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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<meta name="description"
content="A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models">
<meta name="keywords" content="DynaMath, Dyna Math">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title> DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models</title>
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</head>
<body>
<section class="hero">
<div class="hero-body">
<div class="container is-max-desktop">
<div class="columns is-centered">
<div class="column has-text-centered">
<h1 class="title is-1 publication-title is-bold">
<img src="static/images/dyna-logo.png" style="width:1em;vertical-align: middle; width:60px; height:auto;" alt="Logo" />
<span class="dynamath" style="vertical-align: middle">DynaMath</span>
</h1>
<h2 class="subtitle is-3 publication-subtitle" style="vertical-align: middle; font-size: 2.2rem;">
A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models
<!-- <br> -->
<!-- with GPT-4V, Bard, and Other Large Multimodal Models -->
</h2>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://www.linkedin.com/in/chengke-zou-023b49294/">Chengke Zou</a><sup style="color:#050300;">*,</sup><sup style="color:#ffac33;">1,</sup><sup style="color:#6fbf73;">2</sup>,</span>
<span class="author-block">
<a href="https://sites.google.com/view/guoxingang">Xingang Guo</a><sup style="color:#050300;">*,</sup><sup style="color:#ffac33;">1</sup>,</span>
<span class="author-block">
<a href="https://yangrui2015.github.io/">Rui Yang</a><sup style="color:#050300;">*,</sup><sup style="color:#ffac33;">1</sup>,
</span>
<span class="author-block">
<a href="https://jyzhang1208.github.io/">Junyu Zhang</a><sup style="color:#ffac33">1</sup>,
</span>
<span class="author-block">
<a href="https://binhu7.github.io/">Bin Hu</a><sup style="color:#ffac33">1</sup>,
</span>
<span class="author-block">
<a href="https://huan-zhang.com/">Huan Zhang</a><sup style="color:#ffac33">1</sup>
</span>
</div>
<div class="is-size-5 publication-authors">
<span class="author-block"><sup style="color:#ffac33">1</sup>University of Illinois at Urbana-Champaign</span><br>
<!-- <span class="author-block"><sup style="color:#ed4b82">2</sup>University of Washington,</span> -->
<span class="author-block"><sup style="color:#6fbf73;">2</sup>University of California, Berkeley</span><br>
<!-- <span class="paper-block"><b style="color:#f41c1c">ICLR 2024 Oral</b> (85 in 7304, 1.2%)</span> -->
</div>
<div class="is-size-5 publication-authors">
<span class="author-block"><sup>*</sup>Equal contribution</span>
</div>
<div class="is-size-5 publication-authors">
<span class="author-block" style="color:rgb(192, 54, 54);"><b>ICLR 2025</b></span>
</div>
<div class="column has-text-centered">
<div class="publication-links">
<span class="link-block">
<a href="https://arxiv.org/pdf/2411.00836"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="ai ai-arxiv"></i>
</span>
<!-- <span>arXiv</span> -->
<span>Paper</span>
</a>
</span>
<!-- Code Link. -->
<span class="link-block">
<a href="https://github.com/DynaMath/DynaMath"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="fab fa-github"></i>
</span>
<span>Code</span>
</a>
</span>
<!-- Dataset Link. -->
<span class="link-block">
<a href="https://huggingface.co/datasets/DynaMath/DynaMath_Sample"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<!-- <i class="far fa-images"></i> -->
<p style="font-size:18px">🤗</p>
<!-- 🔗 -->
</span>
<span>Dataset</span>
</a>
</span>
</a>
</span>
</div>
</div>
</div>
</div>
</div>
</div>
</section>
<section class="section">
<div class="container" style="margin-top: -150px; margin-bottom: -100px;">
<div class="columns is-centered m-6">
<div class="column is-full has-text-centered content">
<!-- <div id="results-carousel" class="carousel results-carousel"> -->
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/memory-error.png" alt="Q78-variants" width="85%"/>
<p style="font-size: 1.1rem; text-align:center; margin: 0 auto; max-width: 85%;">
This example demonstrates that Claude 3.5 Sonnet does not exhibit consistent performance for different variants of a math question accompanied by visual input.
