Files
zen-blog/blog/qwen2.5-math-prm.html
zeekay 004979143d fix(branding): move decorator to external /zen-decorate.js for React-proof exec
Root cause of HF + GitHub + section icons not appearing in the docs route:
Next.js React hydration was stripping the inline <script> + <style>
elements I'd injected into <body> on every docs page during DOM
reconciliation. The script never registered its setInterval.

Move the decorator to /zen-decorate.js loaded via <script defer src>
in <head>. React leaves external <script src> elements alone, so the
intervals stay alive. The keyframes CSS is now also small enough to
stay in <body> (React will strip it but the @keyframes are already
registered in the global CSSOM by the time it does).
2026-05-19 20:08:58 -07:00

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<!DOCTYPE html><!--i_dnJM_MIpJSOCQWNJVMq--><html lang="en" class="dark"><head><meta charSet="utf-8"/><meta name="viewport" content="width=device-width, initial-scale=1"/><link rel="stylesheet" href="/_next/static/chunks/f2332aac77592f9d.css" data-precedence="next"/><link rel="preload" as="script" fetchPriority="low" href="/_next/static/chunks/e83606e8fa9cc796.js"/><script src="/_next/static/chunks/36d6595f0156cd7e.js" async=""></script><script src="/_next/static/chunks/040e9cea20a8d9c7.js" async=""></script><script src="/_next/static/chunks/d4dffb5a0973d49c.js" async=""></script><script src="/_next/static/chunks/turbopack-967f27a9fd33556d.js" async=""></script><script src="/_next/static/chunks/59d0ad1b64f8544e.js" async=""></script><script src="/_next/static/chunks/4d80e004cf4896dd.js" async=""></script><script src="/_next/static/chunks/350ee4303b732916.js" async=""></script><script src="/_next/static/chunks/8de849ca74fc071f.js" async=""></script><script src="/_next/static/chunks/e62b91212ee7f8ff.js" async=""></script><script src="/_next/static/chunks/f19fe44237e54646.js" async=""></script><script src="/_next/static/chunks/cb0a883bafeb6805.js" async=""></script><meta name="theme-color" media="(prefers-color-scheme: dark)" content="#0A0A0A"/><meta name="theme-color" media="(prefers-color-scheme: light)" content="#fff"/><title>Towards Effective Process Supervision in Mathematical Reasoning — Zen LM Blog | Zen LM</title><meta name="description" content="GITHUB HUGGING FACE MODELSCOPE DISCORD"/><meta property="og:title" content="Zen LM - Open Foundation Models"/><meta property="og:description" content="Zen AI model family by Hanzo AI. 14 frontier models from 4B to 1T+ parameters for code, reasoning, vision, and multimodal tasks."/><meta property="og:url" content="https://zenlm.org"/><meta property="og:site_name" content="Zen LM"/><meta property="og:type" content="website"/><meta name="twitter:card" content="summary_large_image"/><meta name="twitter:site" content="@zenlmorg"/><meta name="twitter:creator" content="@zenlmorg"/><meta name="twitter:title" content="Zen LM - Open Foundation Models"/><meta name="twitter:description" content="Zen AI model family by Hanzo AI. 14 frontier models from 4B to 1T+ parameters for code, reasoning, vision, and multimodal tasks."/><script src="/_next/static/chunks/a6dad97d9634a72d.js" noModule=""></script><script defer src="/zen-decorate.js"></script></head><body class="antialiased"><div hidden=""><!--$--><!--/$--></div><script>((a,b,c,d,e,f,g,h)=>{let i=document.documentElement,j=["light","dark"];function k(b){var c;(Array.isArray(a)?a:[a]).forEach(a=>{let c="class"===a,d=c&&f?e.map(a=>f[a]||a):e;c?(i.classList.remove(...d),i.classList.add(f&&f[b]?f[b]:b)):i.setAttribute(a,b)}),c=b,h&&j.includes(c)&&(i.style.colorScheme=c)}if(d)k(d);else try{let a=localStorage.getItem(b)||c,d=g&&"system"===a?window.matchMedia("(prefers-color-scheme: dark)").matches?"dark":"light":a;k(d)}catch(a){}})("class","theme","system",null,["light","dark"],null,true,true)</script><!--$--><div data-closed="" role="presentation" hidden="" style="user-select:none;-webkit-user-select:none" class="fixed inset-0 z-50 backdrop-blur-xs bg-fd-overlay data-open:animate-fd-fade-in data-closed:animate-fd-fade-out"></div><div class="bg-fd-secondary/50 p-3 empty:hidden"></div><!--/$--><main class="mx-auto w-full max-w-2xl px-4 py-16"><a class="inline-flex items-center gap-1.5 text-sm text-fd-muted-foreground hover:text-fd-foreground mb-10 transition-colors" href="/blog">← Back to Blog</a><div class="mb-8"><time class="text-xs font-mono text-fd-muted-foreground uppercase tracking-wider">January 13, 2025</time><h1 class="text-3xl font-bold mt-2 mb-3">Towards Effective Process Supervision in Mathematical Reasoning</h1><p class="text-fd-muted-foreground text-lg mb-4">GITHUB HUGGING FACE MODELSCOPE DISCORD</p><div class="flex items-center gap-3 pt-4 border-t border-fd-border"><span class="text-sm text-fd-muted-foreground">By <!