Daily Papers

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.

Large language models (LLMs) can transform education, but their optimization for direct question-answering often undermines effective pedagogy which requires strategically withholding answers. To mitigate this, we propose an online reinforcement learning (RL)-based alignment framework that can quickly adapt LLMs into effective tutors using simulated student-tutor interactions by emphasizing pedagogical quality and guided problem-solving over simply giving away answers. We use our method to train a 7B parameter tutor model without human annotations which reaches similar performance to larger proprietary models like LearnLM. We introduce a controllable reward weighting to balance pedagogical support and student solving accuracy, allowing us to trace the Pareto frontier between these two objectives. Our models better preserve reasoning capabilities than single-turn SFT baselines and can optionally enhance interpretability through thinking tags that expose the model's instructional planning.

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.

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.

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.

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.

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

Geometry problem solving has attracted much attention in the NLP community recently. The task is challenging as it requires abstract problem understanding and symbolic reasoning with axiomatic knowledge. However, current datasets are either small in scale or not publicly available. Thus, we construct a new large-scale benchmark, Geometry3K, consisting of 3,002 geometry problems with dense annotation in formal language. We further propose a novel geometry solving approach with formal language and symbolic reasoning, called Interpretable Geometry Problem Solver (Inter-GPS). Inter-GPS first parses the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. Unlike implicit learning in existing methods, Inter-GPS incorporates theorem knowledge as conditional rules and performs symbolic reasoning step by step. Also, a theorem predictor is designed to infer the theorem application sequence fed to the symbolic solver for the more efficient and reasonable searching path. Extensive experiments on the Geometry3K and GEOS datasets demonstrate that Inter-GPS achieves significant improvements over existing methods. The project with code and data is available at https://lupantech.github.io/inter-gps.

Large language models (LLMs) have shown remarkable proficiency in human-level reasoning and generation capabilities, which encourages extensive research on their application in mathematical problem solving. However, current work has been largely focused on text-based mathematical problems, with limited investigation in problems involving geometric information. Addressing this gap, we aim to enable LLMs to solve geometric problems by understanding image input. We first analyze the limitations of current Multimodal Large Language Models (MLLMs) in this area: they struggle to accurately comprehending basic geometric elements and their relationships. To overcome these challenges, we take advantage of the unique characteristics of geometric problems (such as unique geometric logical form, and geometric scalability) and the capacity of the textual LLMs to build an enriched multimodal geometry dataset based on existing data. The augmented dataset, Geo170K, contains more than 170K geometric image-caption and question-answer pairs. Utilizing our constructed Geo170K dataset, we develop G-LLaVA, which demonstrates exceptional performance in solving geometric problems, significantly outperforming GPT-4-V on the MathVista benchmark with only 7B parameters.

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.

Large Language Models (LLMs) have shown impressive progress in mathematical reasoning. While data augmentation is promising to enhance mathematical problem-solving ability, current approaches are predominantly limited to instance-level modifications-such as rephrasing or generating syntactic variations-which fail to capture and leverage the intrinsic relational structures inherent in mathematical knowledge. Inspired by human learning processes, where mathematical proficiency develops through systematic exposure to interconnected concepts, we introduce MathFusion, a novel framework that enhances mathematical reasoning through cross-problem instruction synthesis. MathFusion implements this through three fusion strategies: (1) sequential fusion, which chains related problems to model solution dependencies; (2) parallel fusion, which combines analogous problems to reinforce conceptual understanding; and (3) conditional fusion, which creates context-aware selective problems to enhance reasoning flexibility. By applying these strategies, we generate a new dataset, MathFusionQA, followed by fine-tuning models (DeepSeekMath-7B, Mistral-7B, Llama3-8B) on it. Experimental results demonstrate that MathFusion achieves substantial improvements in mathematical reasoning while maintaining high data efficiency, boosting performance by 18.0 points in accuracy across diverse benchmarks while requiring only 45K additional synthetic instructions, representing a substantial improvement over traditional single-instruction approaches. Our datasets, models, and code are publicly available at https://github.com/QizhiPei/mathfusion.

Large language models (LLMs) have shown excellent mastering of human language, but still struggle in real-world applications that require mathematical problem-solving. While many strategies and datasets to enhance LLMs' mathematics are developed, it remains a challenge to simultaneously maintain and improve both language and mathematical capabilities in deployed LLM systems.In this work, we tailor the Self-Critique pipeline, which addresses the challenge in the feedback learning stage of LLM alignment. We first train a general Math-Critique model from the LLM itself to provide feedback signals. Then, we sequentially employ rejective fine-tuning and direct preference optimization over the LLM's own generations for data collection. Based on ChatGLM3-32B, we conduct a series of experiments on both academic and our newly created challenging dataset, MathUserEval. Results show that our pipeline significantly enhances the LLM's mathematical problem-solving while still improving its language ability, outperforming LLMs that could be two times larger. Related techniques have been deployed to ChatGLM\url{https://chatglm.cn}, an online serving LLM. Related evaluation dataset and scripts are released at https://github.com/THUDM/ChatGLM-Math.

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.

We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, atomic physics, and optics. Each problem requires advanced physics knowledge and mathematical reasoning. We develop a robust automated evaluation system for precise and reliable validation. Our evaluation of leading foundation models reveals substantial limitations. Even the most advanced model, o3-mini, achieves only 59.9% accuracy, highlighting significant challenges in solving high-level scientific problems. Through comprehensive error analysis, exploration of diverse prompting strategies, and Retrieval-Augmented Generation (RAG)-based knowledge augmentation, we identify key areas for improvement, laying the foundation for future advancements.

Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play a pivotal role. To surmount these challenges, we introduce a new framework for language model inference, Tree of Thoughts (ToT), which generalizes over the popular Chain of Thought approach to prompting language models, and enables exploration over coherent units of text (thoughts) that serve as intermediate steps toward problem solving. ToT allows LMs to perform deliberate decision making by considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices. Our experiments show that ToT significantly enhances language models' problem-solving abilities on three novel tasks requiring non-trivial planning or search: Game of 24, Creative Writing, and Mini Crosswords. For instance, in Game of 24, while GPT-4 with chain-of-thought prompting only solved 4% of tasks, our method achieved a success rate of 74%. Code repo with all prompts: https://github.com/ysymyth/tree-of-thought-llm.

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.}.

Mathematical geometric problem solving (GPS) often requires effective integration of multimodal information and verifiable logical coherence. Despite the fast development of large language models in general problem solving, it remains unresolved regarding with both methodology and benchmarks, especially given the fact that exiting synthetic GPS benchmarks are often not self-verified and contain noise and self-contradicted information due to the illusion of LLMs. In this paper, we propose a scalable data engine called TrustGeoGen for problem generation, with formal verification to provide a principled benchmark, which we believe lays the foundation for the further development of methods for GPS. The engine synthesizes geometric data through four key innovations: 1) multimodal-aligned generation of diagrams, textual descriptions, and stepwise solutions; 2) formal verification ensuring rule-compliant reasoning paths; 3) a bootstrapping mechanism enabling complexity escalation via recursive state generation and 4) our devised GeoExplore series algorithms simultaneously produce multi-solution variants and self-reflective backtracking traces. By formal logical verification, TrustGeoGen produces GeoTrust-200K dataset with guaranteed modality integrity, along with GeoTrust-test testset. Experiments reveal the state-of-the-art models achieve only 49.17\% accuracy on GeoTrust-test, demonstrating its evaluation stringency. Crucially, models trained on GeoTrust achieve OOD generalization on GeoQA, significantly reducing logical inconsistencies relative to pseudo-label annotated by OpenAI-o1. Our code is available at https://github.com/Alpha-Innovator/TrustGeoGen

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

In this study, we investigated the effects of self-reflection in large language models (LLMs) on problem-solving performance. We instructed nine popular LLMs to answer a series of multiple-choice questions to provide a performance baseline. For each incorrectly answered question, we instructed eight types of self-reflecting LLM agents to reflect on their mistakes and provide themselves with guidance to improve problem-solving. Then, using this guidance, each self-reflecting agent attempted to re-answer the same questions. Our results indicate that LLM agents are able to significantly improve their problem-solving performance through self-reflection (p < 0.001). In addition, we compared the various types of self-reflection to determine their individual contribution to performance. All code and data are available on GitHub at https://github.com/matthewrenze/self-reflection

The art of mathematical reasoning stands as a fundamental pillar of intellectual progress and is a central catalyst in cultivating human ingenuity. Researchers have recently published a plethora of works centered around the task of solving Math Word Problems (MWP) - a crucial stride towards general AI. These existing models are susceptible to dependency on shallow heuristics and spurious correlations to derive the solution expressions. In order to ameliorate this issue, in this paper, we propose a framework for MWP solvers based on the generation of linguistic variants of the problem text. The approach involves solving each of the variant problems and electing the predicted expression with the majority of the votes. We use DeBERTa (Decoding-enhanced BERT with disentangled attention) as the encoder to leverage its rich textual representations and enhanced mask decoder to construct the solution expressions. Furthermore, we introduce a challenging dataset, Psmall{ARAMAWPS}, consisting of paraphrased, adversarial, and inverse variants of selectively sampled MWPs from the benchmark Msmall{AWPS} dataset. We extensively experiment on this dataset along with other benchmark datasets using some baseline MWP solver models. We show that training on linguistic variants of problem statements and voting on candidate predictions improve the mathematical reasoning and robustness of the model. We make our code and data publicly available.

Plane geometry problem solving (PGPS) has recently gained significant attention as a benchmark to assess the multi-modal reasoning capabilities of large vision-language models. Despite the growing interest in PGPS, the research community still lacks a comprehensive overview that systematically synthesizes recent work in PGPS. To fill this gap, we present a survey of existing PGPS studies. We first categorize PGPS methods into an encoder-decoder framework and summarize the corresponding output formats used by their encoders and decoders. Subsequently, we classify and analyze these encoders and decoders according to their architectural designs. Finally, we outline major challenges and promising directions for future research. In particular, we discuss the hallucination issues arising during the encoding phase within encoder-decoder architectures, as well as the problem of data leakage in current PGPS benchmarks.

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.

Recent advances in Multimodal Large Language Models (MLLMs) have achieved remarkable progress in general domains and demonstrated promise in multimodal mathematical reasoning. However, applying MLLMs to geometry problem solving (GPS) remains challenging due to lack of accurate step-by-step solution data and severe hallucinations during reasoning. In this paper, we propose GeoGen, a pipeline that can automatically generates step-wise reasoning paths for geometry diagrams. By leveraging the precise symbolic reasoning, GeoGen produces large-scale, high-quality question-answer pairs. To further enhance the logical reasoning ability of MLLMs, we train GeoLogic, a Large Language Model (LLM) using synthetic data generated by GeoGen. Serving as a bridge between natural language and symbolic systems, GeoLogic enables symbolic tools to help verifying MLLM outputs, making the reasoning process more rigorous and alleviating hallucinations. Experimental results show that our approach consistently improves the performance of MLLMs, achieving remarkable results on benchmarks for geometric reasoning tasks. This improvement stems from our integration of the strengths of LLMs and symbolic systems, which enables a more reliable and interpretable approach for the GPS task. Codes are available at https://github.com/ycpNotFound/GeoGen.

