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authorYurenHao0426 <Blackhao0426@gmail.com>2026-07-30 02:50:54 -0500
committerYurenHao0426 <Blackhao0426@gmail.com>2026-07-30 02:50:59 -0500
commit71f5be89085eb21c9c31d3563f344b75f7a2cb7c (patch)
tree229b17e13523f16222a03722f65dd6c6a52fd891
parent2ac145ed97ea81d0606c7c5b9fa71fd3e7336296 (diff)
Rewrite grant project page
Diffstat
-rw-r--r--index.html1758
1 files changed, 1429 insertions, 329 deletions
diff --git a/index.html b/index.html
index 334895b..bd76651 100644
--- a/index.html
+++ b/index.html
@@ -1,366 +1,1466 @@
-<!DOCTYPE html>
+<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
-
- <!-- Primary Meta Tags -->
- <meta name="title" content="PAPER_TITLE - AUTHOR_NAMES">
- <meta name="description" content="Standard transformer LMs trained end-to-end by Equilibrium Propagation, matching backprop within 4-5% perplexity at 72M parameters, with matched controls and hardware-grade ablations.">
-
- <meta name="author" content="FIRST_AUTHOR_NAME, SECOND_AUTHOR_NAME">
- <meta name="robots" content="index, follow">
- <meta name="language" content="English">
-
- <!-- Open Graph / Facebook -->
- <meta property="article:published_time" content="2024-01-01T00:00:00.000Z">
- <meta property="article:author" content="FIRST_AUTHOR_NAME">
- <meta property="article:section" content="Research">
- <meta property="article:tag" content="KEYWORD1">
- <meta property="article:tag" content="KEYWORD2">
-
- <!-- Twitter -->
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- <!-- Academic/Research Specific -->
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- <!-- Additional SEO -->
- <meta name="theme-color" content="#2563eb">
- <meta name="msapplication-TileColor" content="#2563eb">
- <meta name="apple-mobile-web-app-capable" content="yes">
- <meta name="apple-mobile-web-app-status-bar-style" content="default">
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- <link rel="preconnect" href="https://documentcloud.adobe.com">
- <link rel="preconnect" href="https://cdn.jsdelivr.net">
-
-
- <title>Training Transformer Language Models Without Backpropagation</title>
<meta name="robots" content="noindex, nofollow, noarchive">
-
- <!-- Favicon and App Icons -->
- <link rel="icon" type="image/x-icon" href="static/images/favicon.ico">
- <link rel="apple-touch-icon" href="static/images/favicon.ico">
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- <!-- Critical CSS - Load synchronously -->
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- <script defer src="static/js/index.js"></script>
-
- <!-- Structured Data for Academic Papers -->
-
-
- <!-- Website/Organization Structured Data -->
-
+ <meta name="description" content="EPT-LM is developing a physics-compatible learning rule for standard Transformer language models, with matched backpropagation controls and a path to analog hardware.">
+ <meta name="theme-color" content="#102640">
+ <title>EPT-LM · Physical learning for Transformer language models</title>
+ <style>
+ :root {
+ --paper: #f3f0e8;
+ --paper-2: #ebe6da;
+ --white: #fffef9;
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+ --shadow: 0 22px 60px rgba(16, 38, 64, 0.12);
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+ * {
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+ html {
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+ background: var(--paper);
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+ background: var(--ink);
+ transition: top 0.2s ease;
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+ top: 12px;
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+ .wrap {
+ width: min(1160px, calc(100% - 44px));
+ margin: 0 auto;
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+ .site-header {
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+ display: flex;
+ align-items: center;
+ justify-content: space-between;
+ gap: 24px;
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+ padding: 13px;
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+ font-size: 13px;
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+ position: relative;
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+ font-size: 22px;
