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arxiv: 2403.14624 · v2 · submitted 2024-03-21 · 💻 cs.CV · cs.AI· cs.CL· cs.LG

Recognition: 2 theorem links

MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?

Renrui Zhang , Dongzhi Jiang , Yichi Zhang , Haokun Lin , Ziyu Guo , Pengshuo Qiu , Aojun Zhou , Pan Lu
show 3 more authors
Kai-Wei Chang Peng Gao Hongsheng Li
Authors on Pith no claims yet

Pith reviewed 2026-05-17 01:22 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.CLcs.LG
keywords multi-modal LLMsvisual math problemsdiagram understandingbenchmark evaluationchain-of-thought reasoningmathematical reasoning
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The pith

MathVerse shows multi-modal LLMs often solve visual math problems using text rather than diagrams.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper argues that existing visual math benchmarks give away too much information in the text, allowing multi-modal LLMs to answer correctly without understanding the diagrams. To fix this, it presents MathVerse, built from 2,612 real math problems that human annotators rewrite into six versions each with different levels of visual and textual detail. This creates a scale from fully supported text to diagram-only cases so that performance drops can be attributed to lack of visual understanding. A new evaluation method scores the quality of reasoning steps in the model's chain of thought instead of just checking the final answer. Readers should care because it offers a clearer way to measure and improve how well these models handle combined visual and mathematical information.

Core claim

MathVerse collects 2,612 high-quality math problems with diagrams from public sources and transforms each into six versions with varying multi-modal information content for a total of 15K samples. This design enables an equitable evaluation of whether MLLMs truly understand visual diagrams when solving math problems. The benchmark further includes a Chain-of-Thought evaluation strategy that uses GPT-4(V) to extract key reasoning steps and provide detailed error analysis on intermediate outputs.

What carries the argument

The multi-version problem transformation that systematically varies the amount of textual information provided alongside the diagram to measure reliance on visual input.

Load-bearing premise

The six versions of each problem preserve the original mathematical intent and difficulty while only changing the distribution of information between text and diagram.

What would settle it

If MLLM accuracy remains consistent even on the versions with the least textual information and greatest dependence on the diagram, the benchmark would fail to show that models need to interpret visuals.

read the original 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

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that existing visual math benchmarks embed excessive textual information in questions, enabling MLLMs to deduce answers without genuinely interpreting diagrams. To enable equitable evaluation, the authors collect 2,612 high-quality multi-subject math problems with diagrams from public sources and have human annotators transform each into six versions that vary the amount of multi-modal information (textual vs. visual), yielding 15K test samples total. They further propose a Chain-of-Thought evaluation that uses GPT-4(V) to extract key reasoning steps and score them with error analysis rather than binary correctness.

Significance. If the version transformations are shown to preserve mathematical semantics and difficulty, MathVerse would provide a valuable, fine-grained benchmark for isolating and measuring visual diagram understanding in MLLMs. The multi-version design and step-level GPT-4 scoring could become a standard protocol for diagnosing whether models truly integrate visual and textual cues in mathematical reasoning, directly informing future architecture and training improvements.

major comments (2)
  1. [§3.2] §3.2 (Human Annotation and Version Transformation): The manuscript describes the process of transforming each problem into six versions with differing textual/visual content but reports no quantitative validation—such as inter-annotator agreement scores, expert equivalence ratings, or solve-rate consistency on a held-out set—to confirm that core problem semantics, difficulty, and mathematical equivalence are preserved. Without these checks, performance gaps across versions could reflect annotation artifacts rather than genuine differences in visual understanding.
  2. [§4.3] §4.3 (CoT Evaluation with GPT-4(V)): The adaptive step-extraction and scoring procedure is presented as enabling fine-grained assessment, yet the paper provides insufficient detail on prompt templates, exact scoring rubrics, or any human-GPT agreement study. This weakens the claim that the method reliably reveals intermediate reasoning quality, as GPT-4(V) errors could systematically bias the reported insights.
minor comments (2)
  1. [§3.1] The selection criteria and filtering steps used to arrive at the final 2,612 problems from public sources are only briefly summarized; a table or paragraph detailing subject distribution, diagram complexity, and exclusion reasons would improve reproducibility.
  2. In the example figures illustrating the six versions, the visual differences between versions could be highlighted with explicit callouts or color coding to make the information-content gradient immediately clear to readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights key areas for strengthening the validation and transparency of MathVerse. We address each major comment below and will incorporate the necessary additions in the revised manuscript.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (Human Annotation and Version Transformation): The manuscript describes the process of transforming each problem into six versions with differing textual/visual content but reports no quantitative validation—such as inter-annotator agreement scores, expert equivalence ratings, or solve-rate consistency on a held-out set—to confirm that core problem semantics, difficulty, and mathematical equivalence are preserved. Without these checks, performance gaps across versions could reflect annotation artifacts rather than genuine differences in visual understanding.

    Authors: We agree that quantitative validation would strengthen confidence in the version transformations. The manuscript details the annotation guidelines and process used by human annotators to derive the six versions through controlled, incremental removal of textual or visual information while aiming to preserve mathematical semantics and difficulty. However, we did not report inter-annotator agreement or equivalence metrics. In the revision, we will add inter-annotator agreement scores on a multi-annotated subset, expert equivalence ratings, and solve-rate consistency analysis on a held-out set to empirically confirm preservation of core problem properties. revision: yes

  2. Referee: [§4.3] §4.3 (CoT Evaluation with GPT-4(V)): The adaptive step-extraction and scoring procedure is presented as enabling fine-grained assessment, yet the paper provides insufficient detail on prompt templates, exact scoring rubrics, or any human-GPT agreement study. This weakens the claim that the method reliably reveals intermediate reasoning quality, as GPT-4(V) errors could systematically bias the reported insights.

    Authors: We concur that greater detail on the evaluation procedure is warranted to support its reliability. The manuscript describes the adaptive use of GPT-4(V) for step extraction and error-annotated scoring as an alternative to binary correctness. In the revised version, we will include the full prompt templates, the precise scoring rubrics with error categories, and a human-GPT agreement study on a sampled set of responses to quantify alignment and address potential biases in the automated assessment. revision: yes

Circularity Check

0 steps flagged

No circularity: benchmark construction is externally grounded

full rationale

The paper collects 2,612 math problems from publicly available sources and applies explicit human annotation to produce six modality variants, yielding 15K samples. No equations, fitted parameters, or model predictions are defined; the evaluation strategy (CoT extraction via GPT-4(V)) operates on external test samples rather than quantities derived from the paper's own outputs. The central claim—that performance differences isolate visual understanding—rests on the annotation process itself, which is described as an independent construction step without self-referential reduction or load-bearing self-citations. The derivation chain is therefore self-contained against external benchmarks and sources.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The benchmark rests on the assumption that human annotators can reliably create information-controlled variants without altering core mathematical content or introducing unintended cues. No free parameters or invented entities are introduced.

axioms (2)
  • domain assumption Human annotators can produce six versions of each problem that differ only in the amount of visual versus textual information while preserving mathematical equivalence.
    Invoked in the description of transforming each of the 2,612 problems into six distinct versions.
  • domain assumption GPT-4(V) can accurately extract and score individual reasoning steps from MLLM outputs for error analysis.
    Used in the proposed Chain-of-Thought evaluation strategy.

pith-pipeline@v0.9.0 · 5608 in / 1409 out tokens · 33382 ms · 2026-05-17T01:22:47.288047+00:00 · methodology

discussion (0)

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