Large Language Models (LLMs) have demonstrated strong capabilities in text-based tasks but struggle with the complex reasoning required for physics problems, particularly in advanced arithmetic and conceptual understanding. While some research has explored ways to enhance LLMs in physics education using techniques such as prompt engineering and Retrieval Augmentation Generation (RAG), not enough effort has been made in addressing their limitations in physics reasoning. This paper presents a novel approach to improving LLM performance on physics questions using Reinforcement Learning with Human and Artificial Intelligence Feedback (RLHAIF). We evaluate several reinforcement learning methods, including Proximal Policy Optimization (PPO), Direct Preference Optimization (DPO), and Remax optimization. These methods are chosen to investigate RL policy performance with different settings on the PhyQA dataset, which includes challenging physics problems from high school textbooks. Our RLHAIF model, tested on leading LLMs like LLaMA2 and Mistral, achieved superior results, notably with the MISTRAL-PPO model, demonstrating marked improvements in reasoning and accuracy. It achieved high scores, with a 58.67 METEOR score and a 0.74 Reasoning score, making it a strong example for future physics reasoning research in this area.

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.

The evaluation of the problem-solving capability under incomplete information scenarios of Large Language Models (LLMs) is increasingly important, encompassing capabilities such as questioning, knowledge search, error detection, and path planning. Current research mainly focus on LLMs' problem-solving capability such as ``Twenty Questions''. However, these kinds of games do not require recognizing misleading cues which are necessary in the incomplete information scenario. Moreover, the existing game such as ``Who is undercover'' are highly subjective, making it challenging for evaluation. Therefore, in this paper, we introduce a novel game named BrainKing based on the ``Who is undercover'' and ``Twenty Questions'' for evaluating LLM capabilities under incomplete information scenarios. It requires LLMs to identify target entities with limited yes-or-no questions and potential misleading answers. By setting up easy, medium, and hard difficulty modes, we comprehensively assess the performance of LLMs across various aspects. Our results reveal the capabilities and limitations of LLMs in BrainKing, providing significant insights of LLM problem-solving levels.

Large Language Models (LLMs) have transformed natural language processing, yet improving their problem-solving capabilities, particularly for complex, reasoning-intensive tasks, remains a persistent challenge. This paper introduces the REAP (Reflection, Explicit Problem Deconstruction, and Advanced Prompting) method, an innovative approach within the dynamic context generation framework. REAP guides LLMs through reflection on the query, deconstructing it into manageable components, and generating relevant context to enhance the solution process. We evaluated REAP using a dataset designed to expose LLM limitations, comparing zero-shot prompting with REAP-enhanced prompts across six state-of-the-art models: OpenAI's o1-preview, o1-mini, GPT-4o, GPT-4o-mini, Google's Gemini 1.5 Pro, and Claude 3.5 Sonnet. The results demonstrate notable performance gains, with o1-mini improving by 40.97%, GPT-4o by 66.26%, and GPT-4o-mini by 112.93%. Despite the already strong baseline performance of OpenAI's o1-preview, modest gains were observed. Beyond performance improvements, REAP offers a cost-effective solution; for example, GPT-4o-mini, which is approximately 100 times cheaper than o1-preview, delivered competitive results. REAP also improves the clarity of model outputs, making it easier for humans to understand the reasoning behind the results and simplifying the process of identifying and addressing any issues. These findings demonstrate REAP's potential to greatly improve the capabilities of LLMs, providing both better performance and increased cost-efficiency across a wide range of applications.

Diffusion models have recently achieved success in solving Bayesian inverse problems with learned data priors. Current methods build on top of the diffusion sampling process, where each denoising step makes small modifications to samples from the previous step. However, this process struggles to correct errors from earlier sampling steps, leading to worse performance in complicated nonlinear inverse problems, such as phase retrieval. To address this challenge, we propose a new method called Decoupled Annealing Posterior Sampling (DAPS) that relies on a novel noise annealing process. Specifically, we decouple consecutive steps in a diffusion sampling trajectory, allowing them to vary considerably from one another while ensuring their time-marginals anneal to the true posterior as we reduce noise levels. This approach enables the exploration of a larger solution space, improving the success rate for accurate reconstructions. We demonstrate that DAPS significantly improves sample quality and stability across multiple image restoration tasks, particularly in complicated nonlinear inverse problems. For example, we achieve a PSNR of 30.72dB on the FFHQ 256 dataset for phase retrieval, which is an improvement of 9.12dB compared to existing methods.

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.

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.

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.

Solving mathematical problems requires advanced reasoning abilities and presents notable challenges for large language models. Previous works usually synthesize data from proprietary models to augment existing datasets, followed by instruction tuning to achieve top-tier results. However, our analysis of these datasets reveals severe biases towards easy queries, with frequent failures to generate any correct response for the most challenging queries. Hypothesizing that difficult queries are crucial to learn complex reasoning, we propose Difficulty-Aware Rejection Tuning (DART), a method that allocates difficult queries more trials during the synthesis phase, enabling more extensive training on difficult samples. Utilizing DART, we have created new datasets for mathematical problem-solving that focus more on difficult queries and are substantially smaller than previous ones. Remarkably, our synthesis process solely relies on a 7B-sized open-weight model, without reliance on the commonly used proprietary GPT-4. We fine-tune various base models on our datasets ranging from 7B to 70B in size, resulting in a series of strong models called DART-MATH. In comprehensive in-domain and out-of-domain evaluation on 6 mathematical benchmarks, DART-MATH outperforms vanilla rejection tuning significantly, being superior or comparable to previous arts, despite using much smaller datasets and no proprietary models. Furthermore, our results position our synthetic datasets as the most effective and cost-efficient publicly available resources for advancing mathematical problem-solving.