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+ margin-top: 28px;
+ padding-top: 24px;
+ border-top: 1px solid rgba(255, 255, 255, 0.2);
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+ display: grid;
+ grid-template-columns: 1fr auto 1fr;
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+ align-items: stretch;
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+ padding: 16px;
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+ border-color: var(--signal);
+ background: rgba(223, 93, 67, 0.1);
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+ display: block;
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+ font-family: var(--mono);
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+ gap: 10px;
+ margin-top: 18px;
+ color: var(--aqua);
+ font-size: 13px;
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+ font-family: var(--serif);
+ font-size: 35px;
+ font-weight: 540;
+ letter-spacing: -0.025em;
+ line-height: 1.1;
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+ font-size: 12px;
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+ }
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+ padding: 112px 0;
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+ background: rgba(255, 254, 249, 0.68);
+ }
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+ color: var(--white);
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+ }
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+ color: var(--aqua);
+ }
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+ margin-bottom: 48px;
+ font-family: var(--serif);
+ font-size: clamp(38px, 5vw, 62px);
+ font-weight: 520;
+ letter-spacing: -0.035em;
+ line-height: 1.05;
+ }
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+ .section-intro {
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+ margin-bottom: 58px;
+ color: var(--ink-2);
+ font-size: 20px;
+ line-height: 1.58;
+ }
+
+ .section-dark .section-intro {
+ color: rgba(255, 255, 255, 0.72);
+ }
+
+ .opportunity-grid {
+ display: grid;
+ grid-template-columns: 1fr 1fr;
+ gap: 70px;
+ }
+
+ .copy-column p {
+ margin-bottom: 20px;
+ color: var(--ink-2);
+ }
+
+ .pull-quote {
+ align-self: start;
+ padding: 34px 36px;
+ border-top: 4px solid var(--signal);
+ background: var(--white);
+ box-shadow: 0 15px 45px rgba(16, 38, 64, 0.08);
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+ font-family: var(--mono);
+ font-size: 11px;
+ letter-spacing: 0.06em;
+ text-transform: uppercase;
+ }
+
+ .method-grid {
+ display: grid;
+ grid-template-columns: repeat(3, 1fr);
+ border-top: 1px solid rgba(255, 255, 255, 0.22);
+ border-bottom: 1px solid rgba(255, 255, 255, 0.22);
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+ padding: 34px 30px;
+ border-left: 1px solid rgba(255, 255, 255, 0.22);
+ }
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+ border-right: 1px solid rgba(255, 255, 255, 0.22);
+ }
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+ display: block;
+ margin-bottom: 52px;
+ color: var(--signal);
+ font-family: var(--mono);
+ font-size: 12px;
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+ font-family: var(--serif);
+ font-size: 27px;
+ font-weight: 520;
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+ color: rgba(255, 255, 255, 0.68);
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+ line-height: 1.65;
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+ .method-note {
+ display: grid;
+ grid-template-columns: auto 1fr;
+ gap: 18px;
+ align-items: center;
+ margin-top: 28px;
+ color: rgba(255, 255, 255, 0.62);
+ font-size: 13px;
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+ padding: 8px 11px;
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+ color: var(--aqua);
+ font-family: var(--mono);
+ font-size: 10px;
+ letter-spacing: 0.08em;
+ text-transform: uppercase;
+ }
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+ display: grid;
+ grid-template-columns: minmax(0, 1.3fr) minmax(300px, 0.7fr);
+ gap: 34px;
+ align-items: stretch;
+ }
+
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+ .control-card {
+ border: 1px solid var(--line);
+ background: var(--white);
+ }
+
+ .result-card {
+ padding: 38px;
