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

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

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<!DOCTYPE html><!--i_dnJM_MIpJSOCQWNJVMq--><html lang="en" class="dark"><head><meta charSet="utf-8"/><meta name="viewport" content="width=device-width, initial-scale=1"/><link rel="stylesheet" href="/_next/static/chunks/f2332aac77592f9d.css" data-precedence="next"/><link rel="preload" as="script" fetchPriority="low" href="/_next/static/chunks/e83606e8fa9cc796.js"/><script src="/_next/static/chunks/36d6595f0156cd7e.js" async=""></script><script src="/_next/static/chunks/040e9cea20a8d9c7.js" async=""></script><script src="/_next/static/chunks/d4dffb5a0973d49c.js" async=""></script><script src="/_next/static/chunks/turbopack-967f27a9fd33556d.js" async=""></script><script src="/_next/static/chunks/59d0ad1b64f8544e.js" async=""></script><script src="/_next/static/chunks/4d80e004cf4896dd.js" async=""></script><script src="/_next/static/chunks/350ee4303b732916.js" async=""></script><script src="/_next/static/chunks/8de849ca74fc071f.js" async=""></script><script src="/_next/static/chunks/e62b91212ee7f8ff.js" async=""></script><script src="/_next/static/chunks/f19fe44237e54646.js" async=""></script><script src="/_next/static/chunks/cb0a883bafeb6805.js" async=""></script><meta name="theme-color" media="(prefers-color-scheme: dark)" content="#0A0A0A"/><meta name="theme-color" media="(prefers-color-scheme: light)" content="#fff"/><title>SuRe + OPCM: Production-Grade Continual Learning for Open Models — Zen LM Blog | Zen LM</title><meta name="description" content="Deep dive on Surprise-Driven Prioritized Replay (SuRe) and Orthogonal Projection Continual Merging (OPCM) — the two SOTA techniques we use for catastrophic-forgetting-free LLM adaptation in the Zen model family."/><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">February 27, 2026</time><h1 class="text-3xl font-bold mt-2 mb-3">SuRe + OPCM: Production-Grade Continual Learning for Open Models</h1><p class="text-fd-muted-foreground text-lg mb-4">Deep dive on Surprise-Driven Prioritized Replay (SuRe) and Orthogonal Projection Continual Merging (OPCM) — the two SOTA techniques we use for catastrophic-forgetting-free LLM adaptation in the Zen model family.</p><div class="flex items-center gap-3 pt-4 border-t border-fd-border"><span class="text-sm text-fd-muted-foreground">By <!-- -->Zen LM Team</span><div class="flex gap-1.5 ml-auto"><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">Continual Learning</span><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">SuRe</span><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">OPCM</span><span class="text-[10px] font-mono uppercase tracking-wider bg-fd-muted text-fd-muted-foreground px-1.5 py-0.5 rounded">OPLoRA</span></div></div></div><div class="prose dark:prose-invert max-w-none"><p><a href="https://arxiv.org/abs/2510.13003" rel="noreferrer noopener" target="_blank">OPLoRA PAPER</a> <a href="https://arxiv.org/abs/2511.22367" rel="noreferrer noopener" target="_blank">SuRe PAPER</a> <a href="https://arxiv.org/abs/2501.09522" rel="noreferrer noopener" target="_blank">OPCM PAPER</a> <a href="https://arxiv.org/abs/2512.24615" rel="noreferrer noopener" target="_blank">YOUTU-AGENT PAPER</a></p>
<p>Every production LLM faces the same brutal constraint: the moment you start adapting a model on new data, it begins forgetting what it already knew. This is catastrophic forgetting — and it is not a theoretical concern. It is the reason most “continually updated” models in production are quietly replaced wholesale every few months rather than genuinely updated in place.</p>
<p>For the Zen model family, wholesale replacement is not acceptable. We ship models that users build workflows around. Breaking behavioral continuity is a product failure, not just a research inconvenience. This post describes the four-technique stack we have assembled to solve this: <strong>OPLoRA</strong> , <strong>SuRe</strong> , <strong>OPCM</strong> , and <strong>Youtu-Agent</strong>.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="the-plasticity-stability-dilemma"><a data-card="" href="#the-plasticity-stability-dilemma" class="peer">The Plasticity-Stability Dilemma</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>The core tension is simple. A model that adapts quickly to new distributions (high plasticity) tends to overwrite representations needed for old tasks (low stability). A model frozen to preserve old capabilities cannot learn anything new. Both extremes are useless in production.</p>
<p>For LLMs specifically, the problem is compounded by scale. You cannot afford to retrain the full model on a joint corpus every time new data arrives — at 480B parameters that is measured in millions of dollars per update. Fine-tuning on new data alone causes forgetting. Replay of old data is expensive and raises data-licensing questions. The field has known this problem for decades but only recently produced techniques that work at LLM scale.</p>
<p>We use four papers from late 2024 / early 2025, each addressing a different layer of the problem.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="oplora-orthogonal-parameter-updates"><a data-card="" href="#oplora-orthogonal-parameter-updates" class="peer">OPLoRA: Orthogonal Parameter Updates</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><strong>Paper</strong> : arXiv:2510.13003</p>
<p>The simplest insight in continual learning is that not all parameter directions are equally important. The top singular vectors of the base model’s weight matrices encode the most “load-bearing” representations — the ones responsible for broad capabilities. Fine-tuning along those directions is how forgetting happens.</p>
<p>OPLoRA adds a projection step after each LoRA update. Let <code>Δ = BA</code> be the standard low-rank update (B ∈ ℝ^{d×r}, A ∈ ℝ^{r×k}). Before applying this update, we project it onto the orthogonal complement of the base model’s top singular subspace:</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"><span></span></span>
<span class="line"><span> Δ_orth = Δ - V_k V_k^T Δ</span></span>
<span class="line"><span> </span></span></code></pre></div></figure>
<p>where <code>V_k</code> are the top-k right singular vectors of the pretrained weight matrix W₀. The result: updates flow only through directions that the base model does not heavily use. New knowledge accumulates in the null space of the existing representation.</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch</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"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> oplora_project</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(delta: torch.Tensor, base_weight: torch.Tensor, k: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">int</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 64</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">) -&gt; torch.Tensor:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> &quot;&quot;&quot;Project LoRA update onto orthogonal complement of base weight top-k subspace.&quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Compute top-k right singular vectors of base weight</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> _, _, Vt </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.linalg.svd(base_weight, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">full_matrices</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">False</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> V_k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> Vt[:k].T </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"># shape: (d_out, k)</span></span>
