mirror of
https://github.com/zenlm/zen-blog.git
synced 2026-11-03 14:11:45 +00:00
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).
240 lines
91 KiB
HTML
240 lines
91 KiB
HTML
<!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>GRPO: Group Relative Policy Optimization — Zen LM Blog | Zen LM</title><meta name="description" content="A companion post to our GRPO paper, explaining group relative policy optimization for language model alignment."/><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">September 17, 2022</time><h1 class="text-3xl font-bold mt-2 mb-3">GRPO: Group Relative Policy Optimization</h1><p class="text-fd-muted-foreground text-lg mb-4">A companion post to our GRPO paper, explaining group relative policy optimization for language model alignment.</p><div class="flex items-center gap-3 pt-4 border-t border-fd-border"><span class="text-sm text-fd-muted-foreground">By <!-- -->Zach Kelling</span><div class="flex gap-1.5 ml-auto"><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">Research</span><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">RLHF</span><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">GRPO</span><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">Alignment</span></div></div></div><div class="prose dark:prose-invert max-w-none"><h1 class="flex scroll-m-28 flex-row items-center gap-2" id="beyond-ppo"><a data-card="" href="#beyond-ppo" class="peer">Beyond PPO</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>Proximal Policy Optimization (PPO) has become the de facto algorithm for reinforcement learning from human feedback. Yet PPO has fundamental limitations when applied to language models:</p>
|
||
<ol>
|
||
<li><strong>Absolute reward dependence</strong> : PPO optimizes absolute reward values, which are noisy and poorly calibrated</li>
|
||
<li><strong>KL divergence sensitivity</strong> : The KL penalty requires careful tuning to avoid collapse or divergence</li>
|
||
<li><strong>Sample inefficiency</strong> : Each prompt generates one response for learning</li>
|
||
<li><strong>Reward hacking</strong> : Models exploit reward model weaknesses</li>
|
||
</ol>
|
||
<p>Group Relative Policy Optimization (GRPO) addresses these issues through a simple insight: <strong>relative comparisons are more informative than absolute scores</strong>.</p>
|
||
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="the-grpo-algorithm"><a data-card="" href="#the-grpo-algorithm" class="peer">The GRPO Algorithm</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>Instead of scoring individual responses, GRPO generates a group of $K$ responses per prompt and learns from their relative rankings.</p>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="response-generation"><a data-card="" href="#response-generation" class="peer">Response Generation</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></h3>
|
||
<p>For each prompt $x$, sample $K$ responses from the current policy:</p>
|
||
<p><code>y_1, y_2, \ldots, y_K \sim \pi_\theta(\cdot | x)</code></p>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="reward-computation"><a data-card="" href="#reward-computation" class="peer">Reward Computation</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></h3>
|
||
<p>Score all responses with the reward model:</p>
|
||
<p><code>r_i = R(x, y_i) \quad \text\{for \} i = 1, \ldots, K</code></p>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="advantage-estimation"><a data-card="" href="#advantage-estimation" class="peer">Advantage Estimation</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></h3>
|
||
<p>Compute group-relative advantages:</p>
|
||
<p><code>A_i = \frac\{r_i - \mu_r\}\{\sigma_r\}</code></p>
|
||
<p>Where $\mu_r$ and $\sigma_r$ are the mean and standard deviation of rewards within the group.</p>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="policy-update"><a data-card="" href="#policy-update" class="peer">Policy Update</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></h3>
|
||
<p>Update the policy to increase probability of high-advantage responses:</p>
|
||
<p><code>\mathcal\{L\}_\{GRPO\} = -\mathbb\{E\}_\{x, y \sim \pi_\theta\}\left[\frac\{\pi_\theta(y|x)\}\{\pi_\{old\}(y|x)\} \cdot A(x, y) \cdot \mathbb\{1\}_\{clip\}\right]</code></p>
|
||
<p>Where $\mathbb{1}_{clip}$ applies PPO-style clipping to the importance ratio.</p>
|
||
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="why-group-relative"><a data-card="" href="#why-group-relative" class="peer">Why Group-Relative?</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>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="noise-robustness"><a data-card="" href="#noise-robustness" class="peer">Noise Robustness</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></h3>
|
||
<p>Reward models are noisy. A response scored 0.7 versus 0.6 may not be meaningfully better. But within a group of responses to the same prompt, relative ordering is more reliable:</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="relative overflow-auto prose-no-margin my-6"><table><thead><tr><th>Metric</th><th>Absolute Score</th><th>Relative Rank</th></tr></thead><tbody><tr><td>Inter-annotator agreement</td><td>0.61</td><td>0.83</td></tr><tr><td>Test-retest reliability</td><td>0.54</td><td>0.79</td></tr><tr><td>Reward model calibration</td><td>Poor</td><td>N/A</td></tr></tbody></table></div>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="natural-normalization"><a data-card="" href="#natural-normalization" class="peer">Natural Normalization</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></h3>
|
||
<p>Group-relative advantages automatically adapt to reward scale and prompt difficulty:</p>
|
||
<ul>
|
||
<li>Easy prompts: All responses score high, advantages near zero</li>
|
||
<li>Hard prompts: Large variance, clear signal for improvement</li>
|
||
<li>Reward drift: Normalization handles changing baselines</li>
|
||
</ul>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="sample-efficiency"><a data-card="" href="#sample-efficiency" class="peer">Sample Efficiency</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></h3>
|
||
<p>Generating $K$ responses per prompt and comparing them provides $\binom{K}{2}$ pairwise comparisons. For $K=8$, that’s 28 learning signals per prompt versus 1 for standard PPO.</p>
|
||