+ }
+
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+ margin-bottom: 36px;
+ color: var(--muted);
+ font-family: var(--mono);
+ font-size: 11px;
+ letter-spacing: 0.08em;
+ text-transform: uppercase;
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+ .score-row {
+ display: grid;
+ grid-template-columns: 1fr 1fr;
+ gap: 26px;
+ margin-bottom: 28px;
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+
+ .score {
+ padding-bottom: 22px;
+ border-bottom: 4px solid var(--ink);
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+ .score.ep {
+ border-color: var(--signal);
+ }
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+ display: block;
+ font-family: var(--serif);
+ font-size: clamp(52px, 7vw, 76px);
+ font-weight: 520;
+ letter-spacing: -0.05em;
+ line-height: 1;
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+ display: block;
+ margin-top: 9px;
+ color: var(--muted);
+ font-size: 12px;
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+ .gap-line {
+ display: flex;
+ align-items: center;
+ justify-content: space-between;
+ gap: 22px;
+ padding: 17px 0;
+ border-top: 1px solid var(--line);
+ border-bottom: 1px solid var(--line);
+ font-size: 13px;
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+ color: var(--signal-dark);
+ font-size: 17px;
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+ margin: 24px 0 0;
+ color: var(--muted);
+ font-size: 12px;
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+ padding: 34px;
+ color: var(--white);
+ border-color: var(--ink);
+ background: var(--ink);
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+ margin-bottom: 23px;
+ font-family: var(--serif);
+ font-size: 27px;
+ font-weight: 520;
+ }
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+ .control-list {
+ margin: 0;
+ padding: 0;
+ list-style: none;
+ }
+
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+ position: relative;
+ padding: 13px 0 13px 24px;
+ border-top: 1px solid rgba(255, 255, 255, 0.16);
+ color: rgba(255, 255, 255, 0.74);
+ font-size: 13px;
+ }
+
+ .control-list li::before {
+ content: "✓";
+ position: absolute;
+ left: 0;
+ color: var(--aqua);
+ font-weight: 800;
+ }
+
+ .evidence-grid {
+ display: grid;
+ grid-template-columns: repeat(3, 1fr);
+ gap: 20px;
+ margin-top: 20px;
+ }
+
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+ min-height: 190px;
+ padding: 28px;
+ border: 1px solid var(--line);
+ background: rgba(255, 254, 249, 0.55);
+ }
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+ display: block;
+ margin-bottom: 17px;
+ color: var(--aqua-dark);
+ font-family: var(--serif);
+ font-size: 31px;
+ font-weight: 540;
+ line-height: 1;
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+ margin-bottom: 8px;
+ font-size: 15px;
+ }
+
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+ margin: 0;
+ color: var(--muted);
+ font-size: 12px;
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+
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+ border-top: 1px solid var(--line);
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+ grid-template-columns: 84px minmax(220px, 0.75fr) minmax(300px, 1.25fr);
+ gap: 34px;
+ padding: 38px 0;
+ border-bottom: 1px solid var(--line);
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+
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+ color: var(--signal-dark);
+ font-family: var(--serif);
+ font-size: 42px;
+ line-height: 1;
+ }
+
+ .program-item h3 {
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+ <span>EPT–LM</span>
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- <a href="https://arxiv.org/abs/PAPER_ID_1" class="work-item" target="_blank">
- <div class="work-info">
- <h5>Paper Title 1</h5>
- <p>Brief description of the work and its main contribution.</p>
- <span class="work-venue">Conference/Journal 2024</span>
+ </nav>
+ </header>
+
+ <main id="main">
+ <section class="hero" id="top">
+ <div class="hero-grid wrap">
+ <div>
+ <p class="eyebrow">Grant project brief · July 2026</p>
+ <h1>Language models that learn by settling.</h1>
+ <p class="hero-lede">
+ EPT-LM is a practical route to train standard Transformer language models without a
