MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?
Introduced MathVerse, a multi-version benchmark with chain-of-thought analysis, revealing most models rely heavily on text rather than visual understanding in math problems.
Key Findings
Methodology
By collecting 2,612 high-quality multi-subject math problems and creating six versions per problem, the study systematically reduces textual content and emphasizes visual features. A novel chain-of-thought (CoT) evaluation using GPT-4(V) extracts reasoning steps, enabling detailed error analysis at each stage. Experiments on both closed- and open-source models compare performance across versions, highlighting the reliance on textual cues and deficiencies in visual encoding. The approach combines dataset design, multi-version transformations, and advanced reasoning analysis to assess true visual understanding in multi-modal models.
Key Results
- Most models perform well on text-rich versions but show significant accuracy drops when visual content is emphasized, with some models outperforming their text-only results by over 5%, indicating reliance on textual shortcuts. GPT-4V demonstrates superior visual comprehension, yet still struggles with spatial relations. Chain-of-thought analysis reveals that models often make intermediate errors in understanding geometric and numerical relationships, underscoring visual encoding bottlenecks.
- Across disciplines—geometry, functions, and solid geometry—models tend to depend heavily on textual clues, with limited gains from visual enhancements. The performance gap suggests current models lack robust visual reasoning capabilities. The multi-version design effectively isolates visual understanding, providing a nuanced view of model strengths and weaknesses.
- The chain-of-thought scoring strategy offers fine-grained insights into reasoning quality, identifying specific steps where models falter, such as spatial reasoning or numerical recognition. Results emphasize that improving visual encoding is critical for advancing multi-modal mathematical reasoning, guiding future research directions.
Significance
This work systematically exposes the gap between current multi-modal models and genuine visual understanding in mathematical reasoning. By employing multi-version datasets and detailed stepwise analysis, it offers a comprehensive framework for evaluating and improving models’ visual encoding capacities. The findings have broad implications for AI in education, scientific computing, and reasoning tasks, pushing the field toward models that truly comprehend visual information rather than relying on textual shortcuts. It addresses a fundamental challenge: enabling AI to interpret complex diagrams accurately, which is essential for real-world applications requiring spatial and numerical reasoning.
Technical Contribution
The study introduces a multi-version dataset with controlled textual content, combined with a novel chain-of-thought evaluation framework leveraging GPT-4(V). This approach allows for detailed step-by-step error analysis, revealing specific weaknesses in visual encoding. The dataset spans multiple math disciplines and problem types, providing a comprehensive benchmark. Unlike prior works that focus solely on final accuracy, this method emphasizes the reasoning process, offering insights into how models interpret visual information and where they fail, thus advancing the state-of-the-art in multi-modal reasoning evaluation.
Novelty
This is the first comprehensive attempt to systematically evaluate multi-modal models’ visual understanding in math through multi-version problem sets coupled with chain-of-thought analysis. The innovative use of GPT-4(V) for extracting and scoring reasoning steps provides a new level of interpretability and diagnostic capability. Unlike previous benchmarks that mainly measure end accuracy, this work emphasizes the reasoning process, making it a significant step forward in understanding and improving visual reasoning in AI.
Limitations
- Models still struggle with complex spatial relationships and high-level geometric reasoning, indicating that visual encoding remains a bottleneck. The dataset, while diverse, focuses on high school-level problems, limiting insights into advanced mathematical reasoning.
- The reliance on GPT-4(V) for reasoning extraction may introduce bias, and the evaluation framework could be complemented with other models for robustness. Computational costs of large models and detailed analysis are also considerations.
- Future work should explore richer datasets, more sophisticated visual encoders, and explainability techniques to further close the gap in visual understanding.
Future Work
Future directions include expanding dataset diversity to cover more advanced topics, integrating multimodal pretraining strategies to enhance visual encoding, and developing explainability methods for reasoning steps. Additionally, creating models that can dynamically adapt their reliance on visual versus textual cues will be crucial. Cross-modal training and multi-task learning could further improve the robustness of visual understanding. Ultimately, the goal is to develop AI systems capable of human-like spatial and numerical reasoning, applicable in scientific research, education, and real-world problem-solving.
AI Executive Summary
The rapid advancement of multi-modal large language models (MLLMs) has opened new horizons in AI's ability to interpret complex visual information. However, their application in mathematical reasoning, especially involving diagrams, remains underexplored and often overestimated due to evaluation biases. Existing benchmarks tend to include redundant textual descriptions that models exploit, masking their true visual understanding capabilities. To address this, the authors introduce MathVerse, a comprehensive benchmark that systematically reduces textual cues across six versions per problem, emphasizing visual content. This design enables a more genuine assessment of whether models can interpret diagrams for mathematical reasoning.
A key innovation is the integration of a chain-of-thought (CoT) evaluation strategy powered by GPT-4(V), which extracts critical reasoning steps and performs detailed error analysis. This approach provides insights into the intermediate reasoning quality, revealing that most models heavily depend on textual clues and lack robust visual encoding. Experiments across multiple models, including GPT-4V, Qwen-VL-Max, and InternLM-XComposer2, demonstrate that models often perform worse when visual content is emphasized, highlighting a significant bottleneck in visual understanding. Interestingly, some models even outperform their text-only versions, indicating reliance on superficial cues rather than genuine comprehension.
The findings underscore the importance of developing models with stronger visual encoding capabilities, especially for applications requiring spatial and numerical reasoning. The comprehensive dataset and evaluation framework set a new standard for assessing multi-modal mathematical understanding. Future work will focus on expanding dataset scope, improving visual encoders, and integrating explainability techniques to foster models that truly see and reason about diagrams, ultimately bridging the gap between AI and human-level visual reasoning in mathematics.
Deep Dive
Abstract
The remarkable progress of Multi-modal Large Language Models (MLLMs) has garnered unparalleled attention, due to their superior performance in visual contexts. However, their capabilities in visual math problem-solving remain insufficiently evaluated and understood. We investigate current benchmarks to incorporate excessive visual content within textual questions, which potentially assist MLLMs in deducing answers without truly interpreting the input diagrams. To this end, we introduce MathVerse, an all-around visual math benchmark designed for an equitable and in-depth evaluation of MLLMs. We meticulously collect 2,612 high-quality, multi-subject math problems with diagrams from publicly available sources. Each problem is then transformed by human annotators into six distinct versions, each offering varying degrees of information content in multi-modality, contributing to 15K test samples in total. This approach allows MathVerse to comprehensively assess whether and how much MLLMs can truly understand the visual diagrams for mathematical reasoning. In addition, we propose a Chain-of-Thought (CoT) evaluation strategy for a fine-grained assessment of the output answers. Rather than naively judging True or False, we employ GPT-4(V) to adaptively extract crucial reasoning steps, and then score each step with detailed error analysis, which can reveal the intermediate CoT reasoning quality by MLLMs. We hope the MathVerse benchmark may provide unique insights to guide the future development of MLLMs. Project page: https://mathverse-cuhk.github.io