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="implementation-details"><a data-card="" href="#implementation-details" class="peer">Implementation Details</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>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="group-size-selection"><a data-card="" href="#group-size-selection" class="peer">Group Size Selection</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></h3>
|
||
<p>We find $K=8$ provides a good tradeoff:</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="relative overflow-auto prose-no-margin my-6"><table><thead><tr><th>K</th><th>Compute</th><th>Signal Quality</th><th>Best Accuracy</th></tr></thead><tbody><tr><td>2</td><td>2x</td><td>Low</td><td>71.2%</td></tr><tr><td>4</td><td>4x</td><td>Medium</td><td>74.8%</td></tr><tr><td>8</td><td>8x</td><td>High</td><td>77.3%</td></tr><tr><td>16</td><td>16x</td><td>Marginal gain</td><td>77.9%</td></tr></tbody></table></div>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="temperature-schedule"><a data-card="" href="#temperature-schedule" class="peer">Temperature Schedule</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></h3>
|
||
<p>Higher temperature during response generation increases group diversity:</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 [&_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 class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> sample_group</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(prompt, policy, K</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">8</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> responses </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> []</span></span>
|
||
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> i </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">in</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> range</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(K):</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> temp </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 0.7</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> +</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 0.3</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> *</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> (i </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> K) </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"># 0.7 to 1.0</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> response </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> policy.sample(prompt, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">temperature</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">temp)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> responses.append(response)</span></span>
|
||
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> responses</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span></code></pre></div></figure>
|
||
<h3 class="flex scroll-m-28 flex-row items-center gap-2" id="kl-regularization"><a data-card="" href="#kl-regularization" class="peer">KL Regularization</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></h3>
|
||
<p>GRPO still benefits from KL regularization, but with reduced sensitivity:</p>
|
||
<p><code>\mathcal\{L\} = \mathcal\{L\}_\{GRPO\} + \beta \cdot D_\{KL\}(\pi_\theta || \pi_\{ref\})</code></p>
|
||
<p>We find $\beta = 0.01$ works across tasks, compared to PPO’s typical $\beta \in [0.001, 0.1]$ sensitivity.</p>
|
||
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="experimental-results"><a data-card="" href="#experimental-results" class="peer">Experimental Results</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>On Anthropic’s HH-RLHF benchmark:</p>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="relative overflow-auto prose-no-margin my-6"><table><thead><tr><th>Method</th><th>Helpfulness</th><th>Harmlessness</th><th>Compute</th></tr></thead><tbody><tr><td>SFT</td><td>3.2/5</td><td>3.8/5</td><td>1x</td></tr><tr><td>PPO</td><td>3.9/5</td><td>4.1/5</td><td>10x</td></tr><tr><td>GRPO</td><td>4.2/5</td><td>4.3/5</td><td>8x</td></tr></tbody></table></div>
|
||
<p>GRPO achieves better alignment with less compute through efficient use of generated samples.</p>
|
||
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="reward-hacking-resistance"><a data-card="" href="#reward-hacking-resistance" class="peer">Reward Hacking Resistance</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>GRPO is naturally resistant to reward hacking because:</p>
|
||
<ol>
|
||
<li><strong>Relative comparison</strong> : Hacked responses must beat other responses, not just achieve high absolute score</li>
|
||
<li><strong>Diverse sampling</strong> : Temperature variation produces varied response styles</li>
|
||
<li><strong>Group normalization</strong> : Exploits that boost all responses equally provide no gradient</li>
|
||
</ol>
|
||
<p>We observe significantly less length gaming and repetition compared to PPO.</p>
|
||
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="code"><a data-card="" href="#code" class="peer">Code</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>Reference implementation:</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 [&_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 class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> grpo_loss</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(policy, prompts, reward_model, K</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">8</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">, clip_eps</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">0.2</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">):</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> losses </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> []</span></span>
|
||
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> prompt </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">in</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> prompts:</span></span>
|
||
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Generate response group</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> responses </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> sample_group(prompt, policy, K)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span>
|
||