+ global backward pass. During training, a small physical nudge turns local state
+ differences into weight updates. At inference, the model is an ordinary Transformer.
+ </p>
+ <div class="hero-actions">
+ <a class="button button-primary" href="#evidence">See the evidence</a>
+ <a class="button button-secondary" href="#program">What funding unlocks</a>
</div>
- <i class="fas fa-external-link-alt"></i>
- </a>
- <a href="https://arxiv.org/abs/PAPER_ID_2" class="work-item" target="_blank">
- <div class="work-info">
- <h5>Paper Title 2</h5>
- <p>Brief description of the work and its main contribution.</p>
- <span class="work-venue">Conference/Journal 2023</span>
+ <p class="hero-byline">
+ Yuren Hao · University of Illinois Urbana-Champaign
+ </p>
+ </div>
+
+ <div class="system-card" role="img" aria-label="Diagram showing ordinary Transformer inference and local equilibrium updates during training">
+ <div class="card-topline">
+ <span><i class="live-dot"></i>Standard model</span>
+ <span>Training changes · inference does not</span>
</div>
- <i class="fas fa-external-link-alt"></i>
- </a>
- <a href="https://arxiv.org/abs/PAPER_ID_3" class="work-item" target="_blank">
- <div class="work-info">
- <h5>Paper Title 3</h5>
- <p>Brief description of the work and its main contribution.</p>
- <span class="work-venue">Conference/Journal 2023</span>
+
+ <div class="model-flow">
+ <div class="phase-heading">
+ <strong>Inference</strong>
+ <span>one forward pass</span>
+ </div>
+ <div class="forward-row">
+ <div class="flow-node">tokens</div>
+ <div class="flow-arrow">→</div>
+ <div class="flow-node blocks">OLMo2-style<br>Transformer blocks</div>
+ <div class="flow-arrow">→</div>
+ <div class="flow-node">logits</div>
+ </div>
</div>
- <i class="fas fa-external-link-alt"></i>
- </a>
- </div>
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-
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- <section class="hero">
- <div class="hero-body">
- <div class="container is-max-desktop">
- <div class="columns is-centered">
- <div class="column has-text-centered">
- <h1 class="title is-1 publication-title">Training Transformer Language Models Without Backpropagation</h1>
- <div class="is-size-5 publication-authors">
- <span class="author-block">Yuren Hao<sup>1</sup>,</span>
- <span class="author-block">Xiang Wan<sup>2</sup>,</span>
- <span class="author-block">Alexi Gladstone<sup>1</sup>,</span>
- <span class="author-block">Zeyi Liu<sup>1</sup>,</span>
- <span class="author-block">ChengXiang Zhai<sup>1</sup></span>
- </div>
-
- <div class="is-size-5 publication-authors">
- <span class="author-block"><sup>1</sup>University of Illinois Urbana-Champaign &nbsp;&middot;&nbsp; <sup>2</sup>Stanford University<br>2026</span>
- </div>
-
- <div class="column has-text-centered">
- <div class="publication-links">
- <span class="link-block">
- <a class="external-link button is-normal is-rounded is-dark" style="pointer-events:none;opacity:.55">
- <span class="icon"><i class="fas fa-file-pdf"></i></span>
- <span>Paper: in preparation</span></a>
- </span>
- <span class="link-block">
- <a class="external-link button is-normal is-rounded is-dark" style="pointer-events:none;opacity:.55">
- <span class="icon"><i class="fab fa-github"></i></span>
- <span>Code: on request</span></a>
- </span>
- <span class="link-block">
- <a href="mailto:yurenh2@illinois.edu" class="external-link button is-normal is-rounded is-dark">
- <span class="icon"><i class="fas fa-envelope"></i></span>
- <span>Contact</span></a>
- </span>
+
+ <div class="training-read">
+ <div class="phase-heading">
+ <strong>Training</strong>
+ <span>local physical read</span>
</div>
+ <div class="nudge-row">
+ <div class="state">
+ <small>Free state</small>
+ <strong>model settles</strong>
+ </div>
+ <div class="difference">Δ</div>
+ <div class="state nudged">
+ <small>Nudged state</small>
+ <strong>target applied</strong>
+ </div>
+ </div>
+ <div class="local-update">Each block updates from its own measured difference</div>
</div>
+
+ <p class="system-caption">
+ No backward activation tape through the stack. No separate inference architecture.
+ The same bidirectional operations map naturally onto analog matrix hardware.