-- -->Zen LM Team</span><div class="flex gap-1.5 ml-auto"></div></div></div><div class="prose dark:prose-invert max-w-none"><p><a href="https://github.com/QwenLM/zen-Math" rel="noreferrer noopener" target="_blank">GITHUB</a> <a href="https://huggingface.co/collections/Qwen/qwen25-math-66eaa240a1b7d5ee65f1da3e" rel="noreferrer noopener" target="_blank">HUGGING FACE</a> <a href="https://modelscope.cn/organization/qwen" rel="noreferrer noopener" target="_blank">MODELSCOPE</a> <a href="https://discord.gg/yPEP2vHTu4" rel="noreferrer noopener" target="_blank">DISCORD</a></p>
<h1 class="flex scroll-m-28 flex-row items-center gap-2" id="introduction"><a data-card="" href="#introduction" class="peer">Introduction</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h1>
<p>In recent years, Large Language Models (LLMs) have made remarkable advances in mathematical reasoning, yet they can make mistakes, such as miscalculations or logical errors, leading to wrong conclusions. Moreover, even when achieving correct final answers, these powerful models can still regularly make up plausible reasoning steps, where the final answers build upon flawed calculations or derivations, which undermine the reliability and trustworthiness of LLMs’ reasoning processes. Hence, automated identification of errors in the reasoning process becomes increasingly significant for their scalable oversight.</p>
<p>Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of LLMs, which aim to identify and mitigate intermediate errors in the reasoning processes. In terms of evaluation, previous studies have predominantly relied on the response-level Best-of-N (BoN) evaluation, which selects the highest-scored response from $N$ candidates according to a PRM.</p>
<p>Today, we release a new state-of-the-art PRM that outperforms existing open-source alternatives for future research in building process supervision models. We also release the step-level benchmark ProcessBench for measuring the model ability to identify erroneous steps in mathematical reasoning.</p>
<h1 class="flex scroll-m-28 flex-row items-center gap-2" id="open-sourcing-processbench"><a data-card="" href="#open-sourcing-processbench" class="peer">Open-Sourcing ProcessBench</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h1>
<p>ProcessBench aims to measure the model ability to identify erroneous steps in mathematical reasoning. It consists of 3,400 test cases, primarily focused on competition- and Olympiad-level math problems. Each test case contains a step-by-step solution with error location annotated by human experts. Models are required to identify the earliest step that contains an error, or conclude that all steps are correct. ProcessBench can be used to evaluate two types of models: PRMs and critic models, where for the latter we prompt general language models to critique each solution step by step.</p>
<h1 class="flex scroll-m-28 flex-row items-center gap-2" id="releasing-process-reward-models"><a data-card="" href="#releasing-process-reward-models" class="peer">Releasing Process Reward Models</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h1>
<p>We release two PRMs fine-tuned on zen-Math-7B-Instruct and zen-Math-72B-Instruct, namely zen-Math-PRM-7B and zen-Math-PRM-72B respectively. Our trained PRMs exhibit both impressive performance in the BoN evaluation and stronger error identification performance in ProcessBench.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="best-of-n-evaluation"><a data-card="" href="#best-of-n-evaluation" class="peer">Best-of-N Evaluation</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h2>
<p>Following zen-Math, we sampled eight responses (i.e., $N=8$) from zen-Math-7B-Instruct across multiple mathematical benchmarks, including GSM8K, MATH, Minerva Math, GaoKao 2023 En, OlympiadBench, College Math, and MMLU STEM. Each candidate response is scored using the product of all the individual scores of each step within the response. We report the result of majority voting among eight samplings (maj@8) as the baseline, and pass@8 (i.e., the proportion of test samples where any of the eight samplings lead to the correct final answers) as the upper bound.</p>
