers. We provide a theoretical analysis demonstrating that an optimal rationale should maximize both the likelihood of rationale generation given the associated concepts and the likelihood of problem generation conditioned on both the rationale and the concepts. Our method is evaluated on standard benchmarks including GSM8K, MATH-500, and AIME2024, where it consistently outperforms existing problem generation methods. Furthermore, we demonstrate that PromptCoT exhibits superior data scalability, consistently maintaining high performance as the dataset size increases, outperforming the baselines. The implementation is available at https://github.com/zhaoxlpku/PromptCoT.

In this paper we look at the ability of recent large language models (LLMs) at solving mathematical problems in combinatorics. We compare models LLaMA-2, LLaMA-3.1, GPT-4, and Mixtral against each other and against human pupils and undergraduates with prior experience in mathematical olympiads. To facilitate these comparisons we introduce the Combi-Puzzles dataset, which contains 125 problem variants based on 25 combinatorial reasoning problems. Each problem is presented in one of five distinct forms, created by systematically manipulating the problem statements through adversarial additions, numeric parameter changes, and linguistic obfuscation. Our variations preserve the mathematical core and are designed to measure the generalisability of LLM problem-solving abilities, while also increasing confidence that problems are submitted to LLMs in forms that have not been seen as training instances. We found that a model based on GPT-4 outperformed all other models in producing correct responses, and performed significantly better in the mathematical variation of the problems than humans. We also found that modifications to problem statements significantly impact the LLM's performance, while human performance remains unaffected.

Socratic questioning is an educational method that allows students to discover answers to complex problems by asking them a series of thoughtful questions. Generation of didactically sound questions is challenging, requiring understanding of the reasoning process involved in the problem. We hypothesize that such questioning strategy can not only enhance the human performance, but also assist the math word problem (MWP) solvers. In this work, we explore the ability of large language models (LMs) in generating sequential questions for guiding math word problem-solving. We propose various guided question generation schemes based on input conditioning and reinforcement learning. On both automatic and human quality evaluations, we find that LMs constrained with desirable question properties generate superior questions and improve the overall performance of a math word problem solver. We conduct a preliminary user study to examine the potential value of such question generation models in the education domain. Results suggest that the difficulty level of problems plays an important role in determining whether questioning improves or hinders human performance. We discuss the future of using such questioning strategies in education.

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.

We study the depth of grade-school math (GSM) problem-solving capabilities of LLMs. To this end, we evaluate their performance on pairs of existing math word problems together so that the answer to the second problem depends on correctly answering the first problem. Our findings reveal a significant reasoning gap in most LLMs, that is performance difference between solving the compositional pairs and solving each question independently. This gap is more pronounced in smaller, more cost-efficient, and math-specialized models. Moreover, instruction-tuning recipes and code generation have varying effects across LLM sizes, while finetuning on GSM can lead to task overfitting. Our analysis indicates that large reasoning gaps are not because of test-set leakage, but due to distraction from additional context and poor second-hop reasoning. Overall, LLMs exhibit systematic differences in their reasoning abilities, despite what their performance on standard benchmarks indicates.

Our work presents a novel angle for evaluating language models' (LMs) mathematical abilities, by investigating whether they can discern skills and concepts enabled by math content. We contribute two datasets: one consisting of 385 fine-grained descriptions of K-12 math skills and concepts, or standards, from Achieve the Core (ATC), and another of 9.9K problems labeled with these standards (MathFish). Working with experienced teachers, we find that LMs struggle to tag and verify standards linked to problems, and instead predict labels that are close to ground truth, but differ in subtle ways. We also show that LMs often generate problems that do not fully align with standards described in prompts. Finally, we categorize problems in GSM8k using math standards, allowing us to better understand why some problems are more difficult to solve for models than others.

We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

Many students struggle with math word problems (MWPs), often finding it difficult to identify key information and select the appropriate mathematical operations.Schema-based instruction (SBI) is an evidence-based strategy that helps students categorize problems based on their structure, improving problem-solving accuracy. Building on this, we propose a Schema-Based Instruction Retrieval-Augmented Generation (SBI-RAG) framework that incorporates a large language model (LLM).Our approach emphasizes step-by-step reasoning by leveraging schemas to guide solution generation. We evaluate its performance on the GSM8K dataset, comparing it with GPT-4 and GPT-3.5 Turbo, and introduce a "reasoning score" metric to assess solution quality. Our findings suggest that SBI-RAG enhances reasoning clarity and problem-solving accuracy, potentially providing educational benefits for students

Reasoning is a fundamental aspect of human intelligence that plays a crucial role in activities such as problem solving, decision making, and critical thinking. In recent years, large language models (LLMs) have made significant progress in natural language processing, and there is observation that these models may exhibit reasoning abilities when they are sufficiently large. However, it is not yet clear to what extent LLMs are capable of reasoning. This paper provides a comprehensive overview of the current state of knowledge on reasoning in LLMs, including techniques for improving and eliciting reasoning in these models, methods and benchmarks for evaluating reasoning abilities, findings and implications of previous research in this field, and suggestions on future directions. Our aim is to provide a detailed and up-to-date review of this topic and stimulate meaningful discussion and future work.

Large Language Models (LLMs) are smart but forgetful. Recent studies, (e.g., (Bubeck et al., 2023)) on modern LLMs have shown that they are capable of performing amazing tasks typically necessitating human-level intelligence. However, unlike humans, frozen LLMs do not improve over time; they neither acquire new knowledge nor learn from their successes or failures. Some approaches to improving the intelligence of LLMs include fine-tuning models based on problem-solving performance (Zelikman et al., 2022), and building bigger and more sophisticated models (Bubeck et al., 2023). However, these methods have the drawback of requiring substantial data and computational resources to retrain existing models. In this paper, we explore the use of Retrieval Augmented Generation, also known as RAG (Lewis et al., 2021) to improve problem-solving performance. We propose ARM-RAG (Auxiliary Rationale Memory for Retrieval Augmented Generation), a system that learns from its successes without incurring high training costs. We demonstrate that the storage and subsequent retrieval of reasoning chains have a positive influence on performance in grade-school math problems.

The recent advent of large language models has reinvigorated debate over whether human cognitive capacities might emerge in such generic models given sufficient training data. Of particular interest is the ability of these models to reason about novel problems zero-shot, without any direct training. In human cognition, this capacity is closely tied to an ability to reason by analogy. Here, we performed a direct comparison between human reasoners and a large language model (the text-davinci-003 variant of GPT-3) on a range of analogical tasks, including a non-visual matrix reasoning task based on the rule structure of Raven's Standard Progressive Matrices. We found that GPT-3 displayed a surprisingly strong capacity for abstract pattern induction, matching or even surpassing human capabilities in most settings; preliminary tests of GPT-4 indicated even better performance. Our results indicate that large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems.

In this paper, we present empirical evidence of skills and directed exploration emerging from a simple RL algorithm long before any successful trials are observed. For example, in a manipulation task, the agent is given a single observation of the goal state and learns skills, first for moving its end-effector, then for pushing the block, and finally for picking up and placing the block. These skills emerge before the agent has ever successfully placed the block at the goal location and without the aid of any reward functions, demonstrations, or manually-specified distance metrics. Once the agent has learned to reach the goal state reliably, exploration is reduced. Implementing our method involves a simple modification of prior work and does not require density estimates, ensembles, or any additional hyperparameters. Intuitively, the proposed method seems like it should be terrible at exploration, and we lack a clear theoretical understanding of why it works so effectively, though our experiments provide some hints.

Visual mathematical reasoning, as a fundamental visual reasoning ability, has received widespread attention from the Large Multimodal Models (LMMs) community. Existing benchmarks, such as MathVista and MathVerse, focus more on the result-oriented performance but neglect the underlying principles in knowledge acquisition and generalization. Inspired by human-like mathematical reasoning, we introduce WE-MATH, the first benchmark specifically designed to explore the problem-solving principles beyond end-to-end performance. We meticulously collect and categorize 6.5K visual math problems, spanning 67 hierarchical knowledge concepts and five layers of knowledge granularity. We decompose composite problems into sub-problems according to the required knowledge concepts and introduce a novel four-dimensional metric, namely Insufficient Knowledge (IK), Inadequate Generalization (IG), Complete Mastery (CM), and Rote Memorization (RM), to hierarchically assess inherent issues in LMMs' reasoning process. With WE-MATH, we conduct a thorough evaluation of existing LMMs in visual mathematical reasoning and reveal a negative correlation between solving steps and problem-specific performance. We confirm the IK issue of LMMs can be effectively improved via knowledge augmentation strategies. More notably, the primary challenge of GPT-4o has significantly transitioned from IK to IG, establishing it as the first LMM advancing towards the knowledge generalization stage. In contrast, other LMMs exhibit a marked inclination towards Rote Memorization - they correctly solve composite problems involving multiple knowledge concepts yet fail to answer sub-problems. We anticipate that WE-MATH will open new pathways for advancements in visual mathematical reasoning for LMMs. The WE-MATH data and evaluation code are available at https://github.com/We-Math/We-Math.

Large language models (LLMs) have recently been shown to deliver impressive performance in various NLP tasks. To tackle multi-step reasoning tasks, few-shot chain-of-thought (CoT) prompting includes a few manually crafted step-by-step reasoning demonstrations which enable LLMs to explicitly generate reasoning steps and improve their reasoning task accuracy. To eliminate the manual effort, Zero-shot-CoT concatenates the target problem statement with "Let's think step by step" as an input prompt to LLMs. Despite the success of Zero-shot-CoT, it still suffers from three pitfalls: calculation errors, missing-step errors, and semantic misunderstanding errors. To address the missing-step errors, we propose Plan-and-Solve (PS) Prompting. It consists of two components: first, devising a plan to divide the entire task into smaller subtasks, and then carrying out the subtasks according to the plan. To address the calculation errors and improve the quality of generated reasoning steps, we extend PS prompting with more detailed instructions and derive PS+ prompting. We evaluate our proposed prompting strategy on ten datasets across three reasoning problems. The experimental results over GPT-3 show that our proposed zero-shot prompting consistently outperforms Zero-shot-CoT across all datasets by a large margin, is comparable to or exceeds Zero-shot-Program-of-Thought Prompting, and has comparable performance with 8-shot CoT prompting on the math reasoning problem. The code can be found at https://github.com/AGI-Edgerunners/Plan-and-Solve-Prompting.

Crossword puzzles are popular linguistic games often used as tools to engage students in learning. Educational crosswords are characterized by less cryptic and more factual clues that distinguish them from traditional crossword puzzles. Despite there exist several publicly available clue-answer pair databases for traditional crosswords, educational clue-answer pairs datasets are missing. In this article, we propose a methodology to build educational clue generation datasets that can be used to instruct Large Language Models (LLMs). By gathering from Wikipedia pages informative content associated with relevant keywords, we use Large Language Models to automatically generate pedagogical clues related to the given input keyword and its context. With such an approach, we created clue-instruct, a dataset containing 44,075 unique examples with text-keyword pairs associated with three distinct crossword clues. We used clue-instruct to instruct different LLMs to generate educational clues from a given input content and keyword. Both human and automatic evaluations confirmed the quality of the generated clues, thus validating the effectiveness of our approach.

Eleven Large Language Models (LLMs) were assessed using a custom-made battery of false-belief tasks, considered a gold standard in testing Theory of Mind (ToM) in humans. The battery included 640 prompts spread across 40 diverse tasks, each one including a false-belief scenario, three closely matched true-belief control scenarios, and the reversed versions of all four. To solve a single task, a model needed to correctly answer 16 prompts across all eight scenarios. Smaller and older models solved no tasks; GPT-3-davinci-003 (from November 2022) and ChatGPT-3.5-turbo (from March 2023) solved 20% of the tasks; ChatGPT-4 (from June 2023) solved 75% of the tasks, matching the performance of six-year-old children observed in past studies. We explore the potential interpretation of these findings, including the intriguing possibility that ToM, previously considered exclusive to humans, may have spontaneously emerged as a byproduct of LLMs' improving language skills.

Despite the strong performance of large language models (LLMs) in tasks like mathematical reasoning, their practical use is limited by high computational demands and proprietary restrictions. Chain-of-thought (CoT) and program-of-thought (PoT) fine-tuning are common methods to transfer LLM knowledge to small language models (SLMs). However, CoT often leads to calculation errors in SLMs, while PoT has shown more promise. While most PoT-based approaches focus on direct problem-to-code conversion or extracting only the key information from questions and then providing code solution for it, this work emphasizes filling the gaps in the question to clearly illustrate the solution path, which can be challenging for an SLM to understand when such information is not explicitly provided. Therefore, this paper introduces Gap-Filling Prompting (GFP), a novel two-step prompting strategy designed to enhance the problem-solving process for SLMs. The first step identifies these gaps and provides hints for filling them, while the second step adds the hints to the question to generate a final code solution. Experimental results on two benchmark datasets demonstrate that GFP significantly improves the mathematical reasoning abilities of SLMs.