+ </p>
</div>
</div>
- </div>
- </div>
-</section>
-
-
-<!-- TLDR -->
-<section class="section">
- <div class="container is-max-desktop">
- <div class="columns is-centered">
- <div class="column is-four-fifths">
- <h2 class="title is-3">TL;DR</h2>
- <div class="content has-text-justified">
- <ul>
- <li><b>The largest models trained from scratch without backpropagation at any level.</b>
- Every parameter update follows the Equilibrium Propagation (EP) rule: no layer, block, or
- output head is trained with a backprop rule. The models are standard transformer LMs
- (OLMo2-style blocks, 32k vocabulary, FineWeb-Edu); the trained network runs ordinary forward inference.</li>
- <li><b>Matches backprop within a 4-5% perplexity band at 72M parameters</b>, against a backprop
- twin trained on identical data, steps, and optimizer: with multi-seed controls on both sides.</li>
- <li><b>First transformer language model in the EP family, at 2.15&times; the size of the largest prior
- EP-family result</b> (VGG10 ImageNet classifier, ~63M params): models trained up to <b>135M</b>
- parameters on 2.7B tokens.</li>
- <li><b>Over 5&times; cheaper per training step than the closest EP-family work:</b> one nudged phase
- with 3 relaxation sweeps per step, versus two phases with 10 iterations each (20 total) in the
- prior state of the art.</li>
- <li><b>Verified gradient fidelity:</b> the EP update maintains cosine &asymp;0.99 to the true backprop
- gradient throughout training: measured, at scale. Larger non-backprop transformers in the
- literature train most parameters with <i>local backprop inside blocks</i>; ours use none.</li>
- <li><b>Hardware compatible, with measurements to show it:</b> 8-bit quantization shows no EP-specific
- penalty against an equally-quantized backprop twin; under injected analog faults (1% forward noise,
- 10% error-channel noise, device-tolerance mismatch) the EP estimator tracks the faulted network at
- cosine &asymp;0.97: learning co-adapts to the hardware.</li>
- </ul>
+ </section>
+
+ <section class="proof-strip" aria-label="Headline project metrics">
+ <div class="proof-grid wrap">
+ <div class="proof">
+ <strong>72M</strong>
+ <span>parameter matched-control language model</span>
</div>
- </div>
- </div>
- </div>
-</section>
-<!-- End TLDR -->
-
-<!-- Paper abstract -->
-<section class="section hero is-light">
- <div class="container is-max-desktop">
- <div class="columns is-centered has-text-centered">
- <div class="column is-four-fifths">
- <h2 class="title is-3">Abstract</h2>
- <div class="content has-text-justified">
- <p>
- Analog and physical accelerators promise order-of-magnitude energy savings for training, but they
- cannot run backpropagation natively: exact gradients on a physical substrate require per-step
- digitization or an adjoint copy of the hardware. Equilibrium Propagation extracts gradients from the
- physics itself: two relaxations and local reads: and is the only member of its family with a
- gradient-equivalence guarantee that we verify directly at scale. What the field has lacked is scale and
- rigor: EP results stopped at mid-size vision models, without matched controls. We train standard
- transformer language models end-to-end with EP: 72M parameters within 4-5% perplexity of a
- matched backprop twin, models up to 135M, with backprop twins,
- multi-seed discipline, and hardware-relevant ablations (quantization, analog faults, nudge operating
- windows, energy accounting) at every stage. Scaling a physical learning rule also surfaces new science:
- the frozen recipe fails one width step up, with sharp measurable structure. Locating the mechanism,
- fitting a transfer law, and validating it blind at the next width is the current phase; the
- instruments for that campaign (a 90-minute estimator-quality screen and a stability probe) are built
- and calibrated.
- </p>
+ <div class="proof">
+ <strong>1.44B</strong>
+ <span>FineWeb-Edu training tokens</span>
</div>
- </div>
- </div>
- </div>
-</section>
-<!-- End paper abstract -->
-
-
-<!-- Results -->
-<section class="section">
- <div class="container is-max-desktop">
- <div class="columns is-centered">
- <div class="column is-four-fifths">
- <h2 class="title is-3">Headline results</h2>
- <div class="content">
- <table class="table is-fullwidth">
- <thead><tr><th>Model</th><th>Data</th><th>EP (val CE)</th><th>BP twin</th><th>Gap</th></tr></thead>
- <tbody>
- <tr><td>72M transformer LM</td><td>FineWeb-Edu, 1.4B tok</td><td>3.33</td><td>3.29</td><td>+4-5% ppl</td></tr>
- <tr><td>135M transformer LM</td><td>FineWeb-Edu, 2.7B tok</td><td colspan="3">trains stably end to end; the frozen
- 72M recipe does not transfer (gap grows to roughly 30% ppl). See the scaling note below.</td></tr>
