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<!DOCTYPE html>
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content="Evaluating mathematical reasoning of foundation models in multi-modal contexts">
<meta name="keywords" content="PolyMath, Poly, Math">
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<title> PolyMATH: A Challenging Multi-Modal Mathematical Reasoning Benchmark</title>
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<h1 class="title is-1 publication-title is-bold">
<img src="static/images/polymath.png" style="width:1em;vertical-align: middle" alt="Logo"/>
<span class="polymath" style="vertical-align: middle">PolyMATH</span>
</h1>
<h2 class="subtitle is-3 publication-subtitle">
A Challenging Multi-Modal Mathematical Reasoning Benchmark
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</h2>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://him1411.github.io/">Himanshu Gupta</a><sup style="color:#6fbf73;">1*</sup>,</span>
<span class="author-block">
<a href="https://shreyas301197.github.io">Shreyas Verma</a><sup style="color:#ed4b82;">2*</sup>,</span>
<span class="author-block">
<a href="https://ujjwalaananth.github.io/">Ujjwala Anantheswaran</a><sup style="color:#6fbf73;">1*</sup>,
</span>
<span class="author-block">
<a href="https://kevinscaria.github.io/">Kevin Scaria</a><sup style="color:#6fbf73">1*</sup>,
</span>
<span class="author-block">
<a href="https://sites.google.com/view/mihir3009">Mihir Parmar</a><sup style="color:#6fbf73">1</sup>,
</span>
<span class="author-block">
<a href="https://swarooprm.github.io/">Swaroop Mishra</a><sup style="color:#6fbf73">1†</sup>,
</span>
<span class="author-block">
<a href="https://search.asu.edu/profile/231973">Chitta Baral</a><sup style="color:#6fbf73">1</sup>,
</span>
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<div class="is-size-5 publication-authors">
<span class="author-block"><sup style="color:#6fbf73;">1</sup>Arizona State University,</span><br>
<span class="author-block"><sup style="color:#ed4b82">2</sup>Asurion,</span></span><br>
<span class="author-block" style="font-size: 12px"><sup style="color:#ed4b82">*</sup>Equal Contribution</span>
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</section>
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<!-- Abstract. -->
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<h2 class="title is-3">Introduction</h2>
<div class="content has-text-justified">
<p>
<b>Multi-modal Large Language Models (MLLMs)</b> exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated.
</p>
<p>
To this end, we present
<img src="static/images/polymath.png" style="width:1.2em;vertical-align: middle" alt="Logo"/>
<span class="polymath">PolyMATH</span>, a challenging benchmark aimed at evaluating the general cognitive reasoning
abilities of MLLMs.
PolyMATH comprises 5,000 manually collected high-quality images of cognitive textual and visual challenges across
10 distinct categories, including pattern recognition, spatial reasoning, and relative reasoning.
We conducted a comprehensive, and quantitative evaluation of 15 MLLMs using four diverse prompting strategies,
including Chain-of-Thought and Step-Back.
</p>
<p>
With
<img src="static/images/polymath.png" style="width:1.2em;vertical-align: middle" alt="Logo"/>
<span class="polymath">PolyMATH</span>, the best scores achieved are ~41%, ~36%, and ~27%,
obtained by Claude-3.5 Sonnet, GPT-4o and Gemini-1.5 Pro respectively highlighting the logical and
visual complexity of these questions.
A further fine-grained error analysis reveals that these models struggle
to understand spatial relations and perform drawn-out,
high-level reasoning. This is further strengthened by our ablation study
estimating MLLM performance when given textual descriptions in place of diagrams.
As evidenced by ~4% improvement over textual descriptions as opposed to actual images,
we discover that models do not truly comprehend visual diagrams and the spatial information therein,
and are thus prone to logical errors.
Finally, we evaluate the OpenAI o1 models and find that their performance only matches the human baseline,
highlighting the difficulty of the benchmark.
</p>
<p>
The results on
<img src="static/images/polymath.png" style="width:1.2em;vertical-align: middle" alt="Logo"/>
<span class="polymath">PolyMATH</span>
highlight the room for improvement in multi-modal reasoning
and provides unique insights to guide the development of future MLLMs.
</p>
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</div>
<!--/ Abstract. -->
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</section>
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