We introduce KnowledgeMath, a novel benchmark designed to evaluate LLMs' capabilities in applying financial knowledge to solve complex math word problems. Compared to prior works, this study features three core advancements. First, KnowledgeMath includes 1,259 problems with a hybrid of textual and tabular content and require college-level knowledge in the finance domain for effective resolution. Second, we provide expert-annotated, detailed solution references in Python program format, ensuring a high-quality benchmark for LLM assessment. Finally, we evaluate a wide spectrum of 14 LLMs with different prompting strategies like Chain-of-Thoughts and Program-of-Thoughts. The current best-performing system (i.e., GPT-4 with Program-of-Thoughts) achieves only 45.4% accuracy, leaving substantial room for improvement. While knowledge-augmented LLMs can improve the performance (e.g., from 23.9% to 32.0% for GPT-3.5), it is still significantly lower the estimated human expert performance of 94%. We believe that KnowledgeMath can facilitate future research on domain-specific knowledge retrieval and augmentation into the math word problem-solving process. We will release the benchmark and code at https://github.com/yale-nlp/KnowledgeMath.

Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the grounded math logic. To address this issue and make a step towards interpretable MWP solving, we first construct a high-quality MWP dataset named InterMWP which consists of 11,495 MWPs and annotates interpretable logical formulas based on algebraic knowledge as the grounded linguistic logic of each solution equation. Different from existing MWP datasets, our InterMWP benchmark asks for a solver to not only output the solution expressions but also predict the corresponding logical formulas. We further propose a novel approach with logical prompt and interpretation generation, called LogicSolver. For each MWP, our LogicSolver first retrieves some highly-correlated algebraic knowledge and then passes them to the backbone model as prompts to improve the semantic representations of MWPs. With these improved semantic representations, our LogicSolver generates corresponding solution expressions and interpretable knowledge formulas in accord with the generated solution expressions, simultaneously. Experimental results show that our LogicSolver has stronger logical formula-based interpretability than baselines while achieving higher answer accuracy with the help of logical prompts, simultaneously. The source code and dataset is available at https://github.com/yangzhch6/InterMWP.

Fine-tuning language models~(LMs) on human-generated data remains a prevalent practice. However, the performance of such models is often limited by the quantity and diversity of high-quality human data. In this paper, we explore whether we can go beyond human data on tasks where we have access to scalar feedback, for example, on math problems where one can verify correctness. To do so, we investigate a simple self-training method based on expectation-maximization, which we call ReST^{EM}, where we (1) generate samples from the model and filter them using binary feedback, (2) fine-tune the model on these samples, and (3) repeat this process a few times. Testing on advanced MATH reasoning and APPS coding benchmarks using PaLM-2 models, we find that ReST^{EM} scales favorably with model size and significantly surpasses fine-tuning only on human data. Overall, our findings suggest self-training with feedback can substantially reduce dependence on human-generated data.

Large Language Models (LLMs) have made significant strides in code generation and problem solving. Current approaches employ external tool-based iterative debuggers that use compiler or other tool-based runtime feedback to refine coarse programs generated by various methods. However, the effectiveness of these approaches heavily relies on the quality of the initial code generation, which remains an open challenge. In this paper, we introduce CodeSim, a novel multi-agent code generation framework that comprehensively addresses the stages of program synthesis-planning, coding, and debugging-through a human-like perception approach. As human verifies their understanding of any algorithms through visual simulation, CodeSim uniquely features a method of plan verification and internal debugging through the step-by-step simulation of input/output. Extensive experiments across seven challenging competitive problem-solving and program synthesis benchmarks demonstrate CodeSim's remarkable code generation capabilities. Our framework achieves new state-of-the-art (pass@1) results-(HumanEval 95.1%, MBPP 90.7%, APPS 22%, and CodeContests 29.1%). Furthermore, our method shows potential for even greater enhancement when cascaded with external debuggers. To facilitate further research and development in this area, we have open-sourced our framework in this link (https://kagnlp.github.io/codesim.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) have demonstrated remarkable performance across multiple tasks through in-context learning. For complex reasoning tasks that require step-by-step thinking, Chain-of-Thought (CoT) prompting has given impressive results, especially when combined with self-consistency. Nonetheless, some tasks remain particularly difficult for LLMs to solve. Tree of Thoughts (ToT) and Graph of Thoughts (GoT) emerged as alternatives, dividing the complex problem into paths of subproblems. In this paper, we propose Tree of Problems (ToP), a simpler version of ToT, which we hypothesise can work better for complex tasks that can be divided into identical subtasks. Our empirical results show that our approach outperforms ToT and GoT, and in addition performs better than CoT on complex reasoning tasks. All code for this paper is publicly available here: https://github.com/ArmelRandy/tree-of-problems.

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.

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

Code synthesis, which requires a deep understanding of complex natural language problem descriptions, generation of code instructions for complex algorithms and data structures, and the successful execution of comprehensive unit tests, presents a significant challenge. While large language models (LLMs) demonstrate impressive proficiency in natural language processing, their performance in code generation tasks remains limited. In this paper, we introduce a new approach to code generation tasks leveraging multi-agent prompting that uniquely replicates the full cycle of program synthesis as observed in human developers. Our framework, MapCoder, consists of four LLM agents specifically designed to emulate the stages of this cycle: recalling relevant examples, planning, code generation, and debugging. After conducting thorough experiments, with multiple LLM ablations and analyses across eight challenging competitive problem-solving and program synthesis benchmarks, MapCoder showcases remarkable code generation capabilities, achieving new state-of-the-art results (pass@1) on HumanEval (93.9%), MBPP (83.1%), APPS (22.0%), CodeContests (28.5%), and xCodeEval (45.3%). Moreover, our method consistently delivers superior performance across various programming languages and varying problem difficulties. We open-source our framework at https://github.com/Md-Ashraful-Pramanik/MapCoder.