- </tbody>
- </table>
- <p class="is-size-6 has-text-grey">Twin discipline: identical architecture, tokenizer, data order,
- optimizer, steps, and evaluation; multi-seed on both sides (BP n=3, band &plusmn;0.006; EP n=2).</p>
- <table class="table is-fullwidth">
- <thead><tr><th>Training cost, EP family</th><th>This work</th><th>Closest EP work (VGG10, ImageNet)</th></tr></thead>
- <tbody>
- <tr><td>Nudged phases per step</td><td><b>1</b></td><td>2</td></tr>
- <tr><td>Relaxation iterations per step</td><td><b>3</b></td><td>20</td></tr>
- <tr><td>Model class and scale</td><td><b>transformer LM, 72M and 135M</b></td><td>convolutional classifier, ~63M</td></tr>
- </tbody>
- </table>
+ <div class="proof">
+ <strong>4–5%</strong>
+ <span>perplexity gap to its backprop twin</span>
+ </div>
+ <div class="proof">
+ <strong>~2×</strong>
+ <span>measured training wall-clock vs backprop</span>
</div>
</div>
- </div>
- </div>
-</section>
-
-<section class="section hero is-light">
- <div class="container is-max-desktop">
- <div class="columns is-centered">
- <div class="column is-four-fifths">
- <h2 class="title is-3">The scaling note</h2>
- <div class="content has-text-justified">
- <p>Scaling the frozen 72M recipe one width step (512 to 768) fails: the EP to BP gap grows from
- 4-5% to roughly 30% perplexity. We treat this as the central result of the current phase and the
- central research object. It has sharp structure: the loss is fully localized to the top half of the
- network, is invisible to every per-step alignment metric, is untouched by estimator symmetrization,
- precision, relaxation depth, and output-head interventions, and is removed completely by
- substituting true gradients in the top half. A mechanism-identification campaign across four widths
- is in progress, with a pre-registered transfer law and a blind holdout at the next width. Positive
- scaling claims are suspended until the law predicts an unseen width with zero tuning.</p>
+ </section>
+
+ <section class="section section-soft" id="opportunity">
+ <div class="wrap">
+ <p class="section-label">The opportunity</p>
+ <h2 class="section-heading">Move learning into the machine.</h2>
+ <div class="opportunity-grid">
+ <div class="copy-column">
+ <p>
+ Analog and in-memory accelerators can perform matrix operations where the weights
+ physically reside. Today, training still routes those operations through a digital
+ backpropagation pipeline: store activations, build a global backward graph, and
+ shuttle data between compute and memory.
+ </p>
+ <p>
+ Equilibrium Propagation offers a different interface. The hardware runs twice,
+ once freely and once with a weak target signal. The difference between those settled
+ states supplies a local learning signal. The device that performs inference can also
+ participate directly in training.
+ </p>
+ <p>
+ Until now, the evidence stopped at vision-scale demonstrations. EPT-LM brings the
+ method to standard autoregressive Transformers, modern language data, and controlled
+ comparisons that make the result useful to both algorithm and hardware reviewers.
+ </p>
+ </div>
+ <aside class="pull-quote">
+ <p>
+ The model does not carry a special “equilibrium” inference path. It deploys as the
+ same forward-only Transformer used everywhere else.
+ </p>
+ <small>Core design constraint</small>
+ </aside>
</div>
- <div class="content" style="display:none">
+ </div>
+ </section>
+
+ <section class="section section-dark" id="approach">
+ <div class="wrap">
+ <p class="section-label">The approach</p>
+ <h2 class="section-heading">A local update for a standard Transformer.</h2>
+ <p class="section-intro">
+ The free state is exactly the model’s forward activations. Training adds a weak loss
+ signal at the output, lets the layer states re-equilibrate, and reads each block locally.
+ Three operations make up the full step.
+ </p>
+
+ <div class="method-grid">
+ <article class="method-step">
+ <span class="step-number">01 / FORWARD</span>
+ <h3>Run the model normally.</h3>
+ <p>
+ Tokens pass through distinct, standard Transformer blocks. This is both the free
+ equilibrium and the deployment-time inference path.
+ </p>
+ </article>
+ <article class="method-step">
+ <span class="step-number">02 / NUDGE</span>
+ <h3>Apply the target once.</h3>
+ <p>
+ A small output nudge propagates through the bidirectional training dynamics. A few
+ local relaxation sweeps produce the perturbed state.
+ </p>
+ </article>
+ <article class="method-step">
+ <span class="step-number">03 / READ</span>
+ <h3>Update each block locally.</h3>
+ <p>
+ Every weight update comes from the block’s own free-to-nudged difference. The
+ training rule does not store or traverse a global backward tape.