<p>As shown in the following table, zen-Math-PRM-7B demonstrates superior performance compared to other PRMs of equivalent model scale. Notably, it outperforms maj@8 across all 7 tasks, achieving an average improvement of 1.4%. Furthermore, zen-Math-PRM-72B exhibits slightly better overall performance than zen-Math-RM-72B, with particularly significant improvements observed in the Minerva Math and MMLU STEM tasks.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="processbench"><a data-card="" href="#processbench" class="peer">ProcessBench</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h2>
<p>We also evaluate our PRMs on ProcessBench to measure the ability of identify erroneous steps. When compared with LLM-as-judge, zen-Math-PRM-7B in smaller model size demonstrates superior performance over all open-source models. For proprietary language models, zen-Math-PRM-7B outperforms GPT-4o-0806, while there remains a performance gap compared to o1-mini. Furthermore, in comparison with existing PRMs, both zen-Math-PRM-7B and zen-Math-PRM-72B exhibit substantial advantages over their counterparts. An interesting observation worth noting is that the Outcome Reward Model (ORM) zen-Math-RM-72B exhibits considerable capability in identifying step errors, even surpassing some open-source PRMs, which validates its potential as a complementary reward beyond solely rule-based mechanism.</p>
<h1 class="flex scroll-m-28 flex-row items-center gap-2" id="conclusion"><a data-card="" href="#conclusion" class="peer">Conclusion</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h1>
<p>ProcessBench demonstrate the current challenges of existing PRMs and fills the gap in step-level evaluation of PRMs. Besides open-sourcing PRMs, we also identify critical limitations in current data construction approaches for PRMs and reveal the potential bias in using response-level BoN evaluation alone for PRMs through extensive empirical studies in our paper. We hope that ProcessBench and the best practices in training our own PRMs can foster future research and development for reasoning process supervision. For more details, please check out our papers in the following!</p>
<h1 class="flex scroll-m-28 flex-row items-center gap-2" id="citation"><a data-card="" href="#citation" class="peer">Citation</a><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100" aria-hidden="true"><path d="M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71"></path><path d="M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71"></path></svg></h1>
<p>If you find our work helpful, feel free to give us a citation.</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"><span></span></span>
<span class="line"><span> @article{processbench,</span></span>
<span class="line"><span> title={{ProcessBench:} Identifying Process Errors in Mathematical Reasoning}, </span></span>
<span class="line"><span> author={</span></span>
<span class="line"><span> Chujie Zheng and Zhenru Zhang and Beichen Zhang and Runji Lin and Keming Lu and</span></span>
<span class="line"><span> Bowen Yu and Dayiheng Liu and Jingren Zhou and Junyang Lin</span></span>
<span class="line"><span> },</span></span>
<span class="line"><span> journal={arXiv preprint arXiv:2412.06559},</span></span>
<span class="line"><span> year={2024}</span></span>
<span class="line"><span> }</span></span>
<span class="line"><span> @article{prmlessons,</span></span>
<span class="line"><span> title={The Lessons of Developing Process Reward Models in Mathematical Reasoning}, </span></span>
<span class="line"><span> author={</span></span>
<span class="line"><span> Zhenru Zhang and Chujie Zheng and Yangzhen Wu and Beichen Zhang and Runji Lin and Bowen Yu and Dayiheng Liu and Jingren Zhou and Junyang Lin</span></span>
<span class="line"><span> },</span></span>
<span class="line"><span> journal={arXiv preprint arXiv:2501.07301},</span></span>
<span class="line"><span> year={2025}</span></span>
<span class="line"><span> }</span></span>
<span class="line"><span> </span></span></code></pre></div></figure></div></main><!--$--><!--/$--><script src="/_next/static/chunks/e83606e8fa9cc796.js" id="_R_" async=""></script><script>(self.__next_f=self.__next_f||[]).push([0])</script><script>self.