As large language models (LLMs) become increasingly advanced, their ability to exhibit compositional generalization -- the capacity to combine learned skills in novel ways not encountered during training -- has garnered significant attention. This type of generalization, particularly in scenarios beyond training data, is also of great interest in the study of AI safety and alignment. A recent study introduced the SKILL-MIX evaluation, where models are tasked with composing a short paragraph demonstrating the use of a specified k-tuple of language skills. While small models struggled with composing even with k=3, larger models like GPT-4 performed reasonably well with k=5 and 6. In this paper, we employ a setup akin to SKILL-MIX to evaluate the capacity of smaller models to learn compositional generalization from examples. Utilizing a diverse set of language skills -- including rhetorical, literary, reasoning, theory of mind, and common sense -- GPT-4 was used to generate text samples that exhibit random subsets of k skills. Subsequent fine-tuning of 7B and 13B parameter models on these combined skill texts, for increasing values of k, revealed the following findings: (1) Training on combinations of k=2 and 3 skills results in noticeable improvements in the ability to compose texts with k=4 and 5 skills, despite models never having seen such examples during training. (2) When skill categories are split into training and held-out groups, models significantly improve at composing texts with held-out skills during testing despite having only seen training skills during fine-tuning, illustrating the efficacy of the training approach even with previously unseen skills. This study also suggests that incorporating skill-rich (potentially synthetic) text into training can substantially enhance the compositional capabilities of models.

In this paper, we introduce the Tree-of-Thought (ToT) framework, a novel approach aimed at improving the problem-solving capabilities of auto-regressive large language models (LLMs). The ToT technique is inspired by the human mind's approach for solving complex reasoning tasks through trial and error. In this process, the human mind explores the solution space through a tree-like thought process, allowing for backtracking when necessary. To implement ToT as a software system, we augment an LLM with additional modules including a prompter agent, a checker module, a memory module, and a ToT controller. In order to solve a given problem, these modules engage in a multi-round conversation with the LLM. The memory module records the conversation and state history of the problem solving process, which allows the system to backtrack to the previous steps of the thought-process and explore other directions from there. To verify the effectiveness of the proposed technique, we implemented a ToT-based solver for the Sudoku Puzzle. Experimental results show that the ToT framework can significantly increase the success rate of Sudoku puzzle solving. Our implementation of the ToT-based Sudoku solver is available on GitHub: https://github.com/jieyilong/tree-of-thought-puzzle-solver.

Large Language Models (LLMs) have recently showcased remarkable generalizability in various domains. Despite their extensive knowledge, LLMs still face challenges in efficiently utilizing encoded knowledge to develop accurate and logical reasoning processes. To mitigate this problem, we introduced Hint-before-Solving Prompting (HSP), which guides the model to generate hints (e.g., specific knowledge or key ideas) for solving the problem and then generate solutions containing intermediate reasoning steps. Since HSP is orthogonal to prompting methods (e.g., Chain-of-Thought (CoT)), we applied HSP to CoT, Least-to-Most, Plan-and-Solve, and Standard promptings. The results of extensive experiments on 6 reasoning benchmarks and 4 open-source LLMs demonstrate that HSP can effectively improve the accuracy of reasoning tasks: (1) By applying high-quality hint-enhanced HSP to CoT prompting, Llama2-70B-Chat shows an improvement of 9.7. (2) Beyond exploring training-free LLM capabilities, we built the HSPMATH dataset based on HSP and fine-tuned Llemma-7B, reaching 64.3 accuracy, surpassing GPT-3.5 and WizardMath-13B. We make our code and dataset publicly available at https://github.com/jinlanfu/HSP.

Automated math word problem solvers based on neural networks have successfully managed to obtain 70-80\% accuracy in solving arithmetic word problems. However, it has been shown that these solvers may rely on superficial patterns to obtain their equations. In order to determine what information math word problem solvers use to generate solutions, we remove parts of the input and measure the model's performance on the perturbed dataset. Our results show that the model is not sensitive to the removal of many words from the input and can still manage to find a correct answer when given a nonsense question. This indicates that automatic solvers do not follow the semantic logic of math word problems, and may be overfitting to the presence of specific words.

Large language models (LLMs) excel on a variety of reasoning benchmarks, but previous studies suggest they sometimes struggle to generalize to unseen questions, potentially due to over-reliance on memorized training examples. However, the precise conditions under which LLMs switch between reasoning and memorization during text generation remain unclear. In this work, we provide a mechanistic understanding of LLMs' reasoning-memorization dynamics by identifying a set of linear features in the model's residual stream that govern the balance between genuine reasoning and memory recall. These features not only distinguish reasoning tasks from memory-intensive ones but can also be manipulated to causally influence model performance on reasoning tasks. Additionally, we show that intervening in these reasoning features helps the model more accurately activate the most relevant problem-solving capabilities during answer generation. Our findings offer new insights into the underlying mechanisms of reasoning and memory in LLMs and pave the way for the development of more robust and interpretable generative AI systems.

In current NLP research, large-scale language models and their abilities are widely being discussed. Some recent works have also found notable failures of these models. Often these failure examples involve complex reasoning abilities. This work focuses on a simple commonsense ability, reasoning about when an action (or its effect) is feasible. To this end, we introduce FeasibilityQA, a question-answering dataset involving binary classification (BCQ) and multi-choice multi-correct questions (MCQ) that test understanding of feasibility. We show that even state-of-the-art models such as GPT-3, GPT-2, and T5 struggle to answer the feasibility questions correctly. Specifically, on MCQ and BCQ questions, GPT-3 achieves an accuracy of just (19%, 62%) and (25%, 64%) in zero-shot and few-shot settings, respectively. We also evaluate models by providing relevant knowledge statements required to answer the question. We find that the additional knowledge leads to a 7% gain in performance, but the overall performance still remains low. These results make one wonder how much commonsense knowledge about action feasibility is encoded in state-of-the-art models and how well they can reason about it.

Recent reasoning LLMs (RLMs), especially those trained with verifier-based reinforcement learning, often perform worse with few-shot CoT than with direct answering. We revisit this paradox using high-quality reasoning traces from DeepSeek-R1 as demonstrations and find that adding more exemplars consistently degrades accuracy, even when demonstrations are optimal. A detailed analysis reveals two mechanisms behind this decline: (i) semantic misguidance, where high textual similarity leads the model to treat the target as the same as the exemplar and to copy intermediate steps verbatim; and (ii) strategy transfer failure, where the model struggles to extract useful reasoning strategies and apply them to target questions. Guided by these, we introduce Insight-to-Solve (I2S), a sequential test-time procedure that turns demonstrations into explicit, reusable insights and derives a target-specific reasoning trace; optionally, the reasoning is self-refined for coherence and correctness (I2S+). Extensive experiments on diverse benchmarks show that I2S and I2S+ consistently outperform both direct answering and test-time scaling baselines across open- and closed-source models. Even for GPT models, our method helps: on AIME'25, GPT-4.1 rises by +14.0%, and o1-mini improves by +2.7% on AIME and +1.7% on GPQA, indicating that in-context demonstrations can be harnessed effectively via insight-refine-solve framework.

Making analogies is fundamental to cognition. Proportional analogies, which consist of four terms, are often used to assess linguistic and cognitive abilities. For instance, completing analogies like "Oxygen is to Gas as <blank> is to <blank>" requires identifying the semantic relationship (e.g., "type of") between the first pair of terms ("Oxygen" and "Gas") and finding a second pair that shares the same relationship (e.g., "Aluminum" and "Metal"). In this work, we introduce a 15K Multiple-Choice Question Answering (MCQA) dataset for proportional analogy completion and evaluate the performance of contemporary Large Language Models (LLMs) in various knowledge-enhanced prompt settings. Specifically, we augment prompts with three types of knowledge: exemplar, structured, and targeted. Our results show that despite extensive training data, solving proportional analogies remains challenging for current LLMs, with the best model achieving an accuracy of 55%. Notably, we find that providing targeted knowledge can better assist models in completing proportional analogies compared to providing exemplars or collections of structured knowledge.

Although LLMs are increasing the productivity of professional programmers, existing work shows that beginners struggle to prompt LLMs to solve text-to-code tasks. Why is this the case? This paper explores two competing hypotheses about the cause of student-LLM miscommunication: (1) students simply lack the technical vocabulary needed to write good prompts, and (2) students do not understand the extent of information that LLMs need to solve code generation tasks. We study (1) with a causal intervention experiment on technical vocabulary and (2) by analyzing graphs that abstract how students edit prompts and the different failures that they encounter. We find that substance beats style: a poor grasp of technical vocabulary is merely correlated with prompt failure; that the information content of prompts predicts success; that students get stuck making trivial edits; and more. Our findings have implications for the use of LLMs in programming education, and for efforts to make computing more accessible with LLMs.

Scaling up language models to billions of parameters has opened up possibilities for in-context learning, allowing instruction tuning and few-shot learning on tasks that the model was not specifically trained for. This has achieved breakthrough performance on language tasks such as translation, summarization, and question-answering. Furthermore, in addition to these associative "System 1" tasks, recent advances in Chain-of-thought prompt learning have demonstrated strong "System 2" reasoning abilities, answering a question in the field of artificial general intelligence whether LLMs can reason. The field started with the question whether LLMs can solve grade school math word problems. This paper reviews the rapidly expanding field of prompt-based reasoning with LLMs. Our taxonomy identifies different ways to generate, evaluate, and control multi-step reasoning. We provide an in-depth coverage of core approaches and open problems, and we propose a research agenda for the near future. Finally, we highlight the relation between reasoning and prompt-based learning, and we discuss the relation between reasoning, sequential decision processes, and reinforcement learning. We find that self-improvement, self-reflection, and some metacognitive abilities of the reasoning processes are possible through the judicious use of prompts. True self-improvement and self-reasoning, to go from reasoning with LLMs to reasoning by LLMs, remains future work.

Problem-solving has been a fundamental driver of human progress in numerous domains. With advancements in artificial intelligence, Large Language Models (LLMs) have emerged as powerful tools capable of tackling complex problems across diverse domains. Unlike traditional computational systems, LLMs combine raw computational power with an approximation of human reasoning, allowing them to generate solutions, make inferences, and even leverage external computational tools. However, applying LLMs to real-world problem-solving presents significant challenges, including multi-step reasoning, domain knowledge integration, and result verification. This survey explores the capabilities and limitations of LLMs in complex problem-solving, examining techniques including Chain-of-Thought (CoT) reasoning, knowledge augmentation, and various LLM-based and tool-based verification techniques. Additionally, we highlight domain-specific challenges in various domains, such as software engineering, mathematical reasoning and proving, data analysis and modeling, and scientific research. The paper further discusses the fundamental limitations of the current LLM solutions and the future directions of LLM-based complex problems solving from the perspective of multi-step reasoning, domain knowledge integration and result verification.

Reasoning, a crucial ability for complex problem-solving, plays a pivotal role in various real-world settings such as negotiation, medical diagnosis, and criminal investigation. It serves as a fundamental methodology in the field of Artificial General Intelligence (AGI). With the ongoing development of foundation models, e.g., Large Language Models (LLMs), there is a growing interest in exploring their abilities in reasoning tasks. In this paper, we introduce seminal foundation models proposed or adaptable for reasoning, highlighting the latest advancements in various reasoning tasks, methods, and benchmarks. We then delve into the potential future directions behind the emergence of reasoning abilities within foundation models. We also discuss the relevance of multimodal learning, autonomous agents, and super alignment in the context of reasoning. By discussing these future research directions, we hope to inspire researchers in their exploration of this field, stimulate further advancements in reasoning with foundation models, and contribute to the development of AGI.

Chain-of-thought (CoT) prompting for language models demonstrates impressive performance across reasoning tasks, but typically needs labeled exemplars of the reasoning process. In this work, we introduce a new prompting approach, Analogical Prompting, designed to automatically guide the reasoning process of large language models. Inspired by analogical reasoning, a cognitive process in which humans draw from relevant past experiences to tackle new problems, our approach prompts language models to self-generate relevant exemplars or knowledge in the context, before proceeding to solve the given problem. This method presents several advantages: it obviates the need for labeling or retrieving exemplars, offering generality and convenience; it can also tailor the generated exemplars and knowledge to each problem, offering adaptability. Experimental results show that our approach outperforms 0-shot CoT and manual few-shot CoT in a variety of reasoning tasks, including math problem solving in GSM8K and MATH, code generation in Codeforces, and other reasoning tasks in BIG-Bench.

One long-term goal of machine learning research is to produce methods that are applicable to reasoning and natural language, in particular building an intelligent dialogue agent. To measure progress towards that goal, we argue for the usefulness of a set of proxy tasks that evaluate reading comprehension via question answering. Our tasks measure understanding in several ways: whether a system is able to answer questions via chaining facts, simple induction, deduction and many more. The tasks are designed to be prerequisites for any system that aims to be capable of conversing with a human. We believe many existing learning systems can currently not solve them, and hence our aim is to classify these tasks into skill sets, so that researchers can identify (and then rectify) the failings of their systems. We also extend and improve the recently introduced Memory Networks model, and show it is able to solve some, but not all, of the tasks.

Large language models have exhibited emergent abilities, demonstrating exceptional performance across diverse tasks for which they were not explicitly trained, including those that require complex reasoning abilities. The emergence of such abilities carries profound implications for the future direction of research in NLP, especially as the deployment of such models becomes more prevalent. However, one key challenge is that the evaluation of these abilities is often confounded by competencies that arise in models through alternative prompting techniques, such as in-context learning and instruction following, which also emerge as the models are scaled up. In this study, we provide the first comprehensive examination of these emergent abilities while accounting for various potentially biasing factors that can influence the evaluation of models. We conduct rigorous tests on a set of 18 models, encompassing a parameter range from 60 million to 175 billion parameters, across a comprehensive set of 22 tasks. Through an extensive series of over 1,000 experiments, we provide compelling evidence that emergent abilities can primarily be ascribed to in-context learning. We find no evidence for the emergence of reasoning abilities, thus providing valuable insights into the underlying mechanisms driving the observed abilities and thus alleviating safety concerns regarding their use.