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Project delta onto orthogonal complement</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> projection </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> V_k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> (V_k.T </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> projection</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"> class</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> OPLoRALayer</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0">torch</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0">nn</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0">Module</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">):</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, base_weight: torch.Tensor, rank: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">int</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 16</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">, k: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">int</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 64</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">):</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> super</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">().</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">__init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">()</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> d_out, d_in </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> base_weight.shape</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.base_weight </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> base_weight</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> k</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.lora_A </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.nn.Parameter(torch.randn(rank, d_in) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">*</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 0.01</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.lora_B </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.nn.Parameter(torch.zeros(d_out, rank))</span></span>
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Cache top-k right singular vectors</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> with</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.no_grad():</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> _, _, Vt </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.linalg.svd(base_weight, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">full_matrices</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">False</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.register_buffer(</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF">&#x27;V_k&#x27;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">, Vt[:k].T)</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"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> forward</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, x: torch.Tensor) -&gt; torch.Tensor:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.lora_B </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.lora_A</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta_orth </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.V_k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.V_k.T </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> x </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.base_weight </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">+</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> delta_orth).T</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span></code></pre></div></figure>
<p>The k hyperparameter controls the trade-off: larger k preserves more of the base model but leaves less room for new knowledge. We use k=64 for most Zen fine-tuning passes.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="sure-surprise-driven-prioritized-replay"><a data-card="" href="#sure-surprise-driven-prioritized-replay" class="peer">SuRe: Surprise-Driven Prioritized Replay</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><strong>Paper</strong> : arXiv:2511.22367</p>
<p>Replay-based continual learning maintains a buffer of old examples and mixes them into each training batch. The problem is buffer efficiency: most buffered examples are easy for the current model and contribute nothing. SuRe fixes this with surprise-based prioritization.</p>
<p>The surprise score for a token sequence x_t is simply the negative log-likelihood under the current model:</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"><span></span></span>
<span class="line"><span> r_t = -log p_θ(x_t | x_{&lt;t})</span></span>
<span class="line"><span> </span></span></code></pre></div></figure>
<p>High surprise means the current model is uncertain about this sequence — it is more likely to be a case where forgetting is occurring. SuRe preferentially replays high-surprise examples, maximizing the utility of a fixed replay budget.</p>
<p>Beyond replay prioritization, SuRe introduces a <strong>dual EMA</strong> (Exponential Moving Average) adapter structure:</p>
<ul>
<li><strong>Fast LoRA</strong> θ_f: high learning rate, adapts quickly to new data</li>
<li><strong>Slow LoRA</strong> θ_s: low learning rate, tracks long-run behavioral drift</li>
</ul>
<p>At merge time, the two adapters are combined:</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"><span></span></span>
<span class="line"><span> θ_merged = (1-α)θ_s + αθ_f</span></span>
<span class="line"><span> </span></span></code></pre></div></figure>
<p>where α is a schedule parameter (typically 0.3). The slow adapter acts as a stability anchor while the fast adapter absorbs new signal. On the LNT (Learn-Not-To-Forget) benchmark, SuRe delivers +5 accuracy points over standard replay.</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> heapq</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> from</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> collections </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> deque</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> from</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> dataclasses </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> dataclass, field</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> from</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> typing </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> List, Tuple</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span>