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Compute rewards and advantages</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> rewards </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> [reward_model(prompt, r) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> r </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">in</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> responses]</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> advantages </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> (rewards </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> np.mean(rewards)) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> (np.std(rewards) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 1e-8</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span>
|
||
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Policy loss</span></span>
|
||
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> response, advantage </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">in</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> zip</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(responses, advantages):</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> ratio </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> policy.prob(response) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> policy.prob_old(response)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> clipped </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.clamp(ratio, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">1</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">clip_eps, </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">1</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">clip_eps)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> loss </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> -</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">torch.min(ratio </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> advantage, clipped </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> advantage)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> losses.append(loss)</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span>
|
||
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.mean(torch.stack(losses))</span></span>
|
||
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span></code></pre></div></figure>
|
||
<h2 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></h2>
|
||
<p>GRPO offers a simple improvement to RLHF: generate multiple responses, compare them relatively, update toward the best. This approach is more robust, more sample-efficient, and more resistant to reward hacking than standard PPO.</p>
|
||
<p>The algorithm is simple enough to implement in an afternoon. The gains are substantial enough to matter.</p>
|
||
<hr/>
|
||
<p><em>Full details in “Group Relative Policy Optimization for Language Model Alignment” (2022). Code at github.com/zen-ai/grpo.</em></p></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\",\"grpo-group-relative-policy-optimization\"],\"q\":\"\",\"i\":false,\"f\":[[[\"\",{\"children\":[\"blog\",{\"children\":[[\"slug\",\"grpo-group-relative-policy-optimization\",\"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. Try the documentation or head home.\"}],[\"$\",\"div\",null,{\"className\":\"flex flex-wrap gap-3 justify-center\",\"children\":[[\"$\",\"$L5\",null,{\"href\":\"/\",\"className\":\"inline-flex items-center gap-2 rounded-lg bg-fd-primary text-fd-primary-foreground px-4 py-2 text-sm font-medium hover:opacity-90 transition\",\"children\":\"Go home\"}],[\"$\",\"$L5\",null,{\"href\":\"/docs\",\"className\":\"inline-flex items-center gap-2 rounded-lg border border-fd-border bg-fd-background px-4 py-2 text-sm font-medium hover:bg-fd-muted transition\",\"children\":\"Documentation\"}],[\"$\",\"$L5\",null,{\"href\":\"/docs/models\",\"className\":\"inline-flex items-center gap-2 rounded-lg border border-fd-border bg-fd-background px-4 py-2 text-sm font-medium hover:bg-fd-muted transition\",\"children\":\"Browse models\"}]]}],[\"$\",\"p\",null,{\"className\":\"mt-16 text-xs font-mono text-fd-muted-foreground opacity-50\",\"children\":\"zenlm.org\"}]]}],[]],\"forbidden\":\"$undefined\",\"unauthorized\":\"$undefined\"}]}]}]}]]}],{\"children\":[[\"$\",\"$1\",\"c\",{\"children\":[null,[\"$\",\"$L3\",null,{\"parallelRouterKey\":\"children\",\"error\":\"$undefined\",\"errorStyles\":\"$undefined\",\"errorScripts\":\"$undefined\",\"template\":[\"$\",\"$L4\",null,{}],\"templateStyles\":\"$undefined\",\"templateScripts\":\"$undefined\",\"notFound\":\"$undefined\",\"forbidden\":\"$undefined\",\"unauthorized\":\"$undefined\"}]]}],{\"children\":[[\"$\",\"$1\",\"c\",{\"children\":[null,[\"$\",\"$L3\",null,{\"parallelRouterKey\":\"children\",\"error\":\"$undefined\",\"errorStyles\":\"$undefined\",\"errorScripts\":\"$undefined\",\"template\":[\"$\",\"$L4\",null,{}],\"templateStyles\":\"$undefined\",\"templateScripts\":\"$undefined\",\"notFound\":\"$undefined\",\"forbidden\":\"$undefined\",\"unauthorized\":\"$undefined\"}]]}],{\"children\":[[\"$\",\"$1\",\"c\",{\"children\":[\"$L6\",[[\"$\",\"script\",\"script-0\",{\"src\":\"/_next/static/chunks/8de849ca74fc071f.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-1\",{\"src\":\"/_next/static/chunks/e62b91212ee7f8ff.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-2\",{\"src\":\"/_next/static/chunks/f19fe44237e54646.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-3\",{\"src\":\"/_next/static/chunks/cb0a883bafeb6805.js\",\"async\":true,\"nonce\":\"$undefined\"}]],[\"$\",\"$L7\",null,{\"children\":[\"$\",\"$8\",null,{\"name\":\"Next.MetadataOutlet\",\"children\":\"$@9\"}]}]]}],{},null,false,false]},null,false,false]},null,false,false]},null,false,false],[\"$\",\"$1\",\"h\",{\"children\":[null,[\"$\",\"$La\",null,{\"children\":\"$Lb\"}],[\"$\",\"div\",null,{\"hidden\":true,\"children\":[\"$\",\"$Lc\",null,{\"children\":[\"$\",\"$8\",null,{\"name\":\"Next.Metadata\",\"children\":\"$Ld\"}]}]}],null]}],false]],\"m\":\"$undefined\",\"G\":[\"$e\",[]],\"S\":true}\n"])</script><script>self.__next_f.push([1,"6:[\"$\",\"main\",null,{\"className\":\"mx-auto w-full max-w-2xl px-4 py-16\",\"children\":[[\"$\",\"$L5\",null,{\"href\":\"/blog\",\"className\":\"inline-flex items-center gap-1.5 text-sm text-fd-muted-foreground hover:text-fd-foreground mb-10 transition-colors\",\"children\":\"← Back to Blog\"}],[\"$\",\"div\",null,{\"className\":\"mb-8\",\"children\":[[\"$\",\"time\",null,{\"className\":\"text-xs font-mono text-fd-muted-foreground uppercase tracking-wider\",\"children\":\"September 17, 2022\"}],[\"$\",\"h1\",null,{\"className\":\"text-3xl font-bold mt-2 mb-3\",\"children\":\"GRPO: Group Relative Policy Optimization\"}],[\"$\",\"p\",null,{\"className\":\"text-fd-muted-foreground text-lg mb-4\",\"children\":\"A companion post to our GRPO paper, explaining group relative policy optimization for language model alignment.