</p>
</div>
<!-- </div> -->
<!-- <div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/Q169-variants.png" alt="Q169-variants" width="90%"/> -->
<!-- <p> Accuracy scores of one leading LLM (i.e., PoT GPT-4), four primary LMMs, random chance, and human performance our proposed
<img src="static/images/mathvista.png" style="width:1.0em;vertical-align: middle" alt="Logo"/>
<span class="mathvista">MathVista</span>
across mathematical reasoning and visual context types. PoT refers to program-of-thought prompting, and PoT GPT-4 is a textual LLM augmented with the caption and OCR text. GPT-4V is manually evaluated via the playground chatbot.
</p> -->
<!-- </div>
</div> -->
</div>
</div>
</div>
</section>
<section class="section">
<div class="container" style="margin-bottom: 2vh;">
<!-- Abstract. -->
<div class="columns is-centered has-text-centered">
<div class="column is-four-fifths">
<h2 class="title is-3" style="font-size: 2.3rem;">Introduction</h2>
<div class="content has-text-justified" style="font-size: 1.2rem;">
<p>
The rapid advancements in Vision-Language Models (VLMs) have shown great potential in tackling mathematical reasoning tasks that involve visual context. Unlike humans who can reliably apply solution steps to similar problems with minor modifications, we found that state-of-the-art VLMs like GPT-4o can consistently fail in these scenarios, revealing limitations in their mathematical reasoning capabilities.
In this paper, we investigate the <b>mathematical reasoning robustness</b> in VLMs and evaluate how well these models perform under different variants of the same question, such as changes in visual numerical values or function graphs.
We introduce <span class="dynamath">DynaMath</span>, a dynamic visual math benchmark designed for in-depth assessment of VLMs. <span class="dynamath">DynaMath</span> includes 501 high-quality, multi-topic <i>seed</i> questions, <i>each represented as</i> <i>a Python program</i>.
Those programs are carefully designed and annotated to enable the automatic generation of a much larger set of concrete questions, including many different types of visual and textual variations.
<span class="dynamath">DynaMath</span> allows us to evaluate the generalization ability of VLMs, by assessing their performance under varying input conditions of a seed question.
</p>
</div>
</div>
</div>
<!--/ Abstract. -->
</div>
</section>
<!-- DATASET SECTION -->
<section class="hero is-light is-small">
<div class="hero-body has-text-centered">
<!-- <h1 class="title is-1 mathvista"><img src="static/images/mathvista.png" style="width:1.0em;vertical-align: middle" alt="Logo"/>MathVista Dataset</h1> -->
<h1 class="title is-1 dynamath">
<!-- <img src="static/images/mathvista.png" style="width:1em;vertical-align: middle" alt="Logo"/> -->
<span class="dynamath" style="vertical-align: middle">DynaMath Dataset</span>
</h1>
</div>
</section>
<section class="section">
<div class="container">
<div class="columns is-centered has-text-centered">
<!-- <div class="column is-full-width has-text-centered"> -->
<div class="column is-four-fifths">
<h2 class="title is-3" style="font-size: 2.3rem;">Overview</h2>
<div class="content has-text-justified" style="font-size: 1.2rem;">
<p>
<!-- <img src="static/images/mathvista.png" style="width:1.0em;vertical-align: middle" alt="Logo"/> -->
We present <span class="dynamath">DynaMath</span>, a curated evaluation dataset aimed at assessing the robustness of visual language models (VLMs) in multimodal mathematical reasoning across a wide variety of mathematical tasks with dynamic visual and textual contexts.
Our benchmark consists of 501 seed questions, each represented as a Python program. There are 227 (45.3%) sourced from established visual math datasets, while 274 (54.7%) are newly collected or developed from public resources.
For each seed question in the dataset, we generate M = 10 variants, resulting in a total of 5, 010 concrete questions.
</p>
<div class="columns is-centered">
<div class="column is-full has-text-centered content">
<div class="columns is-centered" style="width: 100%; text-align: center; margin: 0 auto;">
<div class="column is-centered" style="width: 105%; margin-right: -5rem; margin-top: 1rem;">
<div class="content has-text-centered" style="margin-top: 10px; margin-bottom: 10px;">
<img src="static/images/statistics.png" alt="data-overview" style="max-width: 100%;"/>
<p>
Key statistics of
<span class="dynamath">DynaMath</span>.<br/>
</p>
</div>
</div>
<div class="column is-centered" style="width: 45%; display: flex; flex-direction: column; justify-content: space-between; gap: 0rem;">
<div class="column is-centered" style="margin-right: -5rem; margin-top: 0rem; margin-bottom: -2rem;" >
<div class="content has-text-centered" style="margin-top: 10px; margin-bottom: 10px;">
<img src="static/images/variant-distribution.png" alt="data-overview" style="max-width: 74%;"/>
<p>
Variant number distribution.
