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Oct 29

GeoSense: Evaluating Identification and Application of Geometric Principles in Multimodal Reasoning

Geometry problem-solving (GPS), a challenging task requiring both visual comprehension and symbolic reasoning, effectively measures the reasoning capabilities of multimodal large language models (MLLMs). Humans exhibit strong reasoning ability in this task through accurate identification and adaptive application of geometric principles within visual contexts. However, existing benchmarks fail to jointly assess both dimensions of the human-like geometric reasoning mechanism in MLLMs, remaining a critical gap in assessing their ability to tackle GPS. To this end, we introduce GeoSense, the first comprehensive bilingual benchmark designed to systematically evaluate the geometric reasoning abilities of MLLMs through the lens of geometric principles. GeoSense features a five-level hierarchical framework of geometric principles spanning plane and solid geometry, an intricately annotated dataset of 1,789 problems, and an innovative evaluation strategy. Through extensive experiments on GeoSense with various open-source and closed-source MLLMs, we observe that Gemini-2.0-pro-flash performs best, achieving an overall score of 65.3. Our in-depth analysis reveals that the identification and application of geometric principles remain a bottleneck for leading MLLMs, jointly hindering their reasoning abilities. These findings underscore GeoSense's potential to guide future advancements in MLLMs' geometric reasoning capabilities, paving the way for more robust and human-like reasoning in artificial intelligence.

  • 12 authors
·
Apr 16

MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning

Tool-augmented Large Language Models (TALM) are known to enhance the skillset of large language models (LLM), thereby, leading to their improved reasoning abilities across many tasks. While, TALMs have been successfully employed in different question-answering benchmarks, their efficacy on complex mathematical reasoning benchmarks, and the potential complimentary benefits offered by tools for knowledge retrieval and mathematical equation solving, are open research questions. In this work, we present MATHSENSEI, a tool-augmented large language model for mathematical reasoning. Augmented with tools for knowledge retrieval (Bing Web Search), program execution (Python), and symbolic equation solving (Wolfram-Alpha), we study the complimentary benefits of these tools through evaluations on mathematical reasoning datasets. We perform exhaustive ablations on MATH,a popular dataset for evaluating mathematical reasoning on diverse mathematical disciplines. We also conduct experiments involving well-known tool planners to study the impact of tool sequencing on the model performance. MATHSENSEI achieves 13.5% better accuracy over gpt-3.5-turbo with chain-of-thought on the MATH dataset. We further observe that TALMs are not as effective for simpler math word problems (in GSM-8k), and the benefit increases as the complexity and required knowledge increases (progressively over AQuA, MMLU-Math, and higher level complex questions in MATH). The code and data are available at https://github.com/Debrup-61/MathSensei.

  • 4 authors
·
Feb 27, 2024