\"}],[\"$\",\"div\",null,{\"className\":\"flex items-center gap-3 pt-4 border-t border-fd-border\",\"children\":[[\"$\",\"span\",null,{\"className\":\"text-sm text-fd-muted-foreground\",\"children\":[\"By \",\"Zach Kelling\"]}],[\"$\",\"div\",null,{\"className\":\"flex gap-1.5 ml-auto\",\"children\":[[\"$\",\"span\",\"Research\",{\"className\":\"text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded\",\"children\":\"Research\"}],[\"$\",\"span\",\"RLHF\",{\"className\":\"text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded\",\"children\":\"RLHF\"}],[\"$\",\"span\",\"GRPO\",{\"className\":\"text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded\",\"children\":\"GRPO\"}],[\"$\",\"span\",\"Alignment\",{\"className\":\"text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded\",\"children\":\"Alignment\"}]]}]]}]]}],[\"$\",\"div\",null,{\"className\":\"prose dark:prose-invert max-w-none\",\"children\":[[\"$\",\"h1\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"beyond-ppo\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#beyond-ppo\",\"className\":\"peer\",\"children\":\"Beyond PPO\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\",[\"$\",\"p\",null,{\"children\":\"Proximal Policy Optimization (PPO) has become the de facto algorithm for reinforcement learning from human feedback. Yet PPO has fundamental limitations when applied to language models:\"}],\"\\n\",[\"$\",\"ol\",null,{\"children\":[\"\\n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"Absolute reward dependence\"}],\" : PPO optimizes absolute reward values, which are noisy and poorly calibrated\"]}],\"\\n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"KL divergence sensitivity\"}],\" : The KL penalty requires careful tuning to avoid collapse or divergence\"]}],\"\\n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"Sample inefficiency\"}],\" : Each prompt generates one response for learning\"]}],\"\\n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"Reward hacking\"}],\" : Models exploit reward model weaknesses\"]}],\"\\n\"]}],\"\\n\",[\"$\",\"p\",null,{\"children\":[\"Group Relative Policy Optimization (GRPO) addresses these issues through a simple insight: \",[\"$\",\"strong\",null,{\"children\":\"relative comparisons are more informative than absolute scores\"}],\".\"]}],\"\\n\",[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"the-grpo-algorithm\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#the-grpo-algorithm\",\"className\":\"peer\",\"children\":\"The GRPO Algorithm\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\":[\"$Lf\",\"$L10\",\"$undefined\"]}]]}],\"\\n\",\"$L11\",\"\\n\",\"$L12\",\"\\n\",\"$L13\",\"\\n\",\"$L14\",\"\\n\",\"$L15\",\"\\n\",\"$L16\",\"\\n\",\"$L17\",\"\\n\",\"$L18\",\"\\n\",\"$L19\",\"\\n\",\"$L1a\",\"\\n\",\"$L1b\",\"\\n\",\"$L1c\",\"\\n\",\"$L1d\",\"\\n\",\"$L1e\",\"\\n\",\"$L1f\",\"\\n\",\"$L20\",\"\\n\",\"$L21\",\"\\n\",\"$L22\",\"\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\",\"$L23\",\"\\n\",\"$L24\",\"\\n\",\"$L25\",\"\\n\",\"$L26\",\"\\n\",\"$L27\",\"\\n\",\"$L28\",\"\\n\",\"$L29\",\"\\n\",\"$L2a\",\"\\n\",\"$L2b\",\"\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\",\"$L2c\",\"\\n\",\"$L2d\",\"\\n\",\"$L2e\",\"\\n\",\"$L2f\",\"\\n\",\"$L30\",\"\\n\",\"$L31\",\"\\n\",\"$L32\",\"\\n\",\"$L33\",\"\\n\",\"$L34\",\"\\n\",\"$L35\",\"\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\",\"$L36\",\"\\n\",\"$L37\",\"\\n\",\"$L38\",\"\\n\",\"$L39\",\"\\n\",\"$L3a\",\"\\n\",\"$L3b\",\"\\n\",\"$L3c\",\"\\n\",\"$L3d\",\"\\n\",\"$L3e\",\"\\n\",\"$L3f\",\"\\n\",\"$L40\",\"\\n\",\"$L41\",\"\\n\",\"$L42\",\"\\n\",\"$L43\"]}]]}]\n"])</script><script>self.__next_f.push([1,"44:I[51504,[\"/_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\"],\"CodeBlock\"]\n46:I[51504,[\"/_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\"],\"Pre\"]\nf:[\"$\",\"path\",\"1cjeqo\",{\"d\":\"M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71\"}]\n10:[\"$\",\"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\"}]\n11:[\"$\",\"p\",null,{\"children\":\"Instead of scoring individual responses, GRPO generates a group of $K$ responses per prompt and learns from their relative rankings.\"}]\n12:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"response-generation\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#response-generation\",\"className\":\"peer\",\"children\":\"Response Generation\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n13:[\"$\",\"p\",null,{\"children\":\"For each prompt $x$, sample $K$ responses from the current policy:\"}]\n14:[\"$\",\"p\",null,{\"children\":[\"$\",\"code\",null,{\"children\":\"y_1, y_2, \\\\ldots, y_K \\\\sim \\\\pi_\\\\theta(\\\\cdot | x)\"}]}]\n15:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"reward-computation\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#reward-computation\",\"className\":\"peer\",\"children\":\"Reward Computation\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n16:[\"$\",\"p\",null,{\"children\":\"Score all responses with the reward model:\"}]\n17:[\"$\",\"p\",null,{\"children\":[\"$\",\"code\",null,{\"children\":\"r_i = R(x, y_i) \\\\quad \\\\text\\\\{for \\\\} i = 1, \\\\ldots, K\"}]}]\n18:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"advantage-estimation\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#advantage-estimation\",\"className\":\"peer\",\"children\":\"Advantage Estimation\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n19:[\"$\",\"p\",null,{\"children\":\"Compute group-relative advantages:\"}]\n1a:[\"$\",\"p\",null,{\"children\":[\"$\",\"code\",null,{\"children\":\"A_i = \\\\frac\\\\{r_i - \\\\mu_r\\\\}\\\\{\\\\sigma_r\\\\}\"}]}]\n1b:[\"$\",\"p\",null,{\"children\":\"Where $\\\\mu_r$ and $\\\\sigma_r$ are the mean and standard deviation of rewards within the group.\"}]\n1c:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"policy-update\",\"children\":[["])</script><script>self.__next_f.push([1,"\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#policy-update\",\"className\":\"peer\",\"children\":\"Policy Update\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n1d:[\"$\",\"p\",null,{\"children\":\"Update the policy to increase probability of high-advantage responses:\"}]\n1e:[\"$\",\"p\",null,{\"children\":[\"$\",\"code\",null,{\"children\":\"\\\\mathcal\\\\{L\\\\}_\\\\{GRPO\\\\} = -\\\\mathbb\\\\{E\\\\}_\\\\{x, y \\\\sim \\\\pi_\\\\theta\\\\}\\\\left[\\\\frac\\\\{\\\\pi_\\\\theta(y|x)\\\\}\\\\{\\\\pi_\\\\{old\\\\}(y|x)\\\\} \\\\cdot A(x, y) \\\\cdot \\\\mathbb\\\\{1\\\\}_\\\\{clip\\\\}\\\\right]\"}]}]\n1f:[\"$\",\"p\",null,{\"children\":\"Where $\\\\mathbb{1}_{clip}$ applies PPO-style clipping to the importance ratio.