+ </p>
+ </article>
</div>
- <h2 class="title is-3">Hardware line</h2>
- <div class="content">
- <ul>
- <li>Measured energy projection for an integrated weight-stationary realization:
- <b>0.21-0.63 pJ/MAC</b> (SPICE-measured analog core + datasheet periphery), against a
- 0.3-1 pJ/MAC digital INT8 system envelope.</li>
- <li>Single-column analog prototype: SPICE-modeled, discrete multiplying-DAC parts list: kept at the
- &ldquo;hardware someone can actually build&rdquo; level.</li>
- <li>Nudge-amplitude operating windows and their evolution over training are mapped: the
- dynamic-range spec an analog implementation must meet.</li>
- </ul>
+
+ <div class="method-note">
+ <strong>Hardware fit</strong>
+ <span>
+ Forward and transpose matrix reads, local state storage, and difference measurements
+ are native operations for bidirectional analog arrays.
+ </span>
</div>
- <h2 class="title is-3">Roadmap</h2>
- <div class="content has-text-justified">
- <p>Mechanism first: identify the width-scaling term across four measured widths, freeze a transfer
- law with its thresholds and budgets, then validate blind at 270M with from-scratch runs and two
- seeds. The scaling ladder resumes only on a zero-tuning hit at the holdout width. In parallel: the
- algorithm-to-regime map across the activity-difference family, and a bounded single-column hardware
- feasibility study.</p>
+ </div>
+ </section>
+
+ <section class="section" id="evidence">
+ <div class="wrap">
+ <p class="section-label">Evidence in hand</p>
+ <h2 class="section-heading">Backprop-class quality at 72M parameters.</h2>
+ <p class="section-intro">
+ The flagship experiment trains an OLMo2-style, 32k-vocabulary language model from
+ scratch on FineWeb-Edu. Its control is not a literature number. It is a backprop twin
+ built and trained in the same codebase. To our knowledge, this is the first Transformer
+ language model trained end-to-end with Equilibrium Propagation.
+ </p>
+
+ <div class="evidence-layout">
+ <article class="result-card">
+ <p class="result-kicker">Validation cross-entropy · lower is better</p>
+ <div class="score-row">
+ <div class="score">
+ <strong>3.29</strong>
+ <span>Backpropagation twin</span>
+ </div>
+ <div class="score ep">
+ <strong>3.33</strong>
+ <span>Equilibrium Propagation</span>
+ </div>
+ </div>
+ <div class="gap-line">
+ <span>Difference at the sealed 72M rung</span>
+ <strong>4–5% perplexity</strong>
+ </div>
+ <p class="result-footnote">
+ 1.44B tokens · FineWeb-Edu · 12 layers · width 512 · Muon hybrid optimizer ·
+ matched evaluation protocol
+ </p>
+ </article>
+
+ <aside class="control-card">
+ <h3>What “matched” means</h3>
+ <ul class="control-list">
+ <li>Same architecture and initialization family</li>
+ <li>Same tokenizer and data budget</li>
+ <li>Same optimizer family and schedule</li>
+ <li>Same evaluation data and cadence</li>
+ <li>Multi-seed backprop and EP controls</li>
+ </ul>
+ </aside>
</div>
+
+ <div class="evidence-grid">
+ <article class="evidence-item">
+ <strong>≈0.99</strong>
+ <h3>Gradient audit</h3>
+ <p>
+ The local EP update tracks the corresponding backprop update throughout validated
+ training runs.
+ </p>
+ </article>
+ <article class="evidence-item">
+ <strong>8-bit</strong>
+ <h3>Compute tolerance</h3>
+ <p>
+ Matched quantization probes show no additional EP-specific quality penalty at
+ 8-bit weight and compute precision.
+ </p>
+ </article>
+ <article class="evidence-item">
+ <strong>135M</strong>
+ <h3>Scaling testbed</h3>
+ <p>
+ The next model rung has completed a 2.7B-token training budget and now serves as
+ the mechanism and transfer-law testbed.
+ </p>
+ </article>
</div>
</div>
- </div>
- </div>
-</section>
+ </section>
+ <section class="section section-soft" id="program">
+ <div class="wrap">
+ <p class="section-label">What funding unlocks</p>
+ <h2 class="section-heading">From a compelling result to a predictive engineering program.</h2>
+ <p class="section-intro">
+ The funded objective is not a collection of per-model recipes. It is one frozen,
+ measurable training rule that predicts its operating point before the next model is run.
