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<!DOCTYPE html>
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<meta name="description" content="Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling.">
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<title>Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling</title>
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<!-- Title -->
<h1 class="title is-1 publication-title is-bold">
Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling
</h1>
<!-- Author list -->
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://ryanliu112.github.io/">Runze Liu</a><sup>1,2</sup>,
</span>
<span class="author-block">
<a href="https://scholar.google.com/citations?user=mWpsZ1wAAAAJ">Junqi Gao</a><sup>1,3</sup>,
</span>
<span class="author-block">
<a href="https://openreview.net/profile?id=~Jian_Zhao12">Jian Zhao</a><sup>4</sup>,
</span>
<span class="author-block">
<a href="https://iseesaw.github.io/">Kaiyan Zhang</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://www.sigs.tsinghua.edu.cn/lx/main.htm">Xiu Li</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://biqing-qi.github.io/">Biqing Qi</a><sup>1,†</sup>,
</span>
<span class="author-block">
<a href="https://wlouyang.github.io/">Wanli Ouyang</a><sup>1</sup>,
</span>
<span class="author-block">
<a href="http://c3i.ee.tsinghua.edu.cn/">Bowen Zhou</a><sup>1,2,†</sup>
</span>
</div>
<div class="is-size-5 publication-authors" style="margin-top: 0.3em;">
<div class="author-block"><sup>1</sup>Shanghai AI Laboratory, </div>
<div class="author-block"><sup>2</sup>Tsinghua University, </div>
<div class="author-block"><sup>3</sup>Harbin Institute of Technology, </div>
<div class="author-block"><sup>4</sup>BUPT</div>
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<div>†Corresponding author</div>
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<img src="./static/images/MATH_co_abs.png" alt="" style="max-width: 100%; height: auto;" id="MATH_co_abs">
<h2 class="subtitle has-text-centered">
<strong>Figure 1</strong>: Comparison between the performance of smaller LLMs compute-optimal TTS and that of larger LLMs CoT on MATH-500 and AIME24.
</h2>
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<h2 class="title is-3">Abstract</h2>
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<p>
Test-Time Scaling (TTS) is an important method for improving the performance of Large Language Models (LLMs) by using additional computation during the inference phase. However, current studies do not systematically analyze how policy models, Process Reward Models (PRMs), and problem difficulty influence TTS. This lack of analysis limits the understanding and practical use of TTS methods. In this paper, we focus on two core questions: (1) What is the optimal approach to scale test-time computation across different policy models, PRMs, and problem difficulty levels? (2) To what extent can extended computation improve the performance of LLMs on complex tasks, and can smaller language models outperform larger ones through this approach? Through comprehensive experiments on MATH-500 and challenging AIME24 tasks, we have the following observations: (1) The compute-optimal TTS strategy is highly dependent on the choice of policy model, PRM, and problem difficulty. (2) With our compute-optimal TTS strategy, extremely small policy models can outperform larger models. For example, a 1B LLM can exceed a 405B LLM on MATH-500. Moreover, on both MATH-500 and AIME24, a 0.5B LLM outperforms GPT-4o, a 3B LLM surpasses a 405B LLM, and a 7B LLM beats o1 and DeepSeek-R1, while with higher inference efficiency. These findings show the significance of adapting TTS strategies to the specific characteristics of each task and model and indicate that TTS is a promising approach for enhancing the reasoning abilities of LLMs.
</p>
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<!--/ Abstract. -->
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<h2 class="title is-3">Setup</h2>
<div class="content has-text-justified">
<p>
We consider three TTS methods: Best-of-N (BoN), beam search, and Diverse Verifier Tree Search (DVTS), as shown in Figure 2.
</p>
</div>
<img src="./static/images/tts_method.png" alt="" style="width: 100%; max-width: 1000px; margin-top: 20px; margin-bottom: 10px;" id="tts_method">
<h3 class="has-text-centered">
<strong>Figure 2</strong>: Comparison of different external TTS methods.
</h3>
<!-- <div class="content has-text-justified" style="margin-top: 20px;">
<p>
We use policy models from Llama 3 and Qwen2.5 families with different sizes and all of them are the Instruct version.
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<h2 class="title is-3">Results</h2>
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<p>
</p>
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<img src="./static/images/small_vs_large.png" alt="" style="width: 100%; max-width: 1000px; margin-top: 20px; margin-bottom: 10px;" id="small_vs_large">
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</p>
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<h2 class="title">BibTeX</h2>
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<pre><code>@article{liu2025can,
title = {Can 1B LLM Surpass 405B LLM? Rethinking Compute-Optimal Test-Time Scaling},
author = {Runze Liu and Junqi Gao and Jian Zhao and Kaiyan Zhang and Xiu Li and Biqing Qi and Wanli Ouyang and Bowen Zhou},
journal = {arXiv preprint arXiv:2502.06703},
year = {2025}
}</code></pre>
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