\"}]\n20:[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"why-group-relative\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#why-group-relative\",\"className\":\"peer\",\"children\":\"Why Group-Relative?\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n21:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"noise-robustness\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#noise-robustness\",\"className\":\"peer\",\"children\":\"Noise Robustness\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n22:[\"$\",\"p\",null,{\"children\":\"Reward models are noisy. A response scored 0.7 versus 0.6 may not be meaningfully better. But within a group of responses to the same prompt, relative ordering is more reliable:\"}]\n23:[\"$\",\"div\",null,{\"className\":\"relative overflow-auto prose-no-margin my-6\",\"children\":[\"$\",\"table\",null,{\"children\":[[\"$\",\"thead\",null,{\"children\":[\"$\",\"tr\",null,{\"children\":[[\"$\",\"th\",null,{\"children\":\"Metric\"}],[\"$\",\"th\",null,{\"children\":\"Absolute Score\"}],[\"$\",\"th\",null,{\"children\":\"Relative Rank\"}]]}]}],[\"$\",\"tbody\",null,{\"children\":[[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"Inter-annotator agreement\"}],[\"$\",\"td\",null,{\"children\":\"0.61\"}],[\"$\",\"td\",null,{\"children\":\"0.83\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"Test-retest reliability\"}],[\"$\",\"td\",null,{\"children\":\"0.54\"}],[\"$\",\"td\",null,{\"children\":\"0.79\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"Reward model calibration\"}],[\"$\",\"td\",null,{\"children\":\"Poor\"}],[\"$\",\"td\",null,{\"children\":\"N/A\"}]]}]]}]]}]}]\n24:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"natural-normalization\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#natural-normalization\",\"className\":\"peer\",\"children\":\"Natural Normalization\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://ww"])</script><script>self.__next_f.push([1,"w.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n25:[\"$\",\"p\",null,{\"children\":\"Group-relative advantages automatically adapt to reward scale and prompt difficulty:\"}]\n26:[\"$\",\"ul\",null,{\"children\":[\"\\n\",[\"$\",\"li\",null,{\"children\":\"Easy prompts: All responses score high, advantages near zero\"}],\"\\n\",[\"$\",\"li\",null,{\"children\":\"Hard prompts: Large variance, clear signal for improvement\"}],\"\\n\",[\"$\",\"li\",null,{\"children\":\"Reward drift: Normalization handles changing baselines\"}],\"\\n\"]}]\n27:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"sample-efficiency\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#sample-efficiency\",\"className\":\"peer\",\"children\":\"Sample Efficiency\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n28:[\"$\",\"p\",null,{\"children\":\"Generating $K$ responses per prompt and comparing them provides $\\\\binom{K}{2}$ pairwise comparisons. For $K=8$, that’s 28 learning signals per prompt versus 1 for standard PPO.\"}]\n29:[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"implementation-details\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#implementation-details\",\"className\":\"peer\",\"children\":\"Implementation Details\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n2a:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"group-size-selection\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#group-size-selection\",\"className\":\"peer\",\"children\":\"Group Size Selection\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n2b:[\"$\",\"p\",null,{\"children\":\"We find $K=8$ provides a good tradeoff:\"}]\n2c:[\"$\",\"div\",null,{\"className\":\"relative overflow-auto prose-no-margin my-6\",\"children\":[\"$\",\"table\",null,{\"children\":[[\"$\",\"thead\",null,{\"children\":[\"$\",\"tr\",null,{\"children\":[[\"$\",\"th\",null,{\"children\":\"K\"}],[\"$\",\"th\",null,{\"children\":\"Compute\"}],[\"$\",\"th\",null,{\"children\":\"Signal Quality\"}],[\"$\",\"th\",null,{\"children\":\"Best Accuracy\"}]]}]}],[\"$\",\"tbody\",null,{\"children\":[[\"$\",\"tr\",null,{\"children\":["])</script><script>self.__next_f.push([1,"[\"$\",\"td\",null,{\"children\":\"2\"}],[\"$\",\"td\",null,{\"children\":\"2x\"}],[\"$\",\"td\",null,{\"children\":\"Low\"}],[\"$\",\"td\",null,{\"children\":\"71.2%\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"4\"}],[\"$\",\"td\",null,{\"children\":\"4x\"}],[\"$\",\"td\",null,{\"children\":\"Medium\"}],[\"$\",\"td\",null,{\"children\":\"74.8%\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"8\"}],[\"$\",\"td\",null,{\"children\":\"8x\"}],[\"$\",\"td\",null,{\"children\":\"High\"}],[\"$\",\"td\",null,{\"children\":\"77.3%\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"16\"}],[\"$\",\"td\",null,{\"children\":\"16x\"}],[\"$\",\"td\",null,{\"children\":\"Marginal gain\"}],[\"$\",\"td\",null,{\"children\":\"77.9%\"}]]}]]}]]}]}]\n2d:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"temperature-schedule\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#temperature-schedule\",\"className\":\"peer\",\"children\":\"Temperature Schedule\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n2e:[\"$\",\"p\",null,{\"children\":\"Higher temperature during response generation increases group diversity:\"}]\n45:T5c0,"])</script><script>self.__next_f.push([1,"\u003csvg viewBox=\"0 0 24 24\"\u003e\u003cpath d=\"M14.25.18l.9.2.73.26.59.3.45.32.34.34.25.34.16.33.1.3.04.26.02.2-.01.13V8.5l-.05.63-.13.55-.21.46-.26.38-.3.31-.33.25-.35.19-.35.14-.33.1-.3.07-.26.04-.21.02H8.77l-.69.05-.59.14-.5.22-.41.27-.33.32-.27.35-.2.36-.15.37-.1.35-.07.32-.04.27-.02.21v3.06H3.17l-.21-.03-.28-.07-.32-.12-.35-.18-.36-.26-.36-.36-.35-.46-.32-.59-.28-.73-.21-.88-.14-1.05-.05-1.23.06-1.22.16-1.04.24-.87.32-.71.36-.57.4-.44.42-.33.42-.24.4-.16.36-.1.32-.05.24-.01h.16l.06.01h8.16v-.83H6.18l-.01-2.75-.02-.37.05-.34.11-.31.17-.28.25-.26.31-.23.38-.2.44-.18.51-.15.58-.12.64-.1.71-.06.77-.04.84-.02 1.27.05zm-6.3 1.98l-.23.33-.08.41.08.41.23.34.33.22.41.09.41-.09.33-.22.23-.34.08-.41-.08-.41-.23-.33-.33-.22-.41-.09-.41.09zm13.09 3.95l.28.06.32.12.35.18.36.27.36.35.35.47.32.59.28.73.21.88.14 1.04.05 1.23-.06 1.23-.16 1.04-.24.86-.32.71-.36.57-.4.45-.42.33-.42.24-.4.16-.36.09-.32.05-.24.02-.16-.01h-8.22v.82h5.84l.01 2.76.02.36-.05.34-.11.31-.17.29-.25.25-.31.24-.38.2-.44.17-.51.15-.58.13-.64.09-.71.07-.77.04-.84.01-1.27-.04-1.07-.14-.9-.2-.73-.25-.59-.3-.45-.33-.34-.34-.25-.34-.16-.33-.1-.3-.04-.25-.02-.2.01-.13v-5.34l.05-.64.13-.54.21-.46.26-.38.3-.32.33-.24.35-.2.35-.14.33-.1.3-.06.26-.04.21-.02.13-.01h5.84l.69-.05.59-.14.5-.21.41-.28.33-.32.27-.35.2-.36.15-.36.1-.35.07-.32.04-.28.02-.21V6.07h2.09l.14.01zm-6.47 14.25l-.23.33-.08.41.08.41.23.33.33.23.41.08.41-.08.33-.23.23-.33.08-.41-.08-.41-.23-.33-.33-.23-.41-.08-.41.08z\" fill=\"currentColor\" /\u003e\u003c/svg\u003e"])</script><script>self.