Large Language Models (LLMs) have attained human-level accuracy on medical question-answer (QA) benchmarks. However, their limitations in navigating open-ended clinical scenarios have recently been shown, raising concerns about the robustness and generalizability of LLM reasoning across diverse, real-world medical tasks. To probe potential LLM failure modes in clinical problem-solving, we present the medical abstraction and reasoning corpus (M-ARC). M-ARC assesses clinical reasoning through scenarios designed to exploit the Einstellung effect -- the fixation of thought arising from prior experience, targeting LLM inductive biases toward inflexible pattern matching from their training data rather than engaging in flexible reasoning. We find that LLMs, including current state-of-the-art o1 and Gemini models, perform poorly compared to physicians on M-ARC, often demonstrating lack of commonsense medical reasoning and a propensity to hallucinate. In addition, uncertainty estimation analyses indicate that LLMs exhibit overconfidence in their answers, despite their limited accuracy. The failure modes revealed by M-ARC in LLM medical reasoning underscore the need to exercise caution when deploying these models in clinical settings.

Chain-of-Thought (CoT) plays a crucial role in reasoning for math problem solving. We conduct a comprehensive examination of methods for designing CoT, comparing conventional natural language CoT with various program CoTs, including the self-describing program, the comment-describing program, and the non-describing program. Furthermore, we investigate the impact of programming language on program CoTs, comparing Python and Wolfram Language. Through extensive experiments on GSM8K, MATHQA, and SVAMP, we find that program CoTs often have superior effectiveness in math problem solving. Notably, the best performing combination with 30B parameters beats GPT-3.5-turbo by a significant margin. The results show that self-describing program offers greater diversity and thus can generally achieve higher performance. We also find that Python is a better choice of language than Wolfram for program CoTs. The experimental results provide a valuable guideline for future CoT designs that take into account both programming language and coding style for further advancements. Our datasets and code are publicly available.

We introduce a large-scale dataset of math word problems and an interpretable neural math problem solver that learns to map problems to operation programs. Due to annotation challenges, current datasets in this domain have been either relatively small in scale or did not offer precise operational annotations over diverse problem types. We introduce a new representation language to model precise operation programs corresponding to each math problem that aim to improve both the performance and the interpretability of the learned models. Using this representation language, our new dataset, MathQA, significantly enhances the AQuA dataset with fully-specified operational programs. We additionally introduce a neural sequence-to-program model enhanced with automatic problem categorization. Our experiments show improvements over competitive baselines in our MathQA as well as the AQuA dataset. The results are still significantly lower than human performance indicating that the dataset poses new challenges for future research. Our dataset is available at: https://math-qa.github.io/math-QA/

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.

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.

In most current research, large language models (LLMs) are able to perform reasoning tasks by generating chains of thought through the guidance of specific prompts. However, there still exists a significant discrepancy between their capability in solving complex reasoning problems and that of humans. At present, most approaches focus on chains of thought (COT) and tool use, without considering the adoption and application of human cognitive frameworks. It is well-known that when confronting complex reasoning challenges, humans typically employ various cognitive abilities, and necessitate interaction with all aspects of tools, knowledge, and the external environment information to accomplish intricate tasks. This paper introduces a novel intelligent framework, referred to as OlaGPT. OlaGPT carefully studied a cognitive architecture framework, and propose to simulate certain aspects of human cognition. The framework involves approximating different cognitive modules, including attention, memory, reasoning, learning, and corresponding scheduling and decision-making mechanisms. Inspired by the active learning mechanism of human beings, it proposes a learning unit to record previous mistakes and expert opinions, and dynamically refer to them to strengthen their ability to solve similar problems. The paper also outlines common effective reasoning frameworks for human problem-solving and designs Chain-of-Thought (COT) templates accordingly. A comprehensive decision-making mechanism is also proposed to maximize model accuracy. The efficacy of OlaGPT has been stringently evaluated on multiple reasoning datasets, and the experimental outcomes reveal that OlaGPT surpasses state-of-the-art benchmarks, demonstrating its superior performance. Our implementation of OlaGPT is available on GitHub: https://github.com/oladata-team/OlaGPT.

Recent advancements in large language models (LLMs) have shown remarkable potential in various complex tasks requiring multi-step reasoning methods like tree search to explore diverse reasoning paths. However, existing methods often suffer from computational inefficiency and redundancy. First, they overlook the diversity of task difficulties, leading to unnecessarily extensive searches even for easy tasks. Second, they neglect the semantics of reasoning paths, resulting in redundant exploration of semantically identical paths. To address these limitations, we propose Semantic Exploration with Adaptive Gating (SEAG), a computationally efficient method. SEAG employs an adaptive gating mechanism that dynamically decides whether to conduct a tree search, based on the confidence level of answers from a preceding simple reasoning method. Furthermore, its tree-based exploration consolidates semantically identical reasoning steps, reducing redundant explorations while maintaining or even improving accuracy. Our extensive experiments demonstrate that SEAG significantly improves accuracy by 4.3% on average while requiring only 31% of computational costs compared to existing tree search-based methods on complex reasoning benchmarks including GSM8K and ARC with diverse language models such as Llama2, Llama3, and Mistral.

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...