</p>
</div>
</div>
<div class="column is-centered" style="margin-right: -5rem; margin-bottom: 0rem;">
<div class="content has-text-centered">
<img src="static/images/pie_chart.png" alt="data-overview" style="max-width: 49%;"/>
<p>
Source composition of
<span class="dynamath">DynaMath</span>.<br/>
</p>
</div>
</div>
</div>
</div>
</div>
</div>
<p>In <span class="dynamath">DynaMath</span>, we integrate various types of variants to enrich the diversity of question generation:</p>
<div class="content has-text-centered" style="text-align: center; margin-top: 30px; margin-bottom: 30px;">
<img src="static/images/variation-type.png" alt="variation type" width="95%" style="margin-top: 10px; margin-bottom: 10px;"/>
<p style="margin-top: 5px;"> Several variantion types considered in our
<span class="dynamath">DynaMath</span> benchmark.
</p>
</div>
</div>
<!-- </div> -->
<!-- <div class="container"> -->
<!-- <div class="columns is-centered has-text-centered"> -->
<!-- <div class="column is-full-width has-text-centered"> -->
<!-- <div class="column is-four-fifths"> -->
<h2 class="title is-3" style="text-align: center; margin-top: 70px; margin-bottom: 35px; font-size: 2.3rem;">Dataset Collection</h2>
<div class="content has-text-justified" style="font-size: 1.2rem; max-width: 95%;">
<p>
Our benchmark collection comprises two phases: <b>seed question collection</b> and <b>program-based question generation</b>.
In the initial phase, we selectively curate a set of high-quality mathematics problems that necessitate reasoning based on visual information.
The subsequent phase involves transforming each seed question into code-based prototypes, allowing for the generation of diverse concrete questions under randomly sampled conditions.
</p>
</div>
<div class="content has-text-centered" style="text-align: center; margin-top: 20px; margin-bottom: 30px;">
<img src="static/images/Q169-Variants-Gen.png" alt="generation procedure" width="95%" style="margin-top: 20px; margin-bottom: 10px;"/>
<p style="margin-top: 5px; font-size: 1.2rem;"> Generation Procedure in
<span class="dynamath">DynaMath</span>.
</p>
</div>
</div>
</div>
<div class="columns is-centered m-6">
<div class="column is-full has-text-centered content">
<h2 class="title is-3" style="text-align: center; margin-top: 20px; margin-bottom: 40px; font-size: 2.3rem;">Question Variant Examples</h2>
<div class="content has-text-centered">
<p style="text-align: center; margin-top: 50px; margin-bottom: 30px; font-size: 1.2rem;"><b>Seed Question 169:</b></p>
<img src="static/images/4o-Q169.png" alt="" width="80%"/>
<p style="text-align: center; margin-top: 20px; margin-bottom: 30px; font-size: 1.2rem;"><b>Response from GPT-4o:</b></p>
</div>
<div id="results-carousel" class="carousel results-carousel" style="max-width: 95%;">
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/4o-Q169-var1.png" alt="" width="55%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/4o-Q169-var2.png" alt="" width="55%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/4o-Q169-var3.png" alt="" width="55%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/4o-Q169-var4.png" alt="" width="55%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/4o-Q169-var5.png" alt="" width="55%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/4o-Q169-var6.png" alt="" width="55%"/>
</div>
</div>
</div>
<div class="content has-text-centered">
<p style="text-align: center; margin-top: 50px; margin-bottom: 30px; font-size: 1.2rem;"><b>Seed Question 75:</b></p>
<img src="static/images/gemini-Q75.png" alt="" width="80%"/>
<p style="text-align: center; margin-top: 20px; margin-bottom: 30px; font-size: 1.2rem;"><b>Response from Gemini:</b></p>
</div>
<div id="results-carousel" class="carousel results-carousel" style="max-width: 95%;">
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/gemini-Q75-var1.png" alt="" width="35%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/gemini-Q75-var2.png" alt="" width="35%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/gemini-Q75-var3.png" alt="" width="35%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/gemini-Q75-var4.png" alt="" width="35%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/gemini-Q75-var5.png" alt="" width="35%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/gemini-Q75-var6.png" alt="" width="35%"/>
</div>
</div>
</div>
<div class="content has-text-centered">
<p style="text-align: center; margin-top: 50px; margin-bottom: 30px; font-size: 1.2rem;"><b>Seed Question 346:</b></p>
<img src="static/images/Qwen-Q346.png" alt="" width="80%"/>
<p style="text-align: center; margin-top: 20px; margin-bottom: 30px; font-size: 1.2rem;"><b>Response from Qwen2-VL-72B:</b></p>
</div>
<div id="results-carousel" class="carousel results-carousel" style="max-width: 95%;">