__next_f.push([1,"2f:[\"$\",\"$L44\",null,{\"className\":\"shiki shiki-themes github-light github-dark\",\"style\":{\"--shiki-light\":\"#24292e\",\"--shiki-dark\":\"#e1e4e8\",\"--shiki-light-bg\":\"#fff\",\"--shiki-dark-bg\":\"#24292e\"},\"tabIndex\":\"0\",\"icon\":\"$45\",\"children\":[\"$\",\"$L46\",null,{\"children\":[\"$\",\"code\",null,{\"children\":[[\"$\",\"span\",null,{\"className\":\"line\"}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" def\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#6F42C1\",\"--shiki-dark\":\"#B392F0\"},\"children\":\" sample_group\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"(prompt, policy, K\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\"8\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"):\"}]]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" responses \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" []\"}]]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" for\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" i \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"in\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\" range\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"(K):\"}]]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" temp \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\" 0.7\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" +\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\" 0.3\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" *\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" (i \"}],\"$L47\",\"$L48\",\"$L49\"]}],\"\\n\",\"$L4a\",\"\\n\",\"$L4b\",\"\\n\",\"$L4c\",\"\\n\",\"$L4d\"]}]}]}]\n"])</script><script>self.__next_f.push([1,"30:[\"$\",\"h3\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"kl-regularization\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#kl-regularization\",\"className\":\"peer\",\"children\":\"KL Regularization\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n31:[\"$\",\"p\",null,{\"children\":\"GRPO still benefits from KL regularization, but with reduced sensitivity:\"}]\n32:[\"$\",\"p\",null,{\"children\":[\"$\",\"code\",null,{\"children\":\"\\\\mathcal\\\\{L\\\\} = \\\\mathcal\\\\{L\\\\}_\\\\{GRPO\\\\} + \\\\beta \\\\cdot D_\\\\{KL\\\\}(\\\\pi_\\\\theta || \\\\pi_\\\\{ref\\\\})\"}]}]\n33:[\"$\",\"p\",null,{\"children\":\"We find $\\\\beta = 0.01$ works across tasks, compared to PPO’s typical $\\\\beta \\\\in [0.001, 0.1]$ sensitivity.\"}]\n34:[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"experimental-results\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#experimental-results\",\"className\":\"peer\",\"children\":\"Experimental Results\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n35:[\"$\",\"p\",null,{\"children\":\"On Anthropic’s HH-RLHF benchmark:\"}]\n36:[\"$\",\"div\",null,{\"className\":\"relative overflow-auto prose-no-margin my-6\",\"children\":[\"$\",\"table\",null,{\"children\":[[\"$\",\"thead\",null,{\"children\":[\"$\",\"tr\",null,{\"children\":[[\"$\",\"th\",null,{\"children\":\"Method\"}],[\"$\",\"th\",null,{\"children\":\"Helpfulness\"}],[\"$\",\"th\",null,{\"children\":\"Harmlessness\"}],[\"$\",\"th\",null,{\"children\":\"Compute\"}]]}]}],[\"$\",\"tbody\",null,{\"children\":[[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"SFT\"}],[\"$\",\"td\",null,{\"children\":\"3.2/5\"}],[\"$\",\"td\",null,{\"children\":\"3.8/5\"}],[\"$\",\"td\",null,{\"children\":\"1x\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"PPO\"}],[\"$\",\"td\",null,{\"children\":\"3.9/5\"}],[\"$\",\"td\",null,{\"children\":\"4.1/5\"}],[\"$\",\"td\",null,{\"children\":\"10x\"}]]}],[\"$\",\"tr\",null,{\"children\":[[\"$\",\"td\",null,{\"children\":\"GRPO\"}],[\"$\",\"td\",null,{\"children\":\"4.2/5\"}],[\"$\",\"td\",null,{\"children\":\"4.3/5\"}],[\"$\",\"td\",null,{\"children\":\"8x\"}]]}]]}]]}]}]\n37:[\"$\",\"p\",null,{\"children\":\"GRPO achieves better alignment with less compute through efficient use of generated samples.\"}]\n38:[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"reward-hacking-resistance\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#reward-hacking-resistance\",\"className\":\"peer\",\"children\":\"Reward Hacking Resistance\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n39:[\"$\",\"p\",null,{\"children\":\"GRPO is naturally resistant to reward hacking because:\"}]\n3a:[\"$\",\"ol\",null,{\"children\":[\"\\"])</script><script>self.__next_f.push([1,"n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"Relative comparison\"}],\" : Hacked responses must beat other responses, not just achieve high absolute score\"]}],\"\\n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"Diverse sampling\"}],\" : Temperature variation produces varied response styles\"]}],\"\\n\",[\"$\",\"li\",null,{\"children\":[[\"$\",\"strong\",null,{\"children\":\"Group normalization\"}],\" : Exploits that boost all responses equally provide no gradient\"]}],\"\\n\"]}]\n3b:[\"$\",\"p\",null,{\"children\":\"We observe significantly less length gaming and repetition compared to PPO.\"}]\n3c:[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"code\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#code\",\"className\":\"peer\",\"children\":\"Code\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 24\",\"fill\":\"none\",\"stroke\":\"currentColor\",\"strokeWidth\":2,\"strokeLinecap\":\"round\",\"strokeLinejoin\":\"round\",\"className\":\"lucide lucide-link size-3.5 shrink-0 text-fd-muted-foreground opacity-0 transition-opacity peer-hover:opacity-100\",\"aria-hidden\":true,\"children\":[[\"$\",\"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\"]}]]}]\n3d:[\"$\",\"p\",null,{\"children\":\"Reference implementation:\"}]\n4e:T5c0,"])</script><script>self.