This paper presents GPSM4K, a comprehensive geometry multimodal dataset tailored to augment the problem-solving capabilities of Large Vision Language Models (LVLMs). GPSM4K encompasses 2157 multimodal question-answer pairs manually extracted from mathematics textbooks spanning grades 7-12 and is further augmented to 5340 problems, consisting of both numerical and theorem-proving questions. In contrast to PGPS9k, Geometry3K, and Geo170K which feature only objective-type questions, GPSM4K offers detailed step-by-step solutions in a consistent format, facilitating a comprehensive evaluation of problem-solving approaches. This dataset serves as an excellent benchmark for assessing the geometric reasoning capabilities of LVLMs. Evaluation of our test set shows that there is scope for improvement needed in open-source language models in geometry problem-solving. Finetuning on our training set increases the geometry problem-solving capabilities of models. Further, We also evaluate the effectiveness of techniques such as image captioning and Retrieval Augmentation generation (RAG) on model performance. We leveraged LLM to automate the task of final answer evaluation by providing ground truth and predicted solutions. This research will help to assess and improve the geometric reasoning capabilities of LVLMs.

Large Language Models (LLMs) have revolutionized Natural Language Processing but exhibit limitations, particularly in autonomously addressing novel challenges such as reasoning and problem-solving. Traditional techniques like chain-of-thought prompting necessitate explicit human guidance. This paper introduces a novel multi-agent communication framework, inspired by the CAMEL model, to enhance LLMs' autonomous problem-solving capabilities. The framework employs multiple LLM agents, each with a distinct persona, engaged in role-playing communication, offering a nuanced and adaptable approach to diverse problem scenarios. Extensive experimentation demonstrates the framework's superior performance and adaptability, providing valuable insights into the collaborative potential of multiple agents in overcoming the limitations of individual models.

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.

As language agents tackle increasingly complex tasks, they struggle with effective error correction and experience reuse across domains. We introduce Agent KB, a hierarchical experience framework that enables complex agentic problem solving via a novel Reason-Retrieve-Refine pipeline. Agent KB addresses a core limitation: agents traditionally cannot learn from each other's experiences. By capturing both high-level strategies and detailed execution logs, Agent KB creates a shared knowledge base that enables cross-agent knowledge transfer. Evaluated on the GAIA benchmark, Agent KB improves success rates by up to 16.28 percentage points. On the most challenging tasks, Claude-3 improves from 38.46% to 57.69%, while GPT-4 improves from 53.49% to 73.26% on intermediate tasks. On SWE-bench code repair, Agent KB enables Claude-3 to improve from 41.33% to 53.33%. Our results suggest that Agent KB provides a modular, framework-agnostic infrastructure for enabling agents to learn from past experiences and generalize successful strategies to new tasks.

The increasing adoption of artificial intelligence in telecommunications has raised interest in the capability of Large Language Models (LLMs) to address domain-specific, mathematically intensive tasks. Although recent advancements have improved the performance of LLMs in general mathematical reasoning, their effectiveness within specialized domains, such as signal processing, network optimization, and performance analysis, remains largely unexplored. To address this gap, we introduce TeleMath, the first benchmark dataset specifically designed to evaluate LLM performance in solving mathematical problems with numerical solutions in the telecommunications domain. Comprising 500 question-answer (QnA) pairs, TeleMath covers a wide spectrum of topics in the telecommunications field. This paper outlines the proposed QnAs generation pipeline, starting from a selected seed of problems crafted by Subject Matter Experts. The evaluation of a wide range of open-source LLMs reveals that best performance on TeleMath is achieved by recent models explicitly designed for mathematical or logical reasoning. In contrast, general-purpose models, even those with a large number of parameters, often struggle with these challenges. We have released the dataset and the evaluation code to ease result reproducibility and support future research.

Large language models have made significant progress in various language tasks, yet they still struggle with complex mathematics. In this paper, we propose ToRA a series of Tool-integrated Reasoning Agents designed to solve challenging mathematical problems by seamlessly integrating natural language reasoning with the utilization of external tools (e.g., computation libraries and symbolic solvers), thereby amalgamating the analytical prowess of language and the computational efficiency of tools. To train ToRA, we curate interactive tool-use trajectories on mathematical datasets, apply imitation learning on the annotations, and propose output space shaping to further refine models' reasoning behavior. As a result, ToRA models significantly outperform open-source models on 10 mathematical reasoning datasets across all scales with 13%-19% absolute improvements on average. Notably, ToRA-7B reaches 44.6% on the competition-level dataset MATH, surpassing the best open-source model WizardMath-70B by 22% absolute. ToRA-34B is also the first open-source model that achieves an accuracy exceeding 50% on MATH, which significantly outperforms GPT-4's CoT result, and is competitive with GPT-4 solving problems with programs. Additionally, we conduct a comprehensive analysis of the benefits and remaining challenges of tool interaction for mathematical reasoning, providing valuable insights for future research.

Recent advances in large language models (LLMs) have predominantly focused on maximizing accuracy and reasoning capabilities, often overlooking crucial computational efficiency considerations. While this approach has yielded impressive accuracy improvements, it has led to methods that may be impractical for real-world deployment due to computational overhead and latency constraints. This paper investigates the potential synergy between reasoning enhancement and computational efficiency by analyzing the integration of two contrasting approaches: Quiet-STaR (Self-Taught Reasoner) and REBASE (REward BAlanced SEarch). Through comprehensive empirical analysis using the Mistral-7B model on the GSM8K dataset, we demonstrate that while each method excels in its primary objective-Quiet-STaR achieving superior accuracy (32.03%) despite high computational cost (554.66s runtime, 12.73T FLOPs), and REBASE providing exceptional efficiency (8.47s runtime, 2.35T FLOPs) while maintaining baseline-comparable accuracy (10.94%)-their integration reveals fundamental challenges in reconciling reasoning depth with computational efficiency. The combined approach unexpectedly results in degraded performance (9.38% accuracy, 143.66s runtime), highlighting critical insights about the complex interplay between reasoning enhancement and efficiency optimization in LLMs. Our findings illuminate the need for novel architectures and algorithms specifically designed to bridge the gap between these competing objectives, while providing concrete directions for future research in compute-efficient reasoning methods.