__next_f.push([1,"1:\"$Sreact.fragment\"\n2:I[106,[\"/_next/static/chunks/59d0ad1b64f8544e.js\"],\"RootProvider\"]\n3:I[53113,[\"/_next/static/chunks/4d80e004cf4896dd.js\",\"/_next/static/chunks/350ee4303b732916.js\"],\"default\"]\n4:I[73211,[\"/_next/static/chunks/4d80e004cf4896dd.js\",\"/_next/static/chunks/350ee4303b732916.js\"],\"default\"]\n5:I[10086,[\"/_next/static/chunks/59d0ad1b64f8544e.js\",\"/_next/static/chunks/8de849ca74fc071f.js\",\"/_next/static/chunks/e62b91212ee7f8ff.js\",\"/_next/static/chunks/f19fe44237e54646.js\",\"/_next/static/chunks/cb0a883bafeb6805.js\"],\"\"]\n7:I[89923,[\"/_next/static/chunks/4d80e004cf4896dd.js\",\"/_next/static/chunks/350ee4303b732916.js\"],\"OutletBoundary\"]\n8:\"$Sreact.suspense\"\na:I[89923,[\"/_next/static/chunks/4d80e004cf4896dd.js\",\"/_next/static/chunks/350ee4303b732916.js\"],\"ViewportBoundary\"]\nc:I[89923,[\"/_next/static/chunks/4d80e004cf4896dd.js\",\"/_next/static/chunks/350ee4303b732916.js\"],\"MetadataBoundary\"]\ne:I[6998,[\"/_next/static/chunks/4d80e004cf4896dd.js\",\"/_next/static/chunks/350ee4303b732916.js\"],\"default\"]\n:HL[\"/_next/static/chunks/f2332aac77592f9d.css\",\"style\"]\n"])</script><script>self.__next_f.push([1,"0:{\"P\":null,\"b\":\"i-dnJM_MIpJSOCQWNJVMq\",\"c\":[\"\",\"blog\",\"qwen2.5-math-prm\"],\"q\":\"\",\"i\":false,\"f\":[[[\"\",{\"children\":[\"blog\",{\"children\":[[\"slug\",\"qwen2.5-math-prm\",\"d\"],{\"children\":[\"__PAGE__\",{}]}]}]},\"$undefined\",\"$undefined\",true],[[\"$\",\"$1\",\"c\",{\"children\":[[[\"$\",\"link\",\"0\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/f2332aac77592f9d.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-0\",{\"src\":\"/_next/static/chunks/59d0ad1b64f8544e.js\",\"async\":true,\"nonce\":\"$undefined\"}]],[\"$\",\"html\",null,{\"lang\":\"en\",\"className\":\"dark\",\"suppressHydrationWarning\":true,\"children\":[\"$\",\"body\",null,{\"className\":\"antialiased\",\"children\":[\"$\",\"$L2\",null,{\"children\":[\"$\",\"$L3\",null,{\"parallelRouterKey\":\"children\",\"error\":\"$undefined\",\"errorStyles\":\"$undefined\",\"errorScripts\":\"$undefined\",\"template\":[\"$\",\"$L4\",null,{}],\"templateStyles\":\"$undefined\",\"templateScripts\":\"$undefined\",\"notFound\":[[\"$\",\"main\",null,{\"className\":\"flex min-h-screen flex-col items-center justify-center px-4 text-center\",\"children\":[[\"$\",\"div\",null,{\"className\":\"mb-8 opacity-20\",\"children\":[\"$\",\"svg\",null,{\"width\":\"120\",\"height\":\"120\",\"viewBox\":\"0 0 120 120\",\"fill\":\"none\",\"aria-hidden\":\"true\",\"children\":[\"$\",\"circle\",null,{\"cx\":\"60\",\"cy\":\"60\",\"r\":\"50\",\"stroke\":\"currentColor\",\"strokeWidth\":\"3\",\"strokeLinecap\":\"round\",\"strokeDasharray\":\"280 40\"}]}]}],[\"$\",\"p\",null,{\"className\":\"text-xs font-mono uppercase tracking-[0.3em] text-fd-muted-foreground mb-4\",\"children\":\"404\"}],[\"$\",\"h1\",null,{\"className\":\"text-3xl font-semibold mb-3\",\"children\":\"Page not found\"}],[\"$\",\"p\",null,{\"className\":\"text-fd-muted-foreground max-w-sm mb-10\",\"children\":\"This page doesn't exist, or it may have moved. 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24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"path\",\"1cjeqo\",{\"d\":\"M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71\"}],[\"$\",\"path\",\"19qd67\",{\"d\":\"M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71\"}],\"$undefined\"]}]]}],\"\\n\",[\"$\",\"p\",null,{\"children\":\"In recent years, Large Language Models (LLMs) have made remarkable advances in mathematical reasoning, yet they can make mistakes, such as miscalculations or logical errors, leading to wrong conclusions. Moreover, even when achieving correct final answers, these powerful models can still regularly make up plausible reasoning steps, where the final answers build upon flawed calculations or derivations, which undermine the reliability and trustworthiness of LLMs’ reasoning processes. Hence, automated identification of errors in the reasoning process becomes increasingly significant for their scalable oversight.\"}],\"\\n\",[\"$\",\"p\",null,{\"children\":\"Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of LLMs, which aim to identify and mitigate intermediate errors in the reasoning processes. 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Each candidate response is scored using the product of all the individual scores of each step within the response. We report the result of majority voting among eight samplings (maj@8) as th"])</script><script>self.__next_f.push([1,"e baseline, and pass@8 (i.e., the proportion of test samples where any of the eight samplings lead to the correct final answers) as the upper bound.\"}]\n16:[\"$\",\"p\",null,{\"children\":\"As shown in the following table, zen-Math-PRM-7B demonstrates superior performance compared to other PRMs of equivalent model scale. Notably, it outperforms maj@8 across all 7 tasks, achieving an average improvement of 1.4%. 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