__next_f.push([1,"\u003csvg viewBox=\"0 0 24 24\"\u003e\u003cpath d=\"M14.25.18l.9.2.73.26.59.3.45.32.34.34.25.34.16.33.1.3.04.26.02.2-.01.13V8.5l-.05.63-.13.55-.21.46-.26.38-.3.31-.33.25-.35.19-.35.14-.33.1-.3.07-.26.04-.21.02H8.77l-.69.05-.59.14-.5.22-.41.27-.33.32-.27.35-.2.36-.15.37-.1.35-.07.32-.04.27-.02.21v3.06H3.17l-.21-.03-.28-.07-.32-.12-.35-.18-.36-.26-.36-.36-.35-.46-.32-.59-.28-.73-.21-.88-.14-1.05-.05-1.23.06-1.22.16-1.04.24-.87.32-.71.36-.57.4-.44.42-.33.42-.24.4-.16.36-.1.32-.05.24-.01h.16l.06.01h8.16v-.83H6.18l-.01-2.75-.02-.37.05-.34.11-.31.17-.28.25-.26.31-.23.38-.2.44-.18.51-.15.58-.12.64-.1.71-.06.77-.04.84-.02 1.27.05zm-6.3 1.98l-.23.33-.08.41.08.41.23.34.33.22.41.09.41-.09.33-.22.23-.34.08-.41-.08-.41-.23-.33-.33-.22-.41-.09-.41.09zm13.09 3.95l.28.06.32.12.35.18.36.27.36.35.35.47.32.59.28.73.21.88.14 1.04.05 1.23-.06 1.23-.16 1.04-.24.86-.32.71-.36.57-.4.45-.42.33-.42.24-.4.16-.36.09-.32.05-.24.02-.16-.01h-8.22v.82h5.84l.01 2.76.02.36-.05.34-.11.31-.17.29-.25.25-.31.24-.38.2-.44.17-.51.15-.58.13-.64.09-.71.07-.77.04-.84.01-1.27-.04-1.07-.14-.9-.2-.73-.25-.59-.3-.45-.33-.34-.34-.25-.34-.16-.33-.1-.3-.04-.25-.02-.2.01-.13v-5.34l.05-.64.13-.54.21-.46.26-.38.3-.32.33-.24.35-.2.35-.14.33-.1.3-.06.26-.04.21-.02.13-.01h5.84l.69-.05.59-.14.5-.21.41-.28.33-.32.27-.35.2-.36.15-.36.1-.35.07-.32.04-.28.02-.21V6.07h2.09l.14.01zm-6.47 14.25l-.23.33-.08.41.08.41.23.33.33.23.41.08.41-.08.33-.23.23-.33.08-.41-.08-.41-.23-.33-.33-.23-.41-.08-.41.08z\" fill=\"currentColor\" /\u003e\u003c/svg\u003e"])</script><script>self.__next_f.push([1,"3e:[\"$\",\"$L44\",null,{\"className\":\"shiki shiki-themes github-light github-dark\",\"style\":{\"--shiki-light\":\"#24292e\",\"--shiki-dark\":\"#e1e4e8\",\"--shiki-light-bg\":\"#fff\",\"--shiki-dark-bg\":\"#24292e\"},\"tabIndex\":\"0\",\"icon\":\"$4e\",\"children\":[\"$\",\"$L46\",null,{\"children\":[\"$\",\"code\",null,{\"children\":[[\"$\",\"span\",null,{\"className\":\"line\"}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" def\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#6F42C1\",\"--shiki-dark\":\"#B392F0\"},\"children\":\" grpo_loss\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"(policy, prompts, reward_model, K\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\"8\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\", clip_eps\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\"0.2\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"):\"}]]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" losses \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" []\"}]]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" for\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" prompt \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"in\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" prompts:\"}]]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#6A737D\",\"--shiki-dark\":\"#6A737D\"},\"children\":\" # Generate response group\"}]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" responses \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" sample_group(prompt, policy, K)\"}]]}],\"\\n\",\"$L4f\",\"\\n\",\"$L50\",\"\\n\",\"$L51\",\"\\n\",\"$L52\",\"\\n\",\"$L53\",\"\\n\",\"$L54\",\"\\n\",\"$L55\",\"\\n\",\"$L56\",\"\\n\",\"$L57\",\"\\n\",\"$L58\",\"\\n\",\"$L59\",\"\\n\",\"$L5a\",\"\\n\",\"$L5b\",\"\\n\",\"$L5c\"]}]}]}]\n"])</script><script>self.__next_f.push([1,"3f:[\"$\",\"h2\",null,{\"className\":\"flex scroll-m-28 flex-row items-center gap-2\",\"id\":\"conclusion\",\"children\":[[\"$\",\"a\",null,{\"data-card\":\"\",\"href\":\"#conclusion\",\"className\":\"peer\",\"children\":\"Conclusion\"}],[\"$\",\"svg\",null,{\"ref\":\"$undefined\",\"xmlns\":\"http://www.w3.org/2000/svg\",\"width\":24,\"height\":24,\"viewBox\":\"0 0 24 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\"}],\"$undefined\"]}]]}]\n40:[\"$\",\"p\",null,{\"children\":\"GRPO offers a simple improvement to RLHF: generate multiple responses, compare them relatively, update toward the best. This approach is more robust, more sample-efficient, and more resistant to reward hacking than standard PPO.\"}]\n41:[\"$\",\"p\",null,{\"children\":\"The algorithm is simple enough to implement in an afternoon. The gains are substantial enough to matter.\"}]\n42:[\"$\",\"hr\",null,{}]\n43:[\"$\",\"p\",null,{\"children\":[\"$\",\"em\",null,{\"children\":\"Full details in “Group Relative Policy Optimization for Language Model Alignment” (2022). Code at github.com/zen-ai/grpo.\"}]}]\n"])</script><script>self.__next_f.push([1,"47:[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"/\"}]\n48:[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" K) \"}]\n49:[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#6A737D\",\"--shiki-dark\":\"#6A737D\"},\"children\":\"# 0.7 to 1.0\"}]\n4a:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" response \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" policy.sample(prompt, \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#E36209\",\"--shiki-dark\":\"#FFAB70\"},\"children\":\"temperature\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"temp)\"}]]}]\n4b:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" responses.append(response)\"}]}]\n4c:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" return\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" responses\"}]]}]\n4d:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" \"}]}]\n4f:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" \"}]}]\n50:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#6A737D\",\"--shiki-dark\":\"#6A737D\"},\"children\":\" # Compute rewards and advantages\"}]}]\n51:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" rewards \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" [reward_model(prompt, r) \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"for\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" r \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"in\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" responses]\"}]]}]\n52:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" advantages \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" (rewards \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"-\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" np.mean(rewards)) \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"/\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" (np.std(rewards) \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"+\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\" 1e-8\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\")\"}]]}]\n53:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" \"}]}]\n54:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#6A737D\",\"--shiki-dark\":\"#6A"])</script><script>self.