The optimal training configurations of large language models (LLMs) with respect to model sizes and compute budgets have been extensively studied. But how to optimally configure LLMs during inference has not been explored in sufficient depth. We study compute-optimal inference: designing models and inference strategies that optimally trade off additional inference-time compute for improved performance. As a first step towards understanding and designing compute-optimal inference methods, we assessed the effectiveness and computational efficiency of multiple inference strategies such as Greedy Search, Majority Voting, Best-of-N, Weighted Voting, and their variants on two different Tree Search algorithms, involving different model sizes and computational budgets. We found that a smaller language model with a novel tree search algorithm typically achieves a Pareto-optimal trade-off. These results highlight the potential benefits of deploying smaller models equipped with more sophisticated decoding algorithms in budget-constrained scenarios, e.g., on end-devices, to enhance problem-solving accuracy. For instance, we show that the Llemma-7B model can achieve competitive accuracy to a Llemma-34B model on MATH500 while using 2times less FLOPs. Our findings could potentially apply to any generation task with a well-defined measure of success.

In this paper, we introduce Concise Chain-of-Thought (CCoT) prompting. We compared standard CoT and CCoT prompts to see how conciseness impacts response length and correct-answer accuracy. We evaluated this using GPT-3.5 and GPT-4 with a multiple-choice question-and-answer (MCQA) benchmark. CCoT reduced average response length by 48.70% for both GPT-3.5 and GPT-4 while having a negligible impact on problem-solving performance. However, on math problems, GPT-3.5 with CCoT incurs a performance penalty of 27.69%. Overall, CCoT leads to an average per-token cost reduction of 22.67%. These results have practical implications for AI systems engineers using LLMs to solve real-world problems with CoT prompt-engineering techniques. In addition, these results provide more general insight for AI researchers studying the emergent behavior of step-by-step reasoning in LLMs.

Large language models (LLMs) have demonstrated transformative potential across various domains, yet they face significant challenges in knowledge integration and complex problem reasoning, often leading to hallucinations and unreliable outputs. Retrieval-Augmented Generation (RAG) has emerged as a promising solution to enhance LLMs accuracy by incorporating external knowledge. However, traditional RAG systems struggle with processing complex relational information and multi-step reasoning, limiting their effectiveness in advanced problem-solving tasks. To address these limitations, we propose CogGRAG, a cognition inspired graph-based RAG framework, designed to improve LLMs performance in Knowledge Graph Question Answering (KGQA). Inspired by the human cognitive process of decomposing complex problems and performing self-verification, our framework introduces a three-stage methodology: decomposition, retrieval, and reasoning with self-verification. By integrating these components, CogGRAG enhances the accuracy of LLMs in complex problem solving. We conduct systematic experiments with three LLM backbones on four benchmark datasets, where CogGRAG outperforms the baselines.

Existing approaches to mathematical reasoning with large language models (LLMs) rely on Chain-of-Thought (CoT) for generalizability or Tool-Integrated Reasoning (TIR) for precise computation. While efforts have been made to combine these methods, they primarily rely on post-selection or predefined strategies, leaving an open question: whether LLMs can autonomously adapt their reasoning strategy based on their inherent capabilities. In this work, we propose TATA (Teaching LLMs According to Their Aptitude), an adaptive framework that enables LLMs to personalize their reasoning strategy spontaneously, aligning it with their intrinsic aptitude. TATA incorporates base-LLM-aware data selection during supervised fine-tuning (SFT) to tailor training data to the model's unique abilities. This approach equips LLMs to autonomously determine and apply the appropriate reasoning strategy at test time. We evaluate TATA through extensive experiments on six mathematical reasoning benchmarks, using both general-purpose and math-specialized LLMs. Empirical results demonstrate that TATA effectively combines the complementary strengths of CoT and TIR, achieving superior or comparable performance with improved inference efficiency compared to TIR alone. Further analysis underscores the critical role of aptitude-aware data selection in enabling LLMs to make effective and adaptive reasoning decisions and align reasoning strategies with model capabilities.

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, a algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions.

To enhance large language models (LLMs) for chemistry problem solving, several LLM-based agents augmented with tools have been proposed, such as ChemCrow and Coscientist. However, their evaluations are narrow in scope, leaving a large gap in understanding the benefits of tools across diverse chemistry tasks. To bridge this gap, we develop ChemAgent, an enhanced chemistry agent over ChemCrow, and conduct a comprehensive evaluation of its performance on both specialized chemistry tasks and general chemistry questions. Surprisingly, ChemAgent does not consistently outperform its base LLMs without tools. Our error analysis with a chemistry expert suggests that: For specialized chemistry tasks, such as synthesis prediction, we should augment agents with specialized tools; however, for general chemistry questions like those in exams, agents' ability to reason correctly with chemistry knowledge matters more, and tool augmentation does not always help.

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.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Although pre-trained language models~(PLMs) have recently advanced the research progress in mathematical reasoning, they are not specially designed as a capable multi-task solver, suffering from high cost for multi-task deployment (\eg a model copy for a task) and inferior performance on complex mathematical problems in practical applications. To address these issues, in this paper, we propose JiuZhang~2.0, a unified Chinese PLM specially for multi-task mathematical problem solving. Our idea is to maintain a moderate-sized model and employ the cross-task knowledge sharing to improve the model capacity in a multi-task setting. Specially, we construct a Mixture-of-Experts~(MoE) architecture for modeling mathematical text, so as to capture the common mathematical knowledge across tasks. For optimizing the MoE architecture, we design multi-task continual pre-training and multi-task fine-tuning strategies for multi-task adaptation. These training strategies can effectively decompose the knowledge from the task data and establish the cross-task sharing via expert networks. In order to further improve the general capacity of solving different complex tasks, we leverage large language models~(LLMs) as complementary models to iteratively refine the generated solution by our PLM, via in-context learning. Extensive experiments have demonstrated the effectiveness of our model.