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the LLM to simultaneously decompose and solve the problem. A significant disadvantage is that foundational LLMs are typically not available for fine-tuning, making adaptation computationally prohibitive. We believe (and demonstrate) that problem decomposition and solution generation are distinct capabilites, better addressed in separate modules, than by one monolithic LLM. We introduce DaSLaM, which uses a decomposition generator to decompose complex problems into subproblems that require fewer reasoning steps. These subproblems are answered by a solver. We use a relatively small (13B parameters) LM as the decomposition generator, which we train using policy gradient optimization to interact with a solver LM (regarded as black-box) and guide it through subproblems, thereby rendering our method solver-agnostic. Evaluation on multiple different reasoning datasets reveal that with our method, a 175 billion parameter LM (text-davinci-003) can produce competitive or even better performance, compared to its orders-of-magnitude larger successor, GPT-4. Additionally, we show that DaSLaM is not limited by the solver's capabilities as a function of scale; e.g., solver LMs with diverse sizes give significant performance improvement with our solver-agnostic decomposition technique. Exhaustive ablation studies evince the superiority of our modular finetuning technique over exorbitantly large decomposer LLMs, based on prompting alone.

Many challenging reasoning tasks require not just rapid, intuitive responses, but a more deliberate, multi-step approach. Recent progress in large language models (LLMs) highlights an important shift from the "System 1" way of quick reactions to the "System 2" style of reflection-and-correction problem solving. However, current benchmarks heavily rely on the final-answer accuracy, leaving much of a model's intermediate reasoning steps unexamined. This fails to assess the model's ability to reflect and rectify mistakes within the reasoning process. To bridge this gap, we introduce FINEREASON, a logic-puzzle benchmark for fine-grained evaluation of LLMs' reasoning capabilities. Each puzzle can be decomposed into atomic steps, making it ideal for rigorous validation of intermediate correctness. Building on this, we introduce two tasks: state checking, and state transition, for a comprehensive evaluation of how models assess the current situation and plan the next move. To support broader research, we also provide a puzzle training set aimed at enhancing performance on general mathematical tasks. We show that models trained on our state checking and transition data demonstrate gains in math reasoning by up to 5.1% on GSM8K.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Analogical reasoning is a unique ability of humans to address unfamiliar challenges by transferring strategies from relevant past experiences. One key finding in psychology is that compared with irrelevant past experiences, recalling relevant ones can help humans better handle new tasks. Coincidentally, the NLP community has also recently found that self-generating relevant examples in the context can help large language models (LLMs) better solve a given problem than hand-crafted prompts. However, it is yet not clear whether relevance is the key factor eliciting such capability, i.e., can LLMs benefit more from self-generated relevant examples than irrelevant ones? In this work, we systematically explore whether LLMs can truly perform analogical reasoning on a diverse set of reasoning tasks. With extensive experiments and analysis, we show that self-generated random examples can surprisingly achieve comparable or even better performance, e.g., 4% performance boost on GSM8K with random biological examples. We find that the accuracy of self-generated examples is the key factor and subsequently design two improved methods with significantly reduced inference costs. Overall, we aim to advance a deeper understanding of LLM analogical reasoning and hope this work stimulates further research in the design of self-generated contexts.

Recent advances in test-time scaling have led to the emergence of thinking LLMs that exhibit self-reflective behaviors and multi-step reasoning. While RL drives this self-improvement paradigm, a recent study (Gandhi et al., 2025) shows that RL alone does not truly instill these new reasoning abilities - it merely draws out behaviors already present in the base models. This raises a question: How can we train the models that don't exhibit such thinking behavior to develop it in the first place? To this end, we propose ThinkTuning, a GRPO-based interactive training approach where we augment the rollouts of a student model with the guidance from a teacher model. A simple idea from classroom practice inspires our method: a teacher poses a problem, lets the student try an answer, then gives corrective feedback -- enough to point the mind in the right direction and then show the solution. Each piece of feedback reshapes the student's thoughts, leading them to arrive at the correct solution. Similarly, we find that this type of implicit supervision through feedback from a teacher model of the same size improves the reasoning capabilities of the student model. In particular, on average, our method shows a 3.85% improvement over zero-shot baselines across benchmarks, and on MATH-500, AIME and GPQA-Diamond it shows 2.08%, 2.23% and 3.99% improvements over the vanilla-GRPO baseline. Source code is available at https://github.com/3rdAT/ThinkTuning.

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core "skills" from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an "out of distribution" task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH^2 - a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH^2 than on MATH (b) Higher performance on MATH when using MATH^2 questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models' performance on the new dataset: the success rate on MATH^2 is the square on MATH, suggesting that successfully solving the question in MATH^2 requires a nontrivial combination of two distinct math skills.

Procedural planning aims to implement complex high-level goals by decomposition into sequential simpler low-level steps. Although procedural planning is a basic skill set for humans in daily life, it remains a challenge for large language models (LLMs) that lack a deep understanding of the cause-effect relations in procedures. Previous methods require manual exemplars to acquire procedural planning knowledge from LLMs in the zero-shot setting. However, such elicited pre-trained knowledge in LLMs induces spurious correlations between goals and steps, which impair the model generalization to unseen tasks. In contrast, this paper proposes a neuro-symbolic procedural PLANner (PLAN) that elicits procedural planning knowledge from the LLMs with commonsense-infused prompting. To mitigate spurious goal-step correlations, we use symbolic program executors on the latent procedural representations to formalize prompts from commonsense knowledge bases as a causal intervention toward the Structural Causal Model. Both automatic and human evaluations on WikiHow and RobotHow show the superiority of PLAN on procedural planning without further training or manual exemplars.

Rebuses are puzzles requiring constrained multi-step reasoning to identify a hidden phrase from a set of images and letters. In this work, we introduce a large collection of verbalized rebuses for the Italian language and use it to assess the rebus-solving capabilities of state-of-the-art large language models. While general-purpose systems such as LLaMA-3 and GPT-4o perform poorly on this task, ad-hoc fine-tuning seems to improve models' performance. However, we find that performance gains from training are largely motivated by memorization. Our results suggest that rebus solving remains a challenging test bed to evaluate large language models' linguistic proficiency and sequential instruction-following skills.

Accuracy remains a standard metric for evaluating AI systems, but it offers limited insight into how models arrive at their solutions. In this work, we introduce a benchmark based on brainteasers written in long narrative form to probe more deeply into the types of reasoning strategies that models use. Brainteasers are well-suited for this goal because they can be solved with multiple approaches, such as a few-step solution that uses a creative insight or a longer solution that uses more brute force. We investigate large language models (LLMs) across multiple layers of reasoning, focusing not only on correctness but also on the quality and creativity of their solutions. We investigate many aspects of the reasoning process: (1) semantic parsing of the brainteasers into precise mathematical competition style formats; (2) generating solutions from these mathematical forms; (3) self-correcting solutions based on gold solutions; (4) producing step-by-step sketches of solutions; and (5) making use of hints. We find that LLMs are in many cases able to find creative, insightful solutions to brainteasers, suggesting that they capture some of the capacities needed to solve novel problems in creative ways. Nonetheless, there also remain situations where they rely on brute force despite the availability of more efficient, creative solutions, highlighting a potential direction for improvement in the reasoning abilities of LLMs.

Humans excel at reusing prior knowledge to address new challenges and developing skills while solving problems. This paradigm becomes increasingly popular in the development of autonomous agents, as it develops systems that can self-evolve in response to new challenges like human beings. However, previous methods suffer from limited training efficiency when expanding new skills and fail to fully leverage prior knowledge to facilitate new task learning. In this paper, we propose Parametric Skill Expansion and Composition (PSEC), a new framework designed to iteratively evolve the agents' capabilities and efficiently address new challenges by maintaining a manageable skill library. This library can progressively integrate skill primitives as plug-and-play Low-Rank Adaptation (LoRA) modules in parameter-efficient finetuning, facilitating efficient and flexible skill expansion. This structure also enables the direct skill compositions in parameter space by merging LoRA modules that encode different skills, leveraging shared information across skills to effectively program new skills. Based on this, we propose a context-aware module to dynamically activate different skills to collaboratively handle new tasks. Empowering diverse applications including multi-objective composition, dynamics shift, and continual policy shift, the results on D4RL, DSRL benchmarks, and the DeepMind Control Suite show that PSEC exhibits superior capacity to leverage prior knowledge to efficiently tackle new challenges, as well as expand its skill libraries to evolve the capabilities. Project website: https://ltlhuuu.github.io/PSEC/.

Human reasoning relies on constructing and manipulating mental models-simplified internal representations of situations that we use to understand and solve problems. Conceptual diagrams (for example, sketches drawn by humans to aid reasoning) externalize these mental models, abstracting irrelevant details to efficiently capture relational and spatial information. In contrast, Large Language Models (LLMs) and Large Multimodal Models (LMMs) predominantly reason through textual representations, limiting their effectiveness in complex multi-step combinatorial and planning tasks. In this paper, we propose a zero-shot fully automatic framework that enables LMMs to reason through multiple chains of self-generated intermediate conceptual diagrams, significantly enhancing their combinatorial planning capabilities. Our approach does not require any human initialization beyond a natural language description of the task. It integrates both textual and diagrammatic reasoning within an optimized graph-of-thought inference framework, enhanced by beam search and depth-wise backtracking. Evaluated on multiple challenging PDDL planning domains, our method substantially improves GPT-4o's performance (for example, from 35.5% to 90.2% in Blocksworld). On more difficult planning domains with solution depths up to 40, our approach outperforms even the o1-preview reasoning model (for example, over 13% improvement in Parking). These results highlight the value of conceptual diagrams as a complementary reasoning medium in LMMs.

We introduce a new challenge to test the STEM skills of neural models. The problems in the real world often require solutions, combining knowledge from STEM (science, technology, engineering, and math). Unlike existing datasets, our dataset requires the understanding of multimodal vision-language information of STEM. Our dataset features one of the largest and most comprehensive datasets for the challenge. It includes 448 skills and 1,073,146 questions spanning all STEM subjects. Compared to existing datasets that often focus on examining expert-level ability, our dataset includes fundamental skills and questions designed based on the K-12 curriculum. We also add state-of-the-art foundation models such as CLIP and GPT-3.5-Turbo to our benchmark. Results show that the recent model advances only help master a very limited number of lower grade-level skills (2.5% in the third grade) in our dataset. In fact, these models are still well below (averaging 54.7%) the performance of elementary students, not to mention near expert-level performance. To understand and increase the performance on our dataset, we teach the models on a training split of our dataset. Even though we observe improved performance, the model performance remains relatively low compared to average elementary students. To solve STEM problems, we will need novel algorithmic innovations from the community.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

Mathematical reasoning has long represented one of the most fundamental and challenging frontiers in artificial intelligence research. In recent years, large language models (LLMs) have achieved significant advances in this area. This survey examines the development of mathematical reasoning abilities in LLMs through two high-level cognitive phases: comprehension, where models gain mathematical understanding via diverse pretraining strategies, and answer generation, which has progressed from direct prediction to step-by-step Chain-of-Thought (CoT) reasoning. We review methods for enhancing mathematical reasoning, ranging from training-free prompting to fine-tuning approaches such as supervised fine-tuning and reinforcement learning, and discuss recent work on extended CoT and "test-time scaling". Despite notable progress, fundamental challenges remain in terms of capacity, efficiency, and generalization. To address these issues, we highlight promising research directions, including advanced pretraining and knowledge augmentation techniques, formal reasoning frameworks, and meta-generalization through principled learning paradigms. This survey tries to provide some insights for researchers interested in enhancing reasoning capabilities of LLMs and for those seeking to apply these techniques to other domains.

Large Language Models (LLMs) have demonstrated remarkable performance in solving math problems, a hallmark of human intelligence. Despite high success rates on current benchmarks; however, these often feature simple problems with only one or two unknowns, which do not sufficiently challenge their reasoning capacities. This paper introduces a novel benchmark, BeyondX, designed to address these limitations by incorporating problems with multiple unknowns. Recognizing the challenges in proposing multi-unknown problems from scratch, we developed BeyondX using an innovative automated pipeline that progressively increases complexity by expanding the number of unknowns in simpler problems. Empirical study on BeyondX reveals that the performance of existing LLMs, even those fine-tuned specifically on math tasks, significantly decreases as the number of unknowns increases - with a performance drop of up to 70\% observed in GPT-4. To tackle these challenges, we propose the Formulate-and-Solve strategy, a generalized prompting approach that effectively handles problems with an arbitrary number of unknowns. Our findings reveal that this strategy not only enhances LLM performance on the BeyondX benchmark but also provides deeper insights into the computational limits of LLMs when faced with more complex mathematical challenges.

Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives, intermediate results, or shared procedures, and building upon them. While RL post-training on long chains of thought ultimately aims to uncover this kind of algorithmic behavior, most reasoning traces learned by large models fail to consistently capture or reuse procedures, instead drifting into verbose and degenerate exploration. To address more effective reasoning, we introduce reasoning abstractions: concise natural language descriptions of procedural and factual knowledge that guide the model toward learning successful reasoning. We train models to be capable of proposing multiple abstractions given a problem, followed by RL that incentivizes building a solution while using the information provided by these abstractions. This results in a two-player RL training paradigm, abbreviated as RLAD, that jointly trains an abstraction generator and a solution generator. This setup effectively enables structured exploration, decouples learning signals of abstraction proposal and solution generation, and improves generalization to harder problems. We also show that allocating more test-time compute to generating abstractions is more beneficial for performance than generating more solutions at large test budgets, illustrating the role of abstractions in guiding meaningful exploration.

Geometry problem solving is a well-recognized testbed for evaluating the high-level multi-modal reasoning capability of deep models. In most existing works, two main geometry problems: calculation and proving, are usually treated as two specific tasks, hindering a deep model to unify its reasoning capability on multiple math tasks. However, in essence, these two tasks have similar problem representations and overlapped math knowledge which can improve the understanding and reasoning ability of a deep model on both two tasks. Therefore, we construct a large-scale Unified Geometry problem benchmark, UniGeo, which contains 4,998 calculation problems and 9,543 proving problems. Each proving problem is annotated with a multi-step proof with reasons and mathematical expressions. The proof can be easily reformulated as a proving sequence that shares the same formats with the annotated program sequence for calculation problems. Naturally, we also present a unified multi-task Geometric Transformer framework, Geoformer, to tackle calculation and proving problems simultaneously in the form of sequence generation, which finally shows the reasoning ability can be improved on both two tasks by unifying formulation. Furthermore, we propose a Mathematical Expression Pretraining (MEP) method that aims to predict the mathematical expressions in the problem solution, thus improving the Geoformer model. Experiments on the UniGeo demonstrate that our proposed Geoformer obtains state-of-the-art performance by outperforming task-specific model NGS with over 5.6% and 3.2% accuracies on calculation and proving problems, respectively.

We present PutnamBench, a new multilingual benchmark for evaluating the ability of neural theorem-provers to solve competition mathematics problems. PutnamBench consists of 1697 hand-constructed formalizations of 640 theorems sourced from the William Lowell Putnam Mathematical Competition, the premier undergraduate-level mathematics competition in North America. All the theorems have formalizations in Lean 4 and Isabelle; a substantial subset also has Coq formalizations. Proving the theorems requires significant problem-solving ability and proficiency in a broad range of topics taught in undergraduate mathematics courses. We use PutnamBench to evaluate several established neural and symbolic theorem-provers. These approaches can only solve a handful of the PutnamBench problems, establishing the benchmark as a difficult open challenge for research on neural theorem-proving. PutnamBench is available at https://github.com/trishullab/PutnamBench.

Mathematical understanding and reasoning are crucial tasks for assessing the capabilities of artificial intelligence (AI). However, existing benchmarks either require just a few steps of reasoning, or only contain a small amount of data in one specific topic, making it hard to analyse AI's behaviour with reference to different problems within a specific topic in detail. In this work, we propose Conic10K, a challenging math problem dataset on conic sections in Chinese senior high school education. Our dataset contains various problems with different reasoning depths, while only the knowledge from conic sections is required. Since the dataset only involves a narrow range of knowledge, it is easy to separately analyse the knowledge a model possesses and the reasoning ability it has. For each problem, we provide a high-quality formal representation, the reasoning steps, and the final solution. Experiments show that existing large language models, including GPT-4, exhibit weak performance on complex reasoning. We hope that our findings could inspire more advanced techniques for precise natural language understanding and reasoning. Our dataset and codes are available at https://github.com/whyNLP/Conic10K.

Graphs are widely used for modeling relational data in real-world scenarios, such as social networks and urban computing. Existing LLM-based graph analysis approaches either integrate graph neural networks (GNNs) for specific machine learning tasks, limiting their transferability, or rely solely on LLMs' internal reasoning ability, resulting in suboptimal performance. To address these limitations, we take advantage of recent advances in LLM-based agents, which have shown capabilities of utilizing external knowledge or tools for problem solving. By simulating human problem-solving strategies such as analogy and collaboration, we propose a multi-agent system based on LLMs named GraphTeam, for graph analysis. GraphTeam consists of five LLM-based agents from three modules, and the agents with different specialities can collaborate with each other to address complex problems. Specifically, (1) input-output normalization module: the question agent extracts and refines four key arguments from the original question, facilitating the problem understanding, and the answer agent organizes the results to meet the output requirement; (2) external knowledge retrieval module: we first build a knowledge base consisting of relevant documentation and experience information, and then the search agent retrieves the most relevant entries for each question. (3) problem-solving module: given the retrieved information from search agent, the coding agent uses established algorithms via programming to generate solutions, and in case the coding agent does not work, the reasoning agent will directly compute the results without programming. Extensive experiments on six graph analysis benchmarks demonstrate that GraphTeam achieves state-of-the-art performance with an average 25.85% improvement over the best baseline in terms of accuracy. The code and data are available at https://github.com/BUPT-GAMMA/GraphTeam.

We present Step-Back Prompting, a simple prompting technique that enables LLMs to do abstractions to derive high-level concepts and first principles from instances containing specific details. Using the concepts and principles to guide the reasoning steps, LLMs significantly improve their abilities in following a correct reasoning path towards the solution. We conduct experiments of Step-Back Prompting with PaLM-2L models and observe substantial performance gains on a wide range of challenging reasoning-intensive tasks including STEM, Knowledge QA, and Multi-Hop Reasoning. For instance, Step-Back Prompting improves PaLM-2L performance on MMLU Physics and Chemistry by 7% and 11%, TimeQA by 27%, and MuSiQue by 7%.

The reasoning performance of Large Language Models (LLMs) on a wide range of problems critically relies on chain-of-thought prompting, which involves providing a few chain of thought demonstrations as exemplars in prompts. Recent work, e.g., Tree of Thoughts, has pointed out the importance of exploration and self-evaluation in reasoning step selection for complex problem solving. In this paper, we present Boosting of Thoughts (BoT), an automated prompting framework for problem solving with LLMs by iteratively exploring and self-evaluating many trees of thoughts in order to acquire an ensemble of trial-and-error reasoning experiences, which will serve as a new form of prompting to solve the complex problem. Starting from a simple prompt without requiring examples, BoT iteratively explores and evaluates a large collection of reasoning steps, and more importantly, uses error analysis obtained from the LLM on them to explicitly revise prompting, which in turn enhances reasoning step generation, until a final answer is attained. Our experiments with GPT-4 and Llama2 across extensive complex mathematical problems demonstrate that BoT consistently achieves higher or comparable problem-solving rates than other advanced prompting approaches.

With the rapid advancement of mathematical reasoning capabilities in Large Language Models (LLMs), AI systems are increasingly being adopted in educational settings to support students' comprehension of problem-solving processes. However, a critical component remains underexplored in current LLM-generated explanations: visual explanation. In real-world instructional contexts, human tutors routinely employ visual aids - such as diagrams, markings, and highlights - to enhance conceptual clarity. To bridge this gap, we introduce a novel task of visual solution explanation, which requires generating explanations that incorporate newly introduced visual elements essential for understanding (e.g., auxiliary lines, annotations, or geometric constructions). To evaluate model performance on this task, we propose MathExplain, a multimodal benchmark consisting of 997 math problems annotated with visual keypoints and corresponding explanatory text that references those elements. Our empirical results show that while some closed-source models demonstrate promising capabilities on visual solution-explaining, current open-source general-purpose models perform inconsistently, particularly in identifying relevant visual components and producing coherent keypoint-based explanations. We expect that visual solution-explaining and the MathExplain dataset will catalyze further research on multimodal LLMs in education and advance their deployment as effective, explanation-oriented AI tutors. Code and data will be released publicly.

Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks, previous work has conducted supervised fine-tuning on open-source models by improving the quality and quantity of data. In this paper, we propose a novel approach, named Brain, to imitate human thought processes to enhance mathematical reasoning abilities, using the Frontal Lobe Model to generate plans, and then employing the Parietal Lobe Model to generate code and execute to obtain answers. First, we achieve SOTA performance in comparison with Code LLaMA 7B based models through this method. Secondly, we find that plans can be explicitly extracted from natural language, code, or formal language. Our code and data are publicly available at https://github.com/cyzhh/Brain.

Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning abilities, i.e., the ability to decompose complex questions into step-by-step reasoning chains, but such ability seems only to emerge from models with abundant parameters. This work investigates how to incorporate relatively small LMs with the capabilities of multi-step reasoning. We propose to inject such abilities by continually pre-training LMs on a synthetic dataset MsAT which is composed of Multi-step Arithmetic Tasks. Our experiments on four math word problem datasets show the effectiveness of the proposed method in enhancing LMs' math reasoning abilities.

In this paper, we conduct a thorough investigation into the reasoning capabilities of Large Language Models (LLMs), focusing specifically on the Open Pretrained Transformers (OPT) models as a representative of such models. Our study entails finetuning three different sizes of OPT on a carefully curated reasoning corpus, resulting in two sets of finetuned models: OPT-R, finetuned without explanations, and OPT-RE, finetuned with explanations. We then evaluate all models on 57 out-of-domain tasks drawn from the SUPER-NATURALINSTRUCTIONS benchmark, covering 26 distinct reasoning skills, utilizing three prompting techniques. Through a comprehensive grid of 27 configurations and 6,156 test evaluations, we investigate the dimensions of finetuning, prompting, and scale to understand the role of explanations on different reasoning skills. Our findings reveal that having explanations in the fewshot exemplar has no significant impact on the model's performance when the model is finetuned, while positively affecting the non-finetuned counterpart. Moreover, we observe a slight yet consistent increase in classification accuracy as we incorporate explanations during prompting and finetuning, respectively. Finally, we offer insights on which skills benefit the most from incorporating explanations during finetuning and prompting, such as Numerical (+20.4%) and Analogical (+13.9%) reasoning, as well as skills that exhibit negligible or negative effects.

Divergent thinking, the cognitive process of generating diverse solutions, is a hallmark of human creativity and problem-solving. For machines, sampling diverse solution trajectories in complex reasoning problems is crucial for robust outcomes, data augmentation, and enhanced model generalization. Large language models (LLMs) often struggle with generating high-quality, diverse reasoning. While supervised fine-tuning helps with quality, it requires extensive supervision data to capture the full diversity of solutions. Alternatively, reinforcement learning methods like PPO aim to find limited highest-reward solutions while neglecting the solution diversity, akin to convergent thinking. To address these limitations, we propose Flow of Reasoning (FoR) -- an efficient LLM training approach enabling diverse reasoning with minimal data. FoR formulates multi-step LLM reasoning as a Markovian flow from an initial state to terminal states. The formulation allows to adapt principled GFlowNet approaches to train the LLM as a policy, which is able to sample multiple reasoning paths with probabilities proportional to the unnormalized reward. Empirical results show that, with limited training data (e.g., 15 examples), FoR can discover diverse high-quality solutions that excel greatly beyond current state-of-the-art methods across three tasks, including embodied reasoning (BlocksWorld), math puzzle solving (Game24), and logical reasoning (PrOntoQA). Code is available at https://github.com/Yu-Fangxu/FoR.

Advances in Large Language Models (LLMs) have sparked interest in their ability to solve Olympiad-level math problems. However, the training and evaluation of these models are constrained by the limited size and quality of available datasets, as creating large-scale data for such advanced problems requires extensive effort from human experts. In addition, current benchmarks are prone to contamination, leading to unreliable evaluations. In this paper, we present an automated pipeline that leverages the rich resources of the Art of Problem Solving (AoPS) forum, which predominantly features Olympiad-level problems and community-driven solutions. Using open-source LLMs, we develop a method to extract question-answer pairs from the forum, resulting in AoPS-Instruct, a dataset of more than 600,000 high-quality QA pairs. Our experiments demonstrate that fine-tuning LLMs on AoPS-Instruct improves their reasoning abilities across various benchmarks. Moreover, we build an automatic pipeline that introduces LiveAoPSBench, an evolving evaluation set with timestamps, derived from the latest forum data, providing a contamination-resistant benchmark for assessing LLM performance. Notably, we observe a significant decline in LLM performance over time, suggesting their success on older examples may stem from pre-training exposure rather than true reasoning ability. Our work presents a scalable approach to creating and maintaining large-scale, high-quality datasets for advanced math reasoning, offering valuable insights into the capabilities and limitations of LLMs in this domain. Our benchmark and code is available at https://github.com/DSL-Lab/aops

Large language models (LLMs) demonstrate impressive capabilities across a wide range of tasks, yet it remains unclear whether such success reflects genuine reasoning or sophisticated recall. We introduce AInstein, a framework for testing whether LLMs can generate valid solutions to AI research problems using only their pretrained parametric knowledge -- without domain-specific fine-tuning, retrieval augmentation, or other external aids. Our approach extracts distilled problem statements from high-quality ICLR 2025 submissions, then tasks specialized solver agents with proposing and refining technical solutions through iterative critique loops, mimicking the cycles of proposal, review, and revision central to scientific inquiry. We evaluate AInstein on 1,214 ICLR papers stratified by acceptance tier (Oral, Spotlight, Poster), using an LLM-as-a-judge paradigm guided by a structured rubric, complemented by targeted manual checks. Performance is assessed with three metrics: Success Rate (does the solution address the problem?), Rediscovery (does it align with human-proposed methods?), and Novelty (does it yield valid, original approaches?). Our results reveal that while LLMs can rediscover feasible solutions and occasionally propose creative alternatives, their problem-solving ability remains fragile and highly sensitive to framing. These findings provide the first large-scale evidence on the extent to which LLMs can act as autonomous scientific problem-solvers, highlighting both their latent potential and their current limitations.