__next_f.push([1,"737D\"},\"children\":\" # Policy loss\"}]}]\n55:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" for\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" response, advantage \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"in\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\" zip\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"(responses, advantages):\"}]]}]\n56:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" ratio \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" policy.prob(response) \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"/\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" policy.prob_old(response)\"}]]}]\n57:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" clipped \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" torch.clamp(ratio, \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\"1\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"-\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"clip_eps, \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#005CC5\",\"--shiki-dark\":\"#79B8FF\"},\"children\":\"1\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"+\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"clip_eps)\"}]]}]\n58:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" loss \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"=\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" -\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\"torch.min(ratio \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"*\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" advantage, clipped \"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\"*\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" advantage)\"}]]}]\n59:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" losses.append(loss)\"}]}]\n5a:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" \"}]}]\n5b:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#D73A49\",\"--shiki-dark\":\"#F97583\"},\"children\":\" return\"}],[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" torch.mean(torch.stack(losses))\"}]]}]\n5c:[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"style\":{\"--shiki-light\":\"#24292E\",\"--shiki-dark\":\"#E1E4E8\"},\"children\":\" \"}]}]\n"])</script><script>self.__next_f.push([1,"b:[[\"$\",\"meta\",\"0\",{\"charSet\":\"utf-8\"}],[\"$\",\"meta\",\"1\",{\"name\":\"viewport\",\"content\":\"width=device-width, initial-scale=1\"}],[\"$\",\"meta\",\"2\",{\"name\":\"theme-color\",\"media\":\"(prefers-color-scheme: dark)\",\"content\":\"#0A0A0A\"}],[\"$\",\"meta\",\"3\",{\"name\":\"theme-color\",\"media\":\"(prefers-color-scheme: light)\",\"content\":\"#fff\"}]]\n"])</script><script>self.__next_f.push([1,"9:null\nd:[[\"$\",\"title\",\"0\",{\"children\":\"GRPO: Group Relative Policy Optimization — Zen LM Blog | Zen LM\"}],[\"$\",\"meta\",\"1\",{\"name\":\"description\",\"content\":\"A companion post to our GRPO paper, explaining group relative policy optimization for language model alignment.\"}],[\"$\",\"meta\",\"2\",{\"property\":\"og:title\",\"content\":\"Zen LM - Open Foundation Models\"}],[\"$\",\"meta\",\"3\",{\"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.\"}],[\"$\",\"meta\",\"4\",{\"property\":\"og:url\",\"content\":\"https://zenlm.org\"}],[\"$\",\"meta\",\"5\",{\"property\":\"og:site_name\",\"content\":\"Zen LM\"}],[\"$\",\"meta\",\"6\",{\"property\":\"og:type\",\"content\":\"website\"}],[\"$\",\"meta\",\"7\",{\"name\":\"twitter:card\",\"content\":\"summary_large_image\"}],[\"$\",\"meta\",\"8\",{\"name\":\"twitter:site\",\"content\":\"@zenlmorg\"}],[\"$\",\"meta\",\"9\",{\"name\":\"twitter:creator\",\"content\":\"@zenlmorg\"}],[\"$\",\"meta\",\"10\",{\"name\":\"twitter:title\",\"content\":\"Zen LM - Open Foundation Models\"}],[\"$\",\"meta\",\"11\",{\"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.\"}]]\n"])</script><script>
|
||
(function(){
|
||
// After React renders the lotus emoji from RSC payload, walk the DOM
|
||
// and replace it with the enso SVG. Polls so subsequent React re-renders
|
||
// also get cleaned up.
|
||
function swap(){
|
||
// 1. Replace lotus + ' Zen LM' text inside <a> brand links
|
||
document.querySelectorAll('a').forEach(function(a){
|
||
if (a.dataset.zenLotusSwapped) return;
|
||
var t = (a.textContent || '');
|
||
if (!/.*Zen LM|Zen LM.*/.test(t)) return;
|
||
// Find the lotus text node specifically
|
||
var walker = document.createTreeWalker(a, NodeFilter.SHOW_TEXT, null);
|
||
var node;
|
||
while ((node = walker.nextNode())) {
|
||
if (node.nodeValue && node.nodeValue.indexOf('') !== -1) {
|
||
node.nodeValue = node.nodeValue.replace(/\s?/g, '');
|
||
}
|
||
}
|
||
// Inject enso SVG at start
|
||
if (!a.querySelector('svg[aria-label="Zen LM"]')) {
|
||
var ns = 'http://www.w3.org/2000/svg';
|
||
var svg = document.createElementNS(ns, 'svg');
|
||
svg.setAttribute('viewBox', '0 0 512 512');
|
||
svg.setAttribute('fill', 'none');
|
||
svg.setAttribute('width', '18');
|
||
svg.setAttribute('height', '18');
|
||
svg.setAttribute('aria-label', 'Zen LM');
|
||
svg.style.cssText = 'display:inline-block;vertical-align:-2px;margin-right:6px;flex-shrink:0';
|
||
var p = document.createElementNS(ns, 'path');
|
||
p.setAttribute('d', 'M 256 84 A 172 172 0 1 0 256 428 A 172 172 0 1 0 256 84 Z');
|
||
p.setAttribute('stroke', 'currentColor');
|
||
p.setAttribute('stroke-width', '26');
|
||
p.setAttribute('stroke-linecap', 'round');
|
||
p.setAttribute('stroke-linejoin', 'round');
|
||
svg.appendChild(p);
|
||
a.insertBefore(svg, a.firstChild);
|
||
}
|
||
a.dataset.zenLotusSwapped = '1';
|
||
});
|
||
}
|
||
function start(){ swap(); setInterval(swap, 600); }
|
||
if (document.readyState !== 'loading') start();
|
||
else document.addEventListener('DOMContentLoaded', start);
|
||
})();
|
||
</script>
|
||
|
||
<style id="zenlm-brand-anim">
|
||
@keyframes zenlm-brand-draw { to { stroke-dashoffset: 0; } }
|
||
svg.zenlm-brand-svg .zenlm-brand-path {
|
||
stroke-dasharray: 1100;
|
||
stroke-dashoffset: 1100;
|
||
animation: zenlm-brand-draw 1.4s cubic-bezier(.45,0,.2,1) 0.1s 1 forwards;
|
||
}
|
||
.zen-link-icon { display: inline-block; vertical-align: middle; flex-shrink: 0; }
|
||
</style></body></html> |