No dash punctuation; overhead comparison EP-family only

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

1 files changed, 28 insertions, 26 deletions

diff --git a/index.html b/index.html
index 82ac0b6..9c2210c 100644
--- a/index.html
+++ b/index.html
@@ -154,12 +154,12 @@
                       <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 &mdash; in preparation</span></a>
+                        <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 &mdash; on request</span></a>
+                    <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">
@@ -184,23 +184,24 @@
         <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 &mdash; no layer, block, or
+              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&ndash;5% perplexity band at 72M parameters</b>, against a backprop
-              twin trained on identical data, steps, and optimizer &mdash; with multi-seed controls on both sides.</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>2&times; wall-clock overhead versus backprop &mdash; where the closest prior EP work pays
-              6.7&ndash;12&times;</b>: one nudged phase &times; 3 relaxation sweeps per step versus two phases &times; 10 iterations.</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 &mdash; measured, at scale. Larger non-backprop transformers in the
+              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-ready by measurement, not assumption:</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 &mdash; learning co-adapts to the hardware.</li>
+              cosine &asymp;0.97: learning co-adapts to the hardware.</li>
           </ul>
         </div>
       </div>
@@ -220,15 +221,15 @@
             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 &mdash; two relaxations and local reads &mdash; and is the only member of its family with a
+            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 &mdash; 72M parameters within 4&ndash;5% perplexity of a
-            matched backprop twin, models up to 135M &mdash; at 2&times; backprop wall-clock, with backprop twins,
+            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:
             we identified a width-scaling loss in the EP gradient invisible to per-step alignment metrics, built an
-            instrument that measures it in 90 minutes per candidate recipe, mapped its dose&ndash;response law, and
+            instrument that measures it in 90 minutes per candidate recipe, mapped its dose-response law, and
             demonstrated an estimator-side treatment that recovers 97% of it without touching the model or the
             cost budget.
           </p>
@@ -250,7 +251,7 @@
           <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&ndash;5% ppl</td></tr>
+              <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">trained end-to-end, zero instability
                   events; scaling analysis below</td></tr>
             </tbody>
@@ -258,10 +259,11 @@
           <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>Cost vs backprop</th><th>This work</th><th>Closest EP work (VGG10, ImageNet)</th></tr></thead>
+            <thead><tr><th>Training cost, EP family</th><th>This work</th><th>Closest EP work (VGG10, ImageNet)</th></tr></thead>
             <tbody>
-              <tr><td>Wall-clock overhead</td><td><b>2.0&times;</b></td><td>6.7&times; (single-sided) / 12&times; (centered)</td></tr>
-              <tr><td>Relaxation iterations / step</td><td><b>3</b> (one phase)</td><td>20 (two phases &times; 10)</td></tr>
+              <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>
@@ -277,11 +279,11 @@
         <h2 class="title is-3">The scaling science</h2>
         <div class="content has-text-justified">
           <p>Scaling a physical learning rule surfaces phenomena backprop never meets. Between widths 512 and 768
-          we identified a width-scaling loss in the EP gradient &mdash; localized to the top half of the network,
+          we identified a width-scaling loss in the EP gradient: localized to the top half of the