Recent studies have shown LLMs possess some ability to improve their responses when given external feedback. However, it remains unclear how effectively and thoroughly these models can incorporate extrinsic feedback. In an ideal scenario, if LLMs receive near-perfect and complete feedback, we would expect them to fully integrate the feedback and change their incorrect answers to correct ones. In this paper, we systematically investigate LLMs' ability to incorporate feedback by designing a controlled experimental environment. For each problem, a solver model attempts a solution, then a feedback generator with access to near-complete ground-truth answers produces targeted feedback, after which the solver tries again. We evaluate this pipeline across a diverse range of tasks, including math reasoning, knowledge reasoning, scientific reasoning, and general multi-domain evaluations with state-of-the-art language models including Claude 3.7 (with and without extended thinking). Surprisingly, even under these near-ideal conditions, solver models consistently show resistance to feedback, a limitation that we term FEEDBACK FRICTION. To mitigate this limitation, we experiment with sampling-based strategies like progressive temperature increases and explicit rejection of previously attempted incorrect answers, which yield improvements but still fail to help models achieve target performance. We also perform a rigorous exploration of potential causes of FEEDBACK FRICTION, ruling out factors such as model overconfidence and data familiarity. We hope that highlighting this issue in LLMs and ruling out several apparent causes will help future research in self-improvement.

Chain of Thought (CoT) is significant in improving the reasoning abilities of large language models (LLMs). However, the correlation between the effectiveness of CoT and the length of reasoning steps in prompts remains largely unknown. To shed light on this, we have conducted several empirical experiments to explore the relations. Specifically, we design experiments that expand and compress the rationale reasoning steps within CoT demonstrations, while keeping all other factors constant. We have the following key findings. First, the results indicate that lengthening the reasoning steps in prompts, even without adding new information into the prompt, considerably enhances LLMs' reasoning abilities across multiple datasets. Alternatively, shortening the reasoning steps, even while preserving the key information, significantly diminishes the reasoning abilities of models. This finding highlights the importance of the number of steps in CoT prompts and provides practical guidance to make better use of LLMs' potential in complex problem-solving scenarios. Second, we also investigated the relationship between the performance of CoT and the rationales used in demonstrations. Surprisingly, the result shows that even incorrect rationales can yield favorable outcomes if they maintain the requisite length of inference. Third, we observed that the advantages of increasing reasoning steps are task-dependent: simpler tasks require fewer steps, whereas complex tasks gain significantly from longer inference sequences.

Reasoning is central to a wide range of intellectual activities, and while the capabilities of large language models (LLMs) continue to advance, their performance in reasoning tasks remains limited. The processes and mechanisms underlying reasoning are not yet fully understood, but key elements include path exploration, selection of relevant knowledge, and multi-step inference. Problems are solved through the synthesis of these components. In this paper, we propose a benchmark that focuses on a specific aspect of reasoning ability: the direct evaluation of multi-step inference. To this end, we design a special reasoning task where multi-step inference is specifically focused by largely eliminating path exploration and implicit knowledge utilization. Our dataset comprises pairs of explicit instructions and corresponding questions, where the procedures necessary for solving the questions are entirely detailed within the instructions. This setup allows models to solve problems solely by following the provided directives. By constructing problems that require varying numbers of steps to solve and evaluating responses at each step, we enable a thorough assessment of state-of-the-art LLMs' ability to follow instructions. To ensure the robustness of our evaluation, we include multiple distinct tasks. Furthermore, by comparing accuracy across tasks, utilizing step-aware metrics, and applying separately defined measures of complexity, we conduct experiments that offer insights into the capabilities and limitations of LLMs in reasoning tasks. Our findings have significant implications for the development of LLMs and highlight areas for future research in advancing their reasoning abilities. Our dataset is available at https://huggingface.co/datasets/ifujisawa/procbench and code at https://github.com/ifujisawa/proc-bench.

Math word problem (MWP) solving requires generating a reasoning path based on a given problem description that often contains irrelevant conditions. Existing chain-of-thought (CoT) prompting methods elicited multi-step reasoning abilities of large language models (LLMs) to solve MWPs. However, they were seriously confused by the irrelevant conditions, resulting in low accuracy. In this paper, we propose a novel approach named I^3C that instructs LLMs to identify and ignore irrelevant conditions. It identifies a set of irrelevant condition candidates that have a weak semantic relevance with the question. Then it prompts LLMs to verify the irrelevant conditions. Lastly it instructs the LLMs with the verification on relevant and irrelevant conditions to avoid confusion and improve reasoning paths. Moreover, we propose to select (problem, reasoning paths) pairs as demonstrations to enhance I^3C with few-shot reasoning. We develop I^3C-Select that selects the most confusing problems based on the semantic relevance measurement. We conduct extensive experiments on eight MWP datasets. I^3C can be combined with any CoT prompting methods to improve the performance of solving MWPs. Notably, with GPT-3.5-Turbo and I^3C-Select, we achieve an accuracy of 96.0 and 94.1 on GSM-IC2-1K and GSM-ICM-1K, respectively, significantly outperforming the state-of-the-art few-shot prompting method Complex-CoT by +11.7 and +11.1. Our implementation is made publicly available at https://wzy6642.github.io/I3C.github.io/.

As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based problem-solving agents, the demand for process-level verifiability is rapidly increasing yet underexplored. To fill these gaps, we present a principled formulation of problem-solving as a deterministic Markov decision process; a novel framework, FPS (Formal Problem-Solving), which utilizes existing FTP (formal theorem proving) environments to perform process-verified problem-solving; and D-FPS (Deductive FPS), decoupling solving and answer verification for better human-alignment. The expressiveness, soundness and completeness of the frameworks are proven. We construct three benchmarks on problem-solving: FormalMath500, a formalization of a subset of the MATH500 benchmark; MiniF2F-Solving and PutnamBench-Solving, adaptations of FTP benchmarks MiniF2F and PutnamBench. For faithful, interpretable, and human-aligned evaluation, we propose RPE (Restricted Propositional Equivalence), a symbolic approach to determine the correctness of answers by formal verification. We evaluate four prevalent FTP models and two prompting methods as baselines, solving at most 23.77% of FormalMath500, 27.47% of MiniF2F-Solving, and 0.31% of PutnamBench-Solving.

Large language models (LLMs) demonstrate exceptional performance on complex reasoning tasks. However, despite their strong reasoning capabilities in high-resource languages (e.g., English and Chinese), a significant performance gap persists in other languages. To investigate this gap in Korean, we introduce HRM8K, a benchmark comprising 8,011 English-Korean parallel bilingual math problems. Through systematic analysis of model behaviors, we identify a key finding: these performance disparities stem primarily from difficulties in comprehending non-English inputs, rather than limitations in reasoning capabilities. Based on these findings, we propose UST (Understand, Solve, and Translate), a method that strategically uses English as an anchor for reasoning and solution generation. By fine-tuning the model on 130k synthetically generated data points, UST achieves a 10.91% improvement on the HRM8K benchmark and reduces the multilingual performance gap from 11.6% to 0.7%. Additionally, we show that improvements from UST generalize effectively to different Korean domains, demonstrating that capabilities acquired from machine-verifiable content can be generalized to other areas. We publicly release the benchmark, training dataset, and models.

Scaling high-quality tutoring remains a major challenge in education. Due to growing demand, many platforms employ novice tutors who, unlike experienced educators, struggle to address student mistakes and thus fail to seize prime learning opportunities. Our work explores the potential of large language models (LLMs) to close the novice-expert knowledge gap in remediating math mistakes. We contribute Bridge, a method that uses cognitive task analysis to translate an expert's latent thought process into a decision-making model for remediation. This involves an expert identifying (A) the student's error, (B) a remediation strategy, and (C) their intention before generating a response. We construct a dataset of 700 real tutoring conversations, annotated by experts with their decisions. We evaluate state-of-the-art LLMs on our dataset and find that the expert's decision-making model is critical for LLMs to close the gap: responses from GPT4 with expert decisions (e.g., "simplify the problem") are +76% more preferred than without. Additionally, context-sensitive decisions are critical to closing pedagogical gaps: random decisions decrease GPT4's response quality by -97% than expert decisions. Our work shows the potential of embedding expert thought processes in LLM generations to enhance their capability to bridge novice-expert knowledge gaps. Our dataset and code can be found at: https://github.com/rosewang2008/bridge.

The mathematical capabilities of AI systems are complex and multifaceted. Most existing research has predominantly focused on the correctness of AI-generated solutions to mathematical problems. In this work, we argue that beyond producing correct answers, AI systems should also be capable of, or assist humans in, developing novel solutions to mathematical challenges. This study explores the creative potential of Large Language Models (LLMs) in mathematical reasoning, an aspect that has received limited attention in prior research. We introduce a novel framework and benchmark, CreativeMath, which encompasses problems ranging from middle school curricula to Olympic-level competitions, designed to assess LLMs' ability to propose innovative solutions after some known solutions have been provided. Our experiments demonstrate that, while LLMs perform well on standard mathematical tasks, their capacity for creative problem-solving varies considerably. Notably, the Gemini-1.5-Pro model outperformed other LLMs in generating novel solutions. This research opens a new frontier in evaluating AI creativity, shedding light on both the strengths and limitations of LLMs in fostering mathematical innovation, and setting the stage for future developments in AI-assisted mathematical discovery.

While language models have demonstrated impressive capabilities across a range of tasks, they still struggle with tasks that require complex planning and reasoning. Recent studies have proposed training language models on search processes rather than optimal solutions, resulting in better generalization performance even though search processes are noisy and even suboptimal. However, these studies overlook the value of optimal solutions, which can serve as step-by-step landmarks to guide more effective search. In this work, we explore how to leverage optimal solutions to enhance the search and planning abilities of language models. To this end, we propose guided stream of search (GSoS), which seamlessly incorporates optimal solutions into the self-generation process in a progressive manner, producing high-quality search trajectories. These trajectories are then distilled into the pre-trained model via supervised fine-tuning. Our approach significantly enhances the search and planning abilities of language models on Countdown, a simple yet challenging mathematical reasoning task. Notably, combining our method with RL fine-tuning yields further improvements, whereas previous supervised fine-tuning methods do not benefit from RL. Furthermore, our approach exhibits greater effectiveness than leveraging optimal solutions in the form of subgoal rewards.

Large language models often struggle with length generalization and solving complex problem instances beyond their training distribution. We present a self-improvement approach where models iteratively generate and learn from their own solutions, progressively tackling harder problems while maintaining a standard transformer architecture. Across diverse tasks including arithmetic, string manipulation, and maze solving, self-improving enables models to solve problems far beyond their initial training distribution-for instance, generalizing from 10-digit to 100-digit addition without apparent saturation. We observe that in some cases filtering for correct self-generated examples leads to exponential improvements in out-of-distribution performance across training rounds. Additionally, starting from pretrained models significantly accelerates this self-improvement process for several tasks. Our results demonstrate how controlled weak-to-strong curricula can systematically teach a model logical extrapolation without any changes to the positional embeddings, or the model architecture.

Solving grid puzzles involves a significant amount of logical reasoning. Hence, it is a good domain to evaluate the reasoning capability of a model which can then guide us to improve the reasoning ability of models. However, most existing works evaluate only the final predicted answer of a puzzle, without delving into an in-depth analysis of the LLMs' reasoning chains (such as where they falter) or providing any finer metrics to evaluate them. Since LLMs may rely on simple heuristics or artifacts to predict the final answer, it is crucial to evaluate the generated reasoning chain beyond overall correctness measures, for accurately evaluating the reasoning abilities of LLMs. To this end, we first develop GridPuzzle, an evaluation dataset comprising 274 grid-based puzzles with different complexities. Second, we propose a new error taxonomy derived from manual analysis of reasoning chains from LLMs including GPT-4, Claude-3, Gemini, Mistral, and Llama-2. Then, we develop an LLM-based framework for large-scale subjective evaluation (i.e., identifying errors) and an objective metric, PuzzleEval, to evaluate the correctness of reasoning chains. Evaluating reasoning chains from LLMs leads to several interesting findings. We further show that existing prompting methods used for enhancing models' reasoning abilities do not improve performance on GridPuzzle. This highlights the importance of understanding fine-grained errors and presents a challenge for future research to enhance LLMs' puzzle-solving abilities by developing methods that address these errors. Data and source code are available at https://github.com/Mihir3009/GridPuzzle.