<span class="line"><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> @dataclass</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(</span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">order</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">True</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> class</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> ReplayItem</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> surprise: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">float</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> sequence: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">object</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> field(</span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">compare</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">False</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:#D73A49;--shiki-dark:#F97583"> class</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> SuReBuffer</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, capacity: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">int</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 10_000</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">):</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.capacity </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> capacity</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap: List[ReplayItem] </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> [] </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"># min-heap (lowest surprise at top)</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"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> add</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, sequence, model: torch.nn.Module, tokenizer) -&gt; </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">None</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> with</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.no_grad():</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> inputs </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> tokenizer(sequence, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">return_tensors</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF">&#x27;pt&#x27;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> outputs </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> model(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">**</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">inputs, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">labels</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">inputs[</span><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF">&#x27;input_ids&#x27;</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">])</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> surprise </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> outputs.loss.item() </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"># mean NLL = surprise score</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> item </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> ReplayItem(</span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">surprise</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">surprise, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">sequence</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">sequence)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> if</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> len</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">&lt;</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.capacity:</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> heapq.heappush(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap, item)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> elif</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> surprise </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">&gt;</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">0</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">].surprise:</span></span>
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Replace lowest-surprise item with this higher-surprise one</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> heapq.heapreplace(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap, item)</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"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> sample</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, n: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">) -&gt; List[</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">str</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">]:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> &quot;&quot;&quot;Sample n items, weighted toward high surprise.&quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> if</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> not</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> []</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> items </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> sorted</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">._heap, </span><span style="--shiki-light:#E36209;--shiki-dark:#FFAB70">key</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=lambda</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> x: </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">x.surprise)</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> [item.sequence </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> item </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">in</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> items[:n]]</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"> class</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> DualEMAAdapter</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">:</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, fast_lr: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">float</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 1e-3</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">, slow_lr: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">float</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> =</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> 1e-5</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">, alpha: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">float</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:#24292E;--shiki-dark:#E1E4E8">):</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.fast_lr </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> fast_lr</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.slow_lr </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> slow_lr</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.alpha </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> alpha</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"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> merge</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, theta_fast: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">dict</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">, theta_slow: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">dict</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">) -&gt; </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">dict</span><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"> {</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> k: (</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">1</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> -</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.alpha) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> theta_slow[k] </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">+</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.alpha </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">*</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> theta_fast[k]</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> for</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> k </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">in</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> theta_fast</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> }</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span></code></pre></div></figure>
<p>In practice we run SuRe with a buffer of 50K sequences, sampling 512 high-surprise examples per training batch alongside 512 new-data examples. The buffer is refreshed every 1K steps as model NLL scores shift.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="opcm-orthogonal-projection-continual-merging"><a data-card="" href="#opcm-orthogonal-projection-continual-merging" class="peer">OPCM: Orthogonal Projection Continual Merging</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><strong>Paper</strong> : arXiv:2501.09522</p>
<p>OPLoRA and SuRe handle forgetting during training. OPCM handles forgetting during <strong>merging</strong> — the step where multiple LoRA adapters trained on different task sequences are combined into a single weight delta.</p>
<p>Naive merging (simple average of adapter weights) produces interference between tasks. OPCM applies sequential orthogonal projection: when merging adapter k+1 into the accumulated projection matrix, it removes the component that interferes with previously merged adapters.</p>
<p>The update rule for the projection matrix P is:</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"><span></span></span>
<span class="line"><span> P_{k+1} = P_k - P_k φ_k^T (φ_k P_k φ_k^T)^{-1} φ_k P_k</span></span>
<span class="line"><span> </span></span></code></pre></div></figure>
<p>where φ_k is the gradient direction (or adapter weight direction) of the k-th task. This is the standard Gram-Schmidt orthogonalization applied iteratively to the task gradient subspace.</p>
<p>The memory cost is O(|θ|) — a single projection matrix regardless of the number of tasks. This is a significant improvement over methods that cache full gradient histories. On sequential merge benchmarks, OPCM achieves 5-8% better retention than simultaneous averaging.</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> import</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch</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"> class</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> OPCMStep</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> &quot;&quot;&quot;One step of Orthogonal Projection Continual Merging.&quot;&quot;&quot;</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"> def</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> __init__</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, param_dim: </span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">int</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">):</span></span>
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # P starts as identity — first task goes through unchanged</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.P </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.eye(param_dim)</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"> def</span><span style="--shiki-light:#6F42C1;--shiki-dark:#B392F0"> merge</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">(self, phi: torch.Tensor) -&gt; torch.Tensor:</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> phi: task gradient direction (flattened), shape (d,)</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> Returns: projected phi that is orthogonal to all previous tasks.</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> Updates self.P for the next call.</span></span>
<span class="line"><span style="--shiki-light:#032F62;--shiki-dark:#9ECBFF"> &quot;&quot;&quot;</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> phi_flat </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> phi.view(</span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF">1</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">)</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> Pp </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.P </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> phi_flat</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> denom </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> phi_flat </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">@</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> Pp </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"># scalar: φ P φ^T</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> if</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> denom.abs() </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">&lt;</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:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> Pp </span><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"># already orthogonal</span></span>
<span class="line"><span style="--shiki-light:#6A737D;--shiki-dark:#6A737D"> # Project P to remove this task&#x27;s direction</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> outer </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> torch.outer(Pp, Pp) </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">/</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> denom</span></span>
<span class="line"><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.P </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">=</span><span style="--shiki-light:#005CC5;--shiki-dark:#79B8FF"> self</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8">.P </span><span style="--shiki-light:#D73A49;--shiki-dark:#F97583">-</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> outer</span></span>
<span class="line"><span style="--shiki-light:#D73A49;--shiki-dark:#F97583"> return</span><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> Pp</span></span>