+ The work is organized around three deliverables.
+ </p>
+ <div class="program-list">
+ <article class="program-item">
+ <div class="program-number">01</div>
+ <div>
+ <h3>Predictive scaling law</h3>
+ <span class="outcome">Deliverable · 150M–600M ladder</span>
+ </div>
+ <p>
+ Derive dimensionless controls for nudge amplitude, state displacement, and
+ layer-to-layer transmission. Freeze the rule on smaller models, then test it
+ prospectively on held-out larger widths with matched backprop twins.
+ </p>
+ </article>
-<!--BibTex citation -->
- <section class="section" id="BibTeX">
- <div class="container is-max-desktop content">
- <div class="bibtex-header">
- <h2 class="title">BibTeX</h2>
- <button class="copy-bibtex-btn" onclick="copyBibTeX()" title="Copy BibTeX to clipboard">
- <i class="fas fa-copy"></i>
- <span class="copy-text">Copy</span>
- </button>
- </div>
- <pre id="bibtex-code"><code>@misc{ept2026,
- title={Training Transformer Language Models Without Backpropagation},
- author={Hao, Yuren and Wan, Xiang and Gladstone, Alexi and Liu, Zeyi and Zhai, ChengXiang},
- year={2026},
- note={Project page}
-}</code></pre>
- </div>
-</section>
-<!--End BibTex citation -->
+ <article class="program-item">
+ <div class="program-number">02</div>
+ <div>
+ <h3>Hardware-realistic trainer</h3>
+ <span class="outcome">Deliverable · tolerance specification</span>
+ </div>
+ <p>
+ Train under measured device constraints rather than idealized noise: finite
+ precision, update asymmetry, dynamic range, ADC noise, and device mismatch. The
+ output is a component-level operating envelope tied to model quality.
+ </p>
+ </article>
+ <article class="program-item">
+ <div class="program-number">03</div>
+ <div>
+ <h3>Physical learning demonstrator</h3>
+ <span class="outcome">Deliverable · closed-loop column prototype</span>
+ </div>
+ <p>
+ Build and validate a bidirectional mixed-signal column that performs forward reads,
+ transpose reads, nudging, and local update extraction. Compare measured behavior
+ directly against the simulator’s device model.
+ </p>
+ </article>
+ </div>
- <footer class="footer">
- <div class="container">
- <div class="columns is-centered">
- <div class="column is-8">
- <div class="content">
+ <div class="gates" aria-label="Program decision gates">
+ <div class="gate">
+ <small>Gate A</small>
+ <strong>Quality transfer</strong>
+ <span>A frozen rule lands inside its preregistered EP–BP quality band.</span>
+ </div>
+ <div class="gate">
+ <small>Gate B</small>
+ <strong>Cost transfer</strong>
+ <span>Relaxation count and precision remain inside the quoted training budget.</span>
+ </div>
+ <div class="gate">
+ <small>Gate C</small>
+ <strong>Device transfer</strong>
+ <span>Measured hardware behavior agrees with the simulator’s tolerance envelope.</span>
+ </div>
+ </div>
+ </div>
+ </section>
+ <section class="closing">
+ <div class="closing-inner wrap">
+ <div>
+ <h2>Train where the weights live.</h2>
<p>
- This page was built using the <a href="https://github.com/eliahuhorwitz/Academic-project-page-template" target="_blank">Academic Project Page Template</a> which was adopted from the <a href="https://nerfies.github.io" target="_blank">Nerfies</a> project page.
- You are free to borrow the source code of this website, we just ask that you link back to this page in the footer. <br> This website is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/" target="_blank">Creative
- Commons Attribution-ShareAlike 4.0 International License</a>.
+ EPT-LM has crossed the first credibility threshold: a standard 72M-parameter language
+ model, trained from scratch with local equilibrium updates, remains close to its
+ backprop twin. The next award turns that result into a scaling law and a hardware
+ specification.
</p>
-
</div>
+ <a class="button" href="mailto:yurenh2@illinois.edu?subject=EPT-LM%20grant%20discussion">
+ Discuss the project
+ </a>
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+ <p>Yuren Hao · University of Illinois Urbana-Champaign · yurenh2@illinois.edu</p>
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