Large Language Models (LLMs) have emerged as powerful tools for Text-to-SQL tasks, exhibiting remarkable reasoning capabilities. Different from tasks such as math word problems and commonsense reasoning, SQL solutions have a relatively fixed pattern. This facilitates the investigation of whether LLMs can benefit from categorical thinking, mirroring how humans acquire knowledge through inductive reasoning based on comparable examples. In this study, we propose that employing query group partitioning allows LLMs to focus on learning the thought processes specific to a single problem type, consequently enhancing their reasoning abilities across diverse difficulty levels and problem categories. Our experiments reveal that multiple advanced LLMs, when equipped with PTD-SQL, can either surpass or match previous state-of-the-art (SOTA) methods on the Spider and BIRD datasets. Intriguingly, models with varying initial performances have exhibited significant improvements, mainly at the boundary of their capabilities after targeted drilling, suggesting a parallel with human progress. Code is available at https://github.com/lrlbbzl/PTD-SQL.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation rules. In this paper, we present a new challenge for the evaluation (and eventually the design) of neural architectures and similar system, developing a task suite of mathematics problems involving sequential questions and answers in a free-form textual input/output format. The structured nature of the mathematics domain, covering arithmetic, algebra, probability and calculus, enables the construction of training and test splits designed to clearly illuminate the capabilities and failure-modes of different architectures, as well as evaluate their ability to compose and relate knowledge and learned processes. Having described the data generation process and its potential future expansions, we conduct a comprehensive analysis of models from two broad classes of the most powerful sequence-to-sequence architectures and find notable differences in their ability to resolve mathematical problems and generalize their knowledge.

We advocate for a strong integration of Computational Creativity (CC) with research in large language and vision models (LLVMs) to address a key limitation of these models, i.e., creative problem solving. We present preliminary experiments showing how CC principles can be applied to address this limitation. Our goal is to foster discussions on creative problem solving in LLVMs and CC at prestigious ML venues. Our code is available at: https://github.com/lnairGT/creative-problem-solving-LLMs

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples.

The task of predicting time and location from images is challenging and requires complex human-like puzzle-solving ability over different clues. In this work, we formalize this ability into core skills and implement them using different modules in an expert pipeline called PuzzleGPT. PuzzleGPT consists of a perceiver to identify visual clues, a reasoner to deduce prediction candidates, a combiner to combinatorially combine information from different clues, a web retriever to get external knowledge if the task can't be solved locally, and a noise filter for robustness. This results in a zero-shot, interpretable, and robust approach that records state-of-the-art performance on two datasets -- TARA and WikiTilo. PuzzleGPT outperforms large VLMs such as BLIP-2, InstructBLIP, LLaVA, and even GPT-4V, as well as automatically generated reasoning pipelines like VisProg, by at least 32% and 38%, respectively. It even rivals or surpasses finetuned models.

Prompting methods such as Chain-of-Thought (CoT) have shed new light on enhancing the reasoning capabilities of large language models, and researchers have extensively explored the generation process of rationales and answers. However, they have overlooked the potential challenges posed by the poor quality of reasoning problems, which may influence the reasoning performance significantly. In this work, we propose Self-Polish (SP), a novel method that facilitates the model's problem-solving process by prompting them to progressively refine the given problems to be more comprehensible and solvable. Specifically, the method teaches models to eliminate irrelevant information, rearrange the logic structure and organize local conditions into new ones parallelly. SP is orthogonal to all other prompting methods, making it convenient to integrate with state-of-the-art techniques for further improvement. We conduct thorough experiments on five benchmarks to illustrate the effectiveness of the proposed method. For example, with Text-davinci-003, our method boosts the performance of standard few-shot prompting by 8.0% on GSM8K and 17.8% on MultiArith; it also improves the performance of CoT by 6.0% on GSM8K and 6.0% on MathQA, respectively. Furthermore, our method also showcases impressive performance on robustness evaluation.

Large language models (LLMs) such as ChatGPT and GPT-4 have made significant progress in NLP. However, their ability to memorize, represent, and leverage commonsense knowledge has been a well-known pain point for LLMs. It remains unclear that: (1) Can GPTs effectively answer commonsense questions? (2) Are GPTs knowledgeable in commonsense? (3) Are GPTs aware of the underlying commonsense knowledge for answering a specific question? (4) Can GPTs effectively leverage commonsense for answering questions? To evaluate the above commonsense problems, we conduct a series of experiments to evaluate ChatGPT's commonsense abilities, and the experimental results show that: (1) GPTs can achieve good QA accuracy in commonsense tasks, while they still struggle with certain types of knowledge. (2) ChatGPT is knowledgeable, and can accurately generate most of the commonsense knowledge using knowledge prompts. (3) Despite its knowledge, ChatGPT is an inexperienced commonsense problem solver, which cannot precisely identify the needed commonsense knowledge for answering a specific question, i.e., ChatGPT does not precisely know what commonsense knowledge is required to answer a question. The above findings raise the need to investigate better mechanisms for utilizing commonsense knowledge in LLMs, such as instruction following, better commonsense guidance, etc.

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate language models (LMs). In this paper, we introduce the USACO benchmark with 307 problems from the USA Computing Olympiad, along with high-quality unit tests, reference code, and official analyses for each problem. These resources enable us to construct and test a range of LM inference methods for competitive programming for the first time. We find GPT-4 only achieves a 8.7% pass@1 accuracy with zero-shot chain-of-thought prompting, and our best inference method improves it to 20.2% using a combination of self-reflection and retrieval over episodic knowledge. However, this is far from solving the benchmark. To better understand the remaining challenges, we design a novel human-in-the-loop study and surprisingly find that a small number of targeted hints enable GPT-4 to solve 13 out of 15 problems previously unsolvable by any model and method. Our benchmark, baseline methods, quantitative results, and qualitative analysis serve as an initial step toward LMs with grounded, creative, and algorithmic reasoning.

In recent years, large language models (LLMs) have shown remarkable capabilities in various artificial intelligence problems. However, they fail to plan reliably, even when prompted with a detailed definition of the planning task. Attempts to improve their planning capabilities, such as chain-of-thought prompting, fine-tuning, and explicit "reasoning" still yield incorrect plans and usually fail to generalize to larger tasks. In this paper, we show how to use LLMs to generate correct plans, even for out-of-distribution tasks of increasing size. For a given planning domain, we ask an LLM to generate several domain-dependent heuristic functions in the form of Python code, evaluate them on a set of training tasks within a greedy best-first search, and choose the strongest one. The resulting LLM-generated heuristics solve many more unseen test tasks than state-of-the-art domain-independent heuristics for classical planning. They are even competitive with the strongest learning algorithm for domain-dependent planning. These findings are especially remarkable given that our proof-of-concept implementation is based on an unoptimized Python planner and the baselines all build upon highly optimized C++ code. In some domains, the LLM-generated heuristics expand fewer states than the baselines, revealing that they are not only efficiently computable, but sometimes even more informative than the state-of-the-art heuristics. Overall, our results show that sampling a set of planning heuristic function programs can significantly improve the planning capabilities of LLMs.

A modular design encourages neural models to disentangle and recombine different facets of knowledge to generalise more systematically to new tasks. In this work, we assume that each task is associated with a subset of latent discrete skills from a (potentially small) inventory. In turn, skills correspond to parameter-efficient (sparse / low-rank) model parameterisations. By jointly learning these and a task-skill allocation matrix, the network for each task is instantiated as the average of the parameters of active skills. To favour non-trivial soft partitions of skills across tasks, we experiment with a series of inductive biases, such as an Indian Buffet Process prior and a two-speed learning rate. We evaluate our latent-skill model on two main settings: 1) multitask reinforcement learning for grounded instruction following on 8 levels of the BabyAI platform; and 2) few-shot adaptation of pre-trained text-to-text generative models on CrossFit, a benchmark comprising 160 NLP tasks. We find that the modular design of a network significantly increases sample efficiency in reinforcement learning and few-shot generalisation in supervised learning, compared to baselines with fully shared, task-specific, or conditionally generated parameters where knowledge is entangled across tasks. In addition, we show how discrete skills help interpretability, as they yield an explicit hierarchy of tasks.

What if artificial intelligence could not only solve problems for which it was trained but also learn to teach itself to solve new problems (i.e., meta-learn)? In this study, we demonstrate that a pre-trained transformer fine-tuned with reinforcement learning over multiple episodes develops the ability to solve problems that it has never encountered before - an emergent ability called In-Context Reinforcement Learning (ICRL). This powerful meta-learner not only excels in solving unseen in-distribution environments with remarkable sample efficiency, but also shows strong performance in out-of-distribution environments. In addition, we show that it exhibits robustness to the quality of its training data, seamlessly stitches together behaviors from its context, and adapts to non-stationary environments. These behaviors demonstrate that an RL-trained transformer can iteratively improve upon its own solutions, making it an excellent general-purpose problem solver.

The concept of Artificial Intelligence has gained a lot of attention over the last decade. In particular, AI-based tools have been employed in several scenarios and are, by now, pervading our everyday life. Nonetheless, most of these systems lack many capabilities that we would naturally consider to be included in a notion of "intelligence". In this work, we present an architecture that, inspired by the cognitive theory known as Thinking Fast and Slow by D. Kahneman, is tasked with solving planning problems in different settings, specifically: classical and multi-agent epistemic. The system proposed is an instance of a more general AI paradigm, referred to as SOFAI (for Slow and Fast AI). SOFAI exploits multiple solving approaches, with different capabilities that characterize them as either fast or slow, and a metacognitive module to regulate them. This combination of components, which roughly reflects the human reasoning process according to D. Kahneman, allowed us to enhance the reasoning process that, in this case, is concerned with planning in two different settings. The behavior of this system is then compared to state-of-the-art solvers, showing that the newly introduced system presents better results in terms of generality, solving a wider set of problems with an acceptable trade-off between solving times and solution accuracy.

Puzzlehunts are a genre of complex, multi-step puzzles lacking well-defined problem definitions. In contrast to conventional reasoning benchmarks consisting of tasks with clear instructions, puzzlehunts require models to discover the underlying problem structure from multimodal evidence and iterative reasoning, mirroring real-world domains such as scientific discovery, exploratory data analysis, or investigative problem-solving. Despite recent progress in foundation models, their performance on such open-ended settings remains largely untested. In this paper, we introduce PuzzleWorld, a large-scale benchmark of 667 puzzlehunt-style problems designed to assess step-by-step, open-ended, and creative multimodal reasoning. Each puzzle is annotated with the final solution, detailed reasoning traces, and cognitive skill labels, enabling holistic benchmarking and fine-grained diagnostic analysis. Most state-of-the-art models achieve only 1-2% final answer accuracy, with the best model solving only 14% of puzzles and reaching 40% stepwise accuracy. To demonstrate the value of our reasoning annotations, we show that fine-tuning a small model on reasoning traces improves stepwise reasoning from 4% to 11%, while training on final answers alone degrades performance to near zero. Our error analysis reveals that current models exhibit myopic reasoning, are bottlenecked by the limitations of language-based inference, and lack sketching capabilities crucial for visual and spatial reasoning. We release PuzzleWorld at https://github.com/MIT-MI/PuzzleWorld to support future work on building more general, open-ended, and creative reasoning systems.

Thinking aloud is an effective meta-cognitive strategy human reasoners apply to solve difficult problems. We suggest to improve the reasoning ability of pre-trained neural language models in a similar way, namely by expanding a task's context with problem elaborations that are dynamically generated by the language model itself. Our main result is that dynamic problem elaboration significantly improves the zero-shot performance of GPT-2 in a deductive reasoning and natural language inference task: While the model uses a syntactic heuristic for predicting an answer, it is capable (to some degree) of generating reasoned additional context which facilitates the successful application of its heuristic. We explore different ways of generating elaborations, including fewshot learning, and find that their relative performance varies with the specific problem characteristics (such as problem difficulty). Moreover, the effectiveness of an elaboration can be explained in terms of the degree to which the elaboration semantically coheres with the corresponding problem. In particular, elaborations that are most faithful to the original problem description may boost accuracy by up to 24%.

Critical thinking is essential for rational decision-making and problem-solving. This skill hinges on the ability to provide precise and reasoned critiques and is a hallmark of human intelligence. In the era of large language models (LLMs), this study explores the ability of LLMs to deliver accurate critiques across various tasks. We are interested in this topic as a capable critic model could not only serve as a reliable evaluator, but also as a source of supervised signals for model tuning. Particularly, if a model can self-critique, it has the potential for autonomous self-improvement. To examine this, we introduce a unified evaluation framework for assessing the critique abilities of LLMs. We develop a benchmark called CriticBench, which comprises 3K high-quality natural language queries and corresponding model responses; and annotate the correctness of these responses. The benchmark cover tasks such as math problem-solving, code completion, and question answering. We evaluate multiple LLMs on the collected dataset and our analysis reveals several noteworthy insights: (1) Critique is generally challenging for most LLMs, and this capability often emerges only when models are sufficiently large. (2) In particular, self-critique is especially difficult. Even top-performing LLMs struggle to achieve satisfactory performance. (3) Models tend to have lower critique accuracy on problems where they are most uncertain. To this end, we introduce a simple yet effective baseline named self-check, which leverages self-critique to improve task performance for various models. We hope this study serves as an initial exploration into understanding the critique abilities of LLMs, and aims to inform future research, including the development of more proficient critic models and the application of critiques across diverse tasks.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

In recent years, Large language models (LLMs) have garnered significant attention due to their superior performance in complex reasoning tasks. However, recent studies may diminish their reasoning capabilities markedly when problem descriptions contain irrelevant information, even with the use of advanced prompting techniques. To further investigate this issue, a dataset of primary school mathematics problems containing irrelevant information, named GSMIR, was constructed. Testing prominent LLMs and prompting techniques on this dataset revealed that while LLMs can identify irrelevant information, they do not effectively mitigate the interference it causes once identified. A novel automatic construction method, ATF, which enhances the ability of LLMs to identify and self-mitigate the influence of irrelevant information, is proposed to address this shortcoming. This method operates in two steps: first, analysis of irrelevant information, followed by its filtering. The ATF method, as demonstrated by experimental results, significantly improves the reasoning performance of LLMs and prompting techniques, even in the presence of irrelevant information on the GSMIR dataset.