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/Qwen-Q346-var1.png" alt="" width="40%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/Qwen-Q346-var2.png" alt="" width="40%"/>
</div>
</div>
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<img src="static/images/Qwen-Q346-var3.png" alt="" width="40%"/>
</div>
</div>
<div class="box m-5">
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<img src="static/images/Qwen-Q346-var4.png" alt="" width="40%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/Qwen-Q346-var5.png" alt="" width="40%"/>
</div>
</div>
<div class="box m-5">
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<img src="static/images/Qwen-Q346-var6.png" alt="" width="40%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/Qwen-Q346-var7.png" alt="" width="40%"/>
</div>
</div>
<div class="box m-5">
<div class="content has-text-centered">
<img src="static/images/Qwen-Q346-var8.png" alt="" width="40%"/>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</section>
<!-- RESULTS SECTION -->
<section class="hero is-light is-small">
<div class="hero-body has-text-centered">
<h1 class="title is-1 mathvista">Experiment Results</h1>
</div>
</section>
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<p>To evaluate the mathematical reasoning robustness of existing VLMs on <span class="dynamath">DynaMath</span>, we generate 10 variants, resulting in a total of 5,010 questions to assess their performance.</p>
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<p class="mt-3">Accuracy scores on the <b>testmini</b> subset (1,000 examples) of <img src="static/images/mathvista.png" style="width:1.0em;vertical-align: middle" alt="Logo"/>
<span class="mathvista">MathVista</span>.
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<h2 class="title is-3" style="margin-top: -10px; margin-bottom: -10px; font-size: 2.3rem;">Average-case Accuracy</h2>
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<p>The table below shows the Average-case accuracy of 14 models (three Closed-sourced Large Multimodal Models (LMMs) and 11 Vision Language Models (VLMs)) on
<span class="dynamath">DynaMath</span> with 5,010 generated questions. Question topics (PG, SG, EL, etc) and difficulty levels (EL, HI, UN) are defined in previous table.
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<h2 class="title is-3" style="margin-top: 20px; margin-bottom: -20px; font-size: 2.3rem;">Worst-case Accuracy</h2>
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<p>The table below shows the Worst-case accuracy of 14 models (three Closed-sourced Large Multimodal Models (LMMs) and 11 Vision Language Models (VLMs)) on
<span class="dynamath">DynaMath</span> with 5,010 generated questions. Question topics (PG, SG, EL, etc) and difficulty levels (EL, HI, UN) are defined in previous table.
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<div id="worst-acc"></div>
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<h2 class="title is-3" style="margin-top: 20px; font-size: 2.3rem;">Results Analysis </h2>
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<p style="font-size: 1.1rem; text-align:center; margin: 0 auto; max-width: 85%;">Comparing <b>Reasoning Robustness</b> across different models. Here we define Reasoning Robustness (RR) as the ratio between the average-case
performance and the worst-case performance.
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<img src="static/images/RR_compare.png" alt="" width="85%"/>
<p style="font-size: 1.1rem; text-align:center; margin: 0 auto; max-width: 85%;">Comparing <b>Reasoning Robustness</b> across different topics. Here we define Reasoning Robustness (RR) as the ratio between the average-case
performance and the worst-case performance.
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<img src="static/images/RC.png" alt="" width="75%"/>
<p style="font-size: 1.1rem; text-align:center; margin: 0 auto; max-width: 75%;">The <b>Repetition Consistency</b> for different models over 5 repetitions. The repetition consistency represents the model's confidence in the answer.
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<p style="font-size: 1.1rem; text-align:center; margin: 0 auto; max-width: 85%;">Error Analysis of Claude-3.5 Sonnet.
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<h2 class="title is-3 has-text-centered" style="font-size: 2.3rem;">BibTeX</h2>
<pre style="font-size: 1.1rem;"><code>@misc{zou2024dynamic,
title={DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models},
author={Chengke Zou and Xingang Guo and Rui Yang and Junyu Zhang and Bin Hu and Huan Zhang},
year={2024},
archivePrefix={arXiv},
primaryClass={cs.CL},
}</code></pre>
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