<span class="line"><span style="--shiki-light:#24292E;--shiki-dark:#E1E4E8"> </span></span></code></pre></div></figure>
<p>The key insight is ordering: merge tasks from largest to smallest gradient norm. This ensures the most influential task anchors the subspace, and subsequent tasks fill in orthogonal directions.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="youtu-agent-training-free-grpo-at-inference-time"><a data-card="" href="#youtu-agent-training-free-grpo-at-inference-time" class="peer">Youtu-Agent: Training-Free GRPO at Inference Time</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><strong>Paper</strong> : arXiv:2512.24615</p>
<p>The three techniques above handle training-time continual learning. Youtu-Agent addresses a different but related problem: <strong>eval-time adaptation</strong> without any weight updates.</p>
<p>Standard GRPO (Group Relative Policy Optimization) requires gradient computation — you sample multiple completions, score them, and backpropagate the relative reward signal. Youtu-Agent replaces gradient updates with in-context example accumulation.</p>
<p>The mechanism: maintain an <strong>experience ledger</strong> of (prompt, completion, reward) triples. When a new prompt arrives, retrieve the highest-reward examples for similar prompts and include them in the context window. The model effectively performs few-shot adaptation on its own high-quality past outputs.</p>
<p>This is training-free GRPO: the policy “improves” through demonstration rather than parameter updates. On AIME 2024, Youtu-Agent delivers +2.7% accuracy with zero weight updates. The experience ledger is updated online as new completions are scored.</p>
<p>For Zen, we run Youtu-Agent as a lightweight inference-time layer: the ledger is stored in Redis, similarity search uses Zen Embedding (7680-dim), and retrieval adds ~15ms to inference latency.</p>
<h2 class="flex scroll-m-28 flex-row items-center gap-2" id="how-these-four-stack-for-zen"><a data-card="" href="#how-these-four-stack-for-zen" class="peer">How These Four Stack for Zen</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>The four techniques operate at different timescales and are composable:</p>
<figure dir="ltr" class="my-4 bg-fd-card rounded-xl shiki relative border shadow-sm not-prose overflow-hidden text-sm shiki shiki-themes github-light github-dark" style="--shiki-light:#24292e;--shiki-dark:#e1e4e8;--shiki-light-bg:#fff;--shiki-dark-bg:#24292e" tabindex="-1"><div class="empty:hidden absolute top-3 right-2 z-2 backdrop-blur-lg rounded-lg text-fd-muted-foreground"><button type="button" class="inline-flex items-center justify-center rounded-md text-sm font-medium transition-colors duration-100 disabled:pointer-events-none disabled:opacity-50 focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-fd-ring p-1 [&amp;_svg]:size-4 hover:text-fd-accent-foreground data-checked:text-fd-accent-foreground" aria-label="Copy Text"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clipboard" aria-hidden="true"><rect width="8" height="4" x="8" y="2" rx="1" ry="1"></rect><path d="M16 4h2a2 2 0 0 1 2 2v14a2 2 0 0 1-2 2H6a2 2 0 0 1-2-2V6a2 2 0 0 1 2-2h2"></path></svg></button></div><div role="region" tabindex="0" class="text-[0.8125rem] py-3.5 overflow-auto max-h-[600px] fd-scroll-container focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-inset focus-visible:ring-fd-ring" style="--padding-right:calc(var(--spacing) * 8)"><pre class="min-w-full w-max *:flex *:flex-col"><code><span class="line"><span></span></span>
<span class="line"><span> 1. OPLoRA base training</span></span>
<span class="line"><span> └─ All Zen fine-tuning uses OPLoRA projection</span></span>
<span class="line"><span> Prevents overwriting base model subspace</span></span>
<span class="line"><span> </span></span>
<span class="line"><span> 2. SuRe replay (every training step)</span></span>
<span class="line"><span> └─ High-surprise buffer examples mixed into batches</span></span>
<span class="line"><span> Dual EMA adapters maintain plasticity-stability balance</span></span>
<span class="line"><span> </span></span>
<span class="line"><span> 3. OPCM periodic merge (every 1K-10K steps)</span></span>
<span class="line"><span> └─ Sequential adapter merging with orthogonal projection</span></span>
<span class="line"><span> Accumulated knowledge coexists without interference</span></span>
<span class="line"><span> </span></span>
<span class="line"><span> 4. Youtu-Agent at inference (online)</span></span>
<span class="line"><span> └─ Experience ledger enables training-free behavioral adaptation</span></span>
<span class="line"><span> Zero weight updates, ~15ms overhead</span></span>
<span class="line"><span> </span></span></code></pre></div></figure>
<p>In production, layers 1-3 run during scheduled training passes (nightly for Zen nano/eco, weekly for larger models). Layer 4 is always active.</p>
<p>The combined result: Zen models accumulate behavioral improvements continuously without the forgetting catastrophes that plague naive fine-tuning. We have run this stack for three months on zen-nano with zero regressions on our standard capability benchmarks across 47 sequential fine-tuning events.</p>
<p>The code for all four components is available in the <a href="https://github.com/zenlm/zen-trainer" rel="noreferrer noopener" target="_blank">zen-trainer repository</a>.</p>
<hr/>
<p><em>Zen LM is a joint initiative of Hanzo AI Inc. 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OPCM applies sequential orthogonal projection: when merging adapter k+1 into the accumulated projection matrix, it removes the component that interferes with previously merged adapters.\"}]\n2e:[\"$\",\"p\",null,{\"children\":\"The update rule for the projection matrix P is:\"}]\n2f:[\"$\",\"$L43\",null,{\"className\":\"shiki shiki-themes github-light github-dark\",\"style\":{\"--shiki-light\":\"#24292e\",\"--shiki-dark\":\"#e1e4e8\",\"--shiki-light-bg\":\"#fff\",\"--shiki-dark-bg\":\"#24292e\"},\"tabIndex\":\"0\",\"icon\":\"\u003csvg viewBox=\\\"0 0 24 24\\\"\u003e\u003cpath d=\\\"M 6,1 C 4.354992,1 3,2.354992 3,4 v 16 c 0,1.645008 1.354992,3 3,3 h 12 c 1.645008,0 3,-1.354992 3,-3 V 8 7 A 1.0001,1.0001 0 0 0 20.707031,6.2929687 l -5,-5 A 1.0001,1.0001 0 0 0 15,1 h -1 z m 0,2 h 7 v 3 c 0,1.645008 1.354992,3 3,3 h 3 v 11 c 0,0.564129 -0.435871,1 -1,1 H 6 C 5.4358712,21 5,20.564129 5,20 V 4 C 5,3.4358712 5.4358712,3 6,3 Z M 15,3.4140625 18.585937,7 H 16 C 15.435871,7 15,6.5641288 15,6 Z\\\" fill=\\\"currentColor\\\" /\u003e\u003c/svg\u003e\",\"children\":[\"$\",\"$L44\",null,{\"children\":[\"$\",\"code\",null,{\"children\":[[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{}]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"children\":\" P_{k+1} = P_k - P_k φ_k^T (φ_k P_k φ_k^T)^{-1} φ_k P_k\"}]}],\"\\n\",[\"$\",\"span\",null,{\"className\":\"line\",\"children\":[\"$\",\"span\",null,{\"children\":\" \"}]}]]}]}]}]\n30:[\"$\",\"p\",null,{\"children\":\"where φ_k is the gradient direction (or adapter weight direction) of the k-th task. 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