Recent agent frameworks and inference-time algorithms often struggle with complex planning problems due to limitations in verifying generated plans or reasoning and varying complexity of instances within a single task. Many existing methods for these tasks either perform task-level verification without considering constraints or apply inference-time algorithms without adapting to instance-level complexity. To address these limitations, we propose PlanGEN, a model-agnostic and easily scalable agent framework with three key components: constraint, verification, and selection agents. Specifically, our approach proposes constraint-guided iterative verification to enhance performance of inference-time algorithms--Best of N, Tree-of-Thought, and REBASE. In PlanGEN framework, the selection agent optimizes algorithm choice based on instance complexity, ensuring better adaptability to complex planning problems. Experimental results demonstrate significant improvements over the strongest baseline across multiple benchmarks, achieving state-of-the-art results on NATURAL PLAN (sim8%uparrow), OlympiadBench (sim4%uparrow), DocFinQA (sim7%uparrow), and GPQA (sim1%uparrow). Our key finding highlights that constraint-guided iterative verification improves inference-time algorithms, and adaptive selection further boosts performance on complex planning and reasoning problems.

The performance of large language models (LLMs) on existing reasoning benchmarks has significantly improved over the past years. In response, we present JEEBench, a considerably more challenging benchmark dataset for evaluating the problem solving abilities of LLMs. We curate 515 challenging pre-engineering mathematics, physics and chemistry problems from the highly competitive IIT JEE-Advanced exam. Long-horizon reasoning on top of deep in-domain knowledge is essential for solving problems in this benchmark. Our evaluation on various open-source and proprietary models reveals that the highest performance, even after using techniques like self-consistency, self-refinement and chain-of-thought prompting, is less than 40%. The typical failure modes of GPT-4, the best model, are errors in algebraic manipulation, difficulty in grounding abstract concepts into mathematical equations accurately and failure in retrieving relevant domain-specific concepts. We also observe that by mere prompting, GPT-4 is unable to assess risk introduced by negative marking for incorrect answers. For this, we develop a post-hoc confidence-thresholding method over self-consistency, which enables effective response selection. We hope that our challenging benchmark will guide future re-search in problem-solving using LLMs.

We present the Process Engineering Operations Assistant (PEOA), an AI-driven framework designed to solve complex problems in the chemical and process industries. The framework employs a modular architecture orchestrated by a meta-agent, which serves as the central coordinator, managing an action generator and instruction-tuned small-scale language models (expert models). The action generator decomposes complex problems into sub-tasks and identifies suitable expert models to execute each, delivering precise solutions for multi-step problem-solving. Key techniques include advanced knowledge modeling using property graphs for improved information retrieval, facilitating more accurate and contextually relevant solutions. Additionally, the framework utilizes a teacher-student transfer-learning approach with GPT-4 (Omni) to fine-tune the action generator and expert models for domain adaptation, alongside an iterative problem-solving mechanism with sophisticated error handling. Custom datasets were developed to evaluate the framework against leading proprietary language models on various engineering tasks. The results demonstrate the framework effectiveness in automating calculations, accelerating prototyping, and providing AI-augmented decision support for industrial processes, marking a significant advancement in process engineering capabilities.

Scaling test-time compute has emerged as a key strategy for enhancing the reasoning capabilities of large language models (LLMs), particularly in tasks like mathematical problem-solving. A traditional approach, Self-Consistency (SC), generates multiple solutions to a problem and selects the most common answer via majority voting. Another common method involves scoring each solution with a reward model (verifier) and choosing the best one. Recent advancements in Generative Reward Models (GenRM) reframe verification as a next-token prediction task, enabling inference-time scaling along a new axis. Specifically, GenRM generates multiple verification chains-of-thought to score each solution. Under a limited inference budget, this introduces a fundamental trade-off: should you spend the budget on scaling solutions via SC or generate fewer solutions and allocate compute to verification via GenRM? To address this, we evaluate GenRM against SC under a fixed inference budget. Interestingly, we find that SC is more compute-efficient than GenRM for most practical inference budgets across diverse models and datasets. For instance, GenRM first matches SC after consuming up to 8x the inference compute and requires significantly more compute to outperform it. Furthermore, we derive inference scaling laws for the GenRM paradigm, revealing that compute-optimal inference favors scaling solution generation more aggressively than scaling the number of verifications. Our work provides practical guidance on optimizing test-time scaling by balancing solution generation and verification. The code is available at https://github.com/nishadsinghi/sc-genrm-scaling.

Multimodal scientific problems (MSPs) involve complex issues that require the integration of multiple modalities, such as text and diagrams, presenting a significant challenge in artificial intelligence. While progress has been made in addressing traditional scientific problems, MSPs still face two primary issues: the challenge of multi-modal comprehensive reasoning in scientific problem-solving and the lack of reflective and rethinking capabilities. To address these issues, we introduce a Multi-Agent framework based on the Big Seven Personality and Socratic guidance (MAPS). This framework employs seven distinct agents that leverage feedback mechanisms and the Socratic method to guide the resolution of MSPs. To tackle the first issue, we propose a progressive four-agent solving strategy, where each agent focuses on a specific stage of the problem-solving process. For the second issue, we introduce a Critic agent, inspired by Socratic questioning, which prompts critical thinking and stimulates autonomous learning. We conduct extensive experiments on the EMMA, Olympiad, and MathVista datasets, achieving promising results that outperform the current SOTA model by 15.84% across all tasks. Meanwhile, the additional analytical experiments also verify the model's progress as well as generalization ability.