Reasoning abilities, especially those for solving complex math problems, are crucial components of general intelligence. Recent advances by proprietary companies, such as o-series models of OpenAI, have made remarkable progress on reasoning tasks. However, the complete technical details remain unrevealed, and the techniques that are believed certainly to be adopted are only reinforcement learning (RL) and the long chain of thoughts. This paper proposes a new RL framework, termed OREAL, to pursue the performance limit that can be achieved through Outcome REwArd-based reinforcement Learning for mathematical reasoning tasks, where only binary outcome rewards are easily accessible. We theoretically prove that behavior cloning on positive trajectories from best-of-N (BoN) sampling is sufficient to learn the KL-regularized optimal policy in binary feedback environments. This formulation further implies that the rewards of negative samples should be reshaped to ensure the gradient consistency between positive and negative samples. To alleviate the long-existing difficulties brought by sparse rewards in RL, which are even exacerbated by the partial correctness of the long chain of thought for reasoning tasks, we further apply a token-level reward model to sample important tokens in reasoning trajectories for learning. With OREAL, for the first time, a 7B model can obtain 94.0 pass@1 accuracy on MATH-500 through RL, being on par with 32B models. OREAL-32B also surpasses previous 32B models trained by distillation with 95.0 pass@1 accuracy on MATH-500. Our investigation also indicates the importance of initial policy models and training queries for RL. Code, models, and data will be released to benefit future researchhttps://github.com/InternLM/OREAL.

The recent LLMs like GPT-4 and PaLM-2 have made tremendous progress in solving fundamental math problems like GSM8K by achieving over 90\% accuracy. However, their capabilities to solve more challenging math problems which require domain-specific knowledge (i.e. theorem) have yet to be investigated. In this paper, we introduce TheoremQA, the first theorem-driven question-answering dataset designed to evaluate AI models' capabilities to apply theorems to solve challenging science problems. \dataset is curated by domain experts containing 800 high-quality questions covering 350 theoremse.g. Taylor's theorem, Lagrange's theorem, Huffman coding, Quantum Theorem, Elasticity Theorem, etc from Math, Physics, EE\&CS, and Finance. We evaluate a wide spectrum of 16 large language and code models with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. We found that GPT-4's capabilities to solve these problems are unparalleled, achieving an accuracy of 51\% with Program-of-Thoughts Prompting. All the existing open-sourced models are below 15\%, barely surpassing the random-guess baseline. Given the diversity and broad coverage of \dataset, we believe it can be used as a better benchmark to evaluate LLMs' capabilities to solve challenging science problems. The data and code are released in https://github.com/wenhuchen/TheoremQA.

Large Language Models (LLMs) have shown remarkable capabilities in general natural language processing tasks but often fall short in complex reasoning tasks. Recent studies have explored human-like problem-solving strategies, such as self-correct, to push further the boundary of single-model reasoning ability. In this work, we let a single model "step outside the box" by engaging multiple models to correct each other. We introduce a multi-agent collaboration strategy that emulates the academic peer review process. Each agent independently constructs its own solution, provides reviews on the solutions of others, and assigns confidence levels to its reviews. Upon receiving peer reviews, agents revise their initial solutions. Extensive experiments on three different types of reasoning tasks show that our collaboration approach delivers superior accuracy across all ten datasets compared to existing methods. Further study underscores the effectiveness of integrating confidence in reviews, demonstrates the superiority of feedback exchange over mere solution sharing, and highlights the role of capability and diversity in fostering successful collaboration.

Large Language Models (LLMs) demonstrate promising capabilities in solving simple scientific problems but often produce hallucinations for complex ones. While integrating LLMs with tools can increase reliability, this approach typically results in over-reliance on tools, diminishing the model's ability to solve simple problems through basic reasoning. In contrast, human experts first assess problem complexity using domain knowledge before choosing an appropriate solution approach. Inspired by this human problem-solving process, we propose a novel two-component fine-tuning method. In the first component World Knowledge Distillation (WKD), LLMs learn directly from solutions generated using tool's information to internalize domain knowledge. In the second component Tool Usage Adaptation (TUA), we partition problems into easy and hard categories based on the model's direct answering accuracy. While maintaining the same alignment target for easy problems as in WKD, we train the model to intelligently switch to tool usage for more challenging problems. We validate our method on six scientific benchmark datasets, spanning mathematics, climate science and epidemiology. On average, our models demonstrate a 28.18% improvement in answer accuracy and a 13.89% increase in tool usage precision across all datasets, surpassing state-of-the-art models including GPT-4o and Claude-3.5.

Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified mathematical reasoning benchmark consisting of 23 diverse tasks along four dimensions: (i) mathematical abilities e.g., arithmetic, calculus (ii) language format e.g., question-answering, fill-in-the-blanks (iii) language diversity e.g., no language, simple language (iv) external knowledge e.g., commonsense, physics. We construct our benchmark by extending 20 datasets benchmark by collecting task instructions and solutions in the form of Python programs, thereby obtaining explainable solutions in addition to the correct answer. We additionally introduce two evaluation datasets to measure out-of-distribution performance and robustness to language perturbation. Finally, we introduce BHASKARA, a general-purpose mathematical reasoning model trained on LILA. Importantly, we find that multi-tasking leads to significant improvements (average relative improvement of 21.83% F1 score vs. single-task models), while the best performing model only obtains 60.40%, indicating the room for improvement in general mathematical reasoning and understanding.

Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs.

The capabilities and limitations of Large Language Models have been sketched out in great detail in recent years, providing an intriguing yet conflicting picture. On the one hand, LLMs demonstrate a general ability to solve problems. On the other hand, they show surprising reasoning gaps when compared to humans, casting doubt on the robustness of their generalisation strategies. The sheer volume of data used in the design of LLMs has precluded us from applying the method traditionally used to measure generalisation: train-test set separation. To overcome this, we study what kind of generalisation strategies LLMs employ when performing reasoning tasks by investigating the pretraining data they rely on. For two models of different sizes (7B and 35B) and 2.5B of their pretraining tokens, we identify what documents influence the model outputs for three simple mathematical reasoning tasks and contrast this to the data that are influential for answering factual questions. We find that, while the models rely on mostly distinct sets of data for each factual question, a document often has a similar influence across different reasoning questions within the same task, indicating the presence of procedural knowledge. We further find that the answers to factual questions often show up in the most influential data. However, for reasoning questions the answers usually do not show up as highly influential, nor do the answers to the intermediate reasoning steps. When we characterise the top ranked documents for the reasoning questions qualitatively, we confirm that the influential documents often contain procedural knowledge, like demonstrating how to obtain a solution using formulae or code. Our findings indicate that the approach to reasoning the models use is unlike retrieval, and more like a generalisable strategy that synthesises procedural knowledge from documents doing a similar form of reasoning.

Employing Large Language Models (LLMs) to address mathematical problems is an intriguing research endeavor, considering the abundance of math problems expressed in natural language across numerous science and engineering fields. While several prior works have investigated solving elementary mathematics using LLMs, this work explores the frontier of using GPT-4 for solving more complex and challenging math problems. We evaluate various ways of using GPT-4. Some of them are adapted from existing work, and one is \MathChat, a conversational problem-solving framework newly proposed in this work. We perform the evaluation on difficult high school competition problems from the MATH dataset, which shows the advantage of the proposed conversational approach.

Recently an influx of studies claim emergent cognitive abilities in large language models (LLMs). Yet, most rely on anecdotes, overlook contamination of training sets, or lack systematic Evaluation involving multiple tasks, control conditions, multiple iterations, and statistical robustness tests. Here we make two major contributions. First, we propose CogEval, a cognitive science-inspired protocol for the systematic evaluation of cognitive capacities in Large Language Models. The CogEval protocol can be followed for the evaluation of various abilities. Second, here we follow CogEval to systematically evaluate cognitive maps and planning ability across eight LLMs (OpenAI GPT-4, GPT-3.5-turbo-175B, davinci-003-175B, Google Bard, Cohere-xlarge-52.4B, Anthropic Claude-1-52B, LLaMA-13B, and Alpaca-7B). We base our task prompts on human experiments, which offer both established construct validity for evaluating planning, and are absent from LLM training sets. We find that, while LLMs show apparent competence in a few planning tasks with simpler structures, systematic evaluation reveals striking failure modes in planning tasks, including hallucinations of invalid trajectories and getting trapped in loops. These findings do not support the idea of emergent out-of-the-box planning ability in LLMs. This could be because LLMs do not understand the latent relational structures underlying planning problems, known as cognitive maps, and fail at unrolling goal-directed trajectories based on the underlying structure. Implications for application and future directions are discussed.

Large Language Models (LLMs) have recently showcased remarkable reasoning abilities. However, larger models often surpass their smaller counterparts in reasoning tasks, posing the challenge of effectively transferring these capabilities from larger models. Existing approaches heavily rely on extensive fine-tuning data or continuous interactions with a superior teacher LLM during inference. We introduce a principle-based teacher-student framework called ``Teaching via Principle Discovery'' (TPD) to address these limitations. Inspired by human learning mechanisms, TPD mimics the interaction between a teacher and a student using a principle-based approach. The teacher LLM generates problem-solving instructions and corrective principles based on the student LLM's errors. These principles guide the refinement of instructions and the selection of instructive examples from a validation set. This enables the student model to learn from both the teacher's guidance and its own mistakes. Once the student model begins making inferences, TPD requires no further intervention from the teacher LLM or humans. Through extensive experiments across eight reasoning tasks, we demonstrate the effectiveness of TPD. Compared to standard chain-of-thought prompting, TPD significantly improves the student model's performance, achieving 6.2% improvement on average.

While language models are powerful and versatile, they often fail to address highly complex problems. This is because solving complex problems requires deliberate thinking, which has been only minimally guided during training. In this paper, we propose a new method called Cumulative Reasoning (CR), which employs language models in a cumulative and iterative manner to emulate human thought processes. By decomposing tasks into smaller components, CR streamlines the problem-solving process, rendering it both more manageable and effective. For logical inference tasks, CR consistently outperforms existing methods with an improvement up to 9.3%, and achieves the astonishing accuracy of 98.04% on the curated FOLIO wiki dataset. In the context of the Game of 24, CR achieves an accuracy of 98%, which signifies a substantial enhancement of 24% over the previous state-of-the-art method. Finally, on the MATH dataset, we establish new state-of-the-art results with 58.0% overall accuracy, surpassing the previous best approach by a margin of 4.2%, and achieving 43% relative improvement on the hardest level 5 problems (22.4% to 32.1%). Code is available at https://github.com/iiis-ai/cumulative-reasoning.

Large Language Models (LLMs) have revolutionized natural language processing and hold immense potential for advancing Artificial Intelligence. However, the core architecture of most mainstream LLMs -- the Transformer -- has inherent limitations in computational depth, rendering them theoretically incapable of solving many reasoning tasks that demand increasingly deep computations. Chain of Thought (CoT) prompting has emerged as a technique to address these architectural limitations, as evidenced by several theoretical studies. It offers a promising approach to solving complex reasoning tasks that were previously beyond the capabilities of these models. Despite its successes, CoT and its variants (such as Tree of Thought, Graph of Thought, etc.) rely on a "one-prompt-for-all" approach, using a single prompt structure (e.g., "think step by step") for a wide range of tasks -- from counting and sorting to solving mathematical and algorithmic problems. This approach poses significant challenges for models to generate the correct reasoning steps, as the model must navigate through a vast prompt template space to find the appropriate template for each task. In this work, we build upon previous theoretical analyses of CoT to demonstrate how the one-prompt-for-all approach can negatively affect the computability of LLMs. We partition the solution search space into two: the prompt space and the answer space. Our findings show that task-specific supervision is essential for navigating the prompt space accurately and achieving optimal performance. Through experiments with state-of-the-art LLMs, we reveal a gap in reasoning performance when supervision is applied versus when it is not.

Prompting Large Language Models (LLMs), or providing context on the expected model of operation, is an effective way to steer the outputs of such models to satisfy human desiderata after they have been trained. But in rapidly evolving domains, there is often need to fine-tune LLMs to improve either the kind of knowledge in their memory or their abilities to perform open ended reasoning in new domains. When human's learn new concepts, we often do so by linking the new material that we are studying to concepts we have already learned before. To that end, we ask, "can prompting help us teach LLMs how to learn". In this work, we study a novel generalization of instruction tuning, called contextual fine-tuning, to fine-tune LLMs. Our method leverages instructional prompts designed to mimic human cognitive strategies in learning and problem-solving to guide the learning process during training, aiming to improve the model's interpretation and understanding of domain-specific knowledge. We empirically demonstrate that this simple yet effective modification improves the ability of LLMs to be fine-tuned rapidly on new datasets both within the medical and financial domains.

A language model's ability to reflect on its own reasoning provides a key advantage for solving complex problems. While most recent research has focused on how this ability develops during reinforcement learning, we show that it actually begins to emerge much earlier - during the model's pre-training. To study this, we introduce deliberate errors into chains-of-thought and test whether the model can still arrive at the correct answer by recognizing and correcting these mistakes. By tracking performance across different stages of pre-training, we observe that this self-correcting ability appears early and improves steadily over time. For instance, an OLMo2-7B model pre-trained on 4 trillion tokens displays self-correction on our six self-reflection tasks.

In their recent Nature Human Behaviour paper, "Emergent analogical reasoning in large language models," (Webb, Holyoak, and Lu, 2023) the authors argue that "large language models such as GPT-3 have acquired an emergent ability to find zero-shot solutions to a broad range of analogy problems." In this response, we provide counterexamples of the letter string analogies. In our tests, GPT-3 fails to solve even the easiest variants of the problems presented in the original paper. Zero-shot reasoning is an extraordinary claim that requires extraordinary evidence. We do not see that evidence in our experiments. To strengthen claims of humanlike reasoning such as zero-shot reasoning, it is important that the field develop approaches that rule out data memorization.

The surprising ability of Large Language Models (LLMs) to perform well on complex reasoning with only few-shot chain-of-thought prompts is believed to emerge only in very large-scale models (100+ billion parameters). We show that such abilities can, in fact, be distilled down from GPT-3.5 (ge 175B) to T5 variants (le 11B). We propose model specialization, to specialize the model's ability towards a target task. The hypothesis is that large models (commonly viewed as larger than 100B) have strong modeling power, but are spread on a large spectrum of tasks. Small models (commonly viewed as smaller than 10B) have limited model capacity, but if we concentrate their capacity on a specific target task, the model can achieve a decent improved performance. We use multi-step math reasoning as our testbed because it is a very typical emergent ability. We show two important aspects of model abilities: (1). there exists a very complex balance/ tradeoff between language models' multi-dimensional abilities; (2). by paying the price of decreased generic ability, we can clearly lift up the scaling curve of models smaller than 10B towards a specialized multi-step math reasoning ability. We further give comprehensive discussions about important design choices for better generalization, including the tuning data format, the start model checkpoint, and a new model selection method. We hope our practice and discoveries can serve as an important attempt towards specialized smaller models in the new research paradigm set by LLMs.

Training reasoning language models (LMs) with reinforcement learning (RL) for one-hot correctness inherently relies on the LM being able to explore and solve its task with some chance at initialization. Furthermore, a key use case of reasoning LMs is to act as teachers for distilling new students and cold-starting future RL iterations rather than being deployed themselves. From these considerations, we introduce a new framework that avoids RL's exploration challenge by training a new class of Reinforcement-Learned Teachers (RLTs) focused on yielding the most effective downstream distillation. RLTs are prompted with both the question and solution to each problem, and tasked to simply "connect-the-dots" with detailed explanations tailored for their students. We train RLTs with dense rewards obtained by feeding each explanation to the student and testing its understanding of the problem's solution. In practice, the raw outputs of a 7B RLT provide higher final performance on competition and graduate-level tasks than existing distillation and cold-starting pipelines that collect and postprocess the reasoning traces of orders of magnitude larger LMs. Furthermore, RLTs maintain their effectiveness when training larger students and when applied zero-shot to out-of-distribution tasks, unlocking new levels of efficiency and re-usability for the RL reasoning framework.

Test-time compute has led to remarkable success in the large language model (LLM) community, particularly for complex tasks, where longer chains of thought (CoTs) are generated to enhance reasoning capabilities. However, growing evidence reveals that such reasoning models often produce CoTs plagued by excessive redundancy, including unnecessary verification steps and repetitive reasoning shifts. The root cause lies in post-training of them that overly rely on outcome reward paradigms, as the data of process reward paradigms, which regulate intermediate reasoning steps, is difficult to construct at scale. To address this, we propose PI, a novel framework for Test-time Prompt Intervention. PI provides an interface to dynamically guide and regulate reasoning paths during inference through timely (When module) and proper (How module) interventions and post-intervention sampling (Which module). This allows human problem-solving expertise and cognitive science principles to be seamlessly integrated into LLMs' reasoning processes, enhancing controllability and interpretability. Extensive experiments across multiple models and datasets demonstrate that PI significantly shortens CoTs while reducing hallucination, yielding more concise and reliable reasoning.

Language models are rarely shown fruitful mistakes while training. They then struggle to look beyond the next token, suffering from a snowballing of errors and struggling to predict the consequence of their actions several steps ahead. In this paper, we show how language models can be taught to search by representing the process of search in language, as a flattened string -- a stream of search (SoS). We propose a unified language for search that captures an array of different symbolic search strategies. We demonstrate our approach using the simple yet difficult game of Countdown, where the goal is to combine input numbers with arithmetic operations to reach a target number. We pretrain a transformer-based language model from scratch on a dataset of streams of search generated by heuristic solvers. We find that SoS pretraining increases search accuracy by 25% over models trained to predict only the optimal search trajectory. We further finetune this model with two policy improvement methods: Advantage-Induced Policy Alignment (APA) and Self-Taught Reasoner (STaR). The finetuned SoS models solve 36% of previously unsolved problems, including problems that cannot be solved by any of the heuristic solvers. Our results indicate that language models can learn to solve problems via search, self-improve to flexibly use different search strategies, and potentially discover new ones.

Reinforcement learning (RL) has become the dominant paradigm for endowing language models with advanced reasoning capabilities. Despite the substantial empirical gains demonstrated by RL-based training methods like GRPO, a granular understanding of their advantages is still lacking. To address this gap, we introduce a fine-grained analytic framework to dissect the impact of RL on reasoning. Our framework specifically investigates key elements that have been hypothesized to benefit from RL training: (1) plan-following and execution, (2) problem decomposition, and (3) improved reasoning and knowledge utilization. Using this framework, we gain insights beyond mere accuracy. For instance, providing models with explicit step-by-step plans surprisingly degrades performance on the most challenging benchmarks, yet RL-tuned models exhibit greater robustness, experiencing markedly smaller performance drops than their base counterparts. This suggests that RL may not primarily enhance the execution of external plans but rather empower models to formulate and follow internal strategies better suited to their reasoning processes. Conversely, we observe that RL enhances the model's capacity to integrate provided knowledge into its reasoning process, leading to performance improvements across diverse tasks. We also study difficulty, showing improved training by developing new ways to exploit hard problems. Our findings lay a foundation for more principled training and evaluation of reasoning models.

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has not received enough attention, though. This study presents the ICPC benchmark, which consists of 254 international collegiate programming contest (ICPC) tasks. Each problem includes official analysis, reference code, and sample, high-quality unit, and hidden tests. We are able to develop and evaluate a variety of LM inference techniques for competitive programming with these resources. With zero-shot chain-of-thought prompting, we find that o1 only achieves a 19.1\% pass@1 solve rate. With our best inference technique, which combines multi-turn self-judge with reflection and retrieval over episodic information, raises this to 42.2\%. Furthermore, we conduct a new human-in-the-loop investigation to gain a deeper understanding of the remaining difficulties. Surprisingly, we discover that o1 can solve 17 out of 18 problems that were previously unsolvable by any model or technique with just a few specific instructions. A footstep toward LMs with grounded, imaginative, and algorithmic thinking is provided by our quantitative findings and qualitative research. We open-source our code and data at https://github.com/kraritt/zolve.

Large Reasoning Models (LRMs) have become a central focus in today's large language model (LLM) research, where models are designed to output a step-by-step thinking process before arriving at a final answer to handle complex reasoning tasks. Despite their promise, recent empirical studies (e.g., [Shojaee et al., 2025] from Apple) suggest that this thinking process may not actually enhance reasoning ability, where LLMs without explicit reasoning actually outperform LRMs on tasks with low or high complexity. In this work, we revisit these findings and investigate whether the limitations of LRMs persist when tool augmentations are introduced. We incorporate two types of tools, Python interpreters and scratchpads, and evaluate three representative LLMs and their LRM counterparts on Apple's benchmark reasoning puzzles. Our results show that, with proper tool use, LRMs consistently outperform their non-reasoning counterparts across all levels of task complexity. These findings challenge the recent narrative that reasoning is an illusion and highlight the potential of tool-augmented LRMs for solving complex problems.

Exploiting large language models (LLMs) to tackle deductive reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex deductive problems, characterized by plenty of premises (i.e., facts or rules) entailing intricate relationships among entities and requiring multi-hop reasoning. One intuitive solution is to decompose the original task into smaller sub-tasks, and then chain the multiple casual reasoning steps together in a forward (e.g., Selection-Inference) or backward (e.g., LAMBADA) direction. However, these techniques inevitably necessitate a large number of overall stages, leading to computationally expensive operations and a higher possibility of making misleading steps. In addition to stage-by-stage decomposition, we draw inspiration from another aspect of human problem-solving. Humans tend to distill the most relevant information and organize their thoughts systematically (e.g., creating mind maps), which assists them in answering questions or drawing conclusions precisely and quickly. In light of this, we propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to efficiently identify the most pertinent information while eliminating redundancy. It then prompts the LLMs in a more organized form that adapts to the model's inference process. By perceiving concise and organized proofs, the deductive reasoning abilities of LLMs can be better elicited, and the risk of acquiring errors caused by excessive reasoning stages is mitigated. Furthermore, our approach can be combined with the aforementioned ones to further boost their performance. Extensive experimental results on three popular deductive benchmarks (i.e., ProofWriter, PrOntoQA and PrOntoQA-OOD) show that COP significantly outperforms previous state-of-the-art methods.

Large language models (LLMs) can solve an increasing number of complex reasoning tasks while making surprising mistakes in basic numerical understanding and processing (such as 9.11 > 9.9). The latter ability is essential for tackling complex arithmetic and mathematical problems and serves as a foundation for most reasoning tasks, but previous work paid little attention to it or only discussed several restricted tasks (like integer addition). In this paper, we comprehensively investigate the numerical understanding and processing ability (NUPA) of LLMs. Firstly, we introduce a benchmark covering four common numerical representations and 17 distinct numerical tasks in four major categories, resulting in 41 meaningful combinations in total. These tasks are derived from primary and secondary education curricula, encompassing nearly all everyday numerical understanding and processing scenarios, and the rules of these tasks are very simple and clear. Through the benchmark, we find that current LLMs fail frequently in many of the tasks. To study the problem, we train small models with existing and potential techniques for enhancing NUPA (such as tokenizers, PEs, and number formats), comprehensively evaluating their effectiveness using our testbed. We also finetune practical-scale LLMs on our proposed NUPA tasks and find that 1) naive finetuning can improve NUPA a lot on many but not all tasks, and 2) surprisingly, techniques designed to enhance NUPA prove ineffective for finetuning pretrained models. We further explore the impact of chain-of-thought techniques on NUPA. Our work provides a more detailed and comprehensive understanding of NUPA in LLMs. Our benchmark and code are released at https://github.com/GraphPKU/number_cookbook.

In this paper, I introduce the retrieval problem, a simple reasoning task that can be solved only by transformers with a minimum number of layers. The task has an adjustable difficulty that can further increase the required number of layers to any arbitrary value. I demonstrate that large language models can solve the task under different prompting formulations without any fine-tuning. To understand how transformers solve the retrieval problem, I train several transformers on a minimal formulation. I find that successful learning occurs only under the presence of an implicit curriculum. I uncover the learned mechanisms by studying the attention maps in the trained transformers. I also study the training process, uncovering that attention heads always emerge in a specific sequence.

Large language models (LLMs) have demonstrated remarkable performance across a wide range of tasks. Advances in prompt engineering and fine-tuning techniques have further enhanced their ability to address complex reasoning challenges. However, these advanced capabilities are often exclusive to models exceeding 100 billion parameters. Although Chain-of-Thought (CoT) fine-tuning methods have been explored for smaller models (under 10 billion parameters), they typically depend on extensive CoT training data, which can introduce inconsistencies and limit effectiveness in low-data settings. To overcome these limitations, this paper introduce a new reasoning strategy Solution Guidance (SG) and a plug-and-play training paradigm Solution-Guidance Fine-Tuning (SGFT) for enhancing the reasoning capabilities of small language models. SG focuses on problem understanding and decomposition at the semantic and logical levels, rather than specific computations, which can effectively improve the SLMs' generalization and reasoning abilities. With only a small amount of SG training data, SGFT can fine-tune a SLM to produce accurate problem-solving guidances, which can then be flexibly fed to any SLM as prompts, enabling it to generate correct answers directly. Experimental results demonstrate that our method significantly improves the performance of SLMs on various reasoning tasks, enhancing both their practicality and efficiency within resource-constrained environments.

Recent Large Language Models (LLMs) have reported high accuracy on reasoning benchmarks. However, it is still unclear whether the observed results arise from true reasoning or from statistical recall of the training set. Inspired by the ladder of causation (Pearl, 2009) and its three levels (associations, interventions and counterfactuals), this paper introduces RE-IMAGINE, a framework to characterize a hierarchy of reasoning ability in LLMs, alongside an automated pipeline to generate problem variations at different levels of the hierarchy. By altering problems in an intermediate symbolic representation, RE-IMAGINE generates arbitrarily many problems that are not solvable using memorization alone. Moreover, the framework is general and can work across reasoning domains, including math, code, and logic. We demonstrate our framework on four widely-used benchmarks to evaluate several families of LLMs, and observe reductions in performance when the models are queried with problem variations. These assessments indicate a degree of reliance on statistical recall for past performance, and open the door to further research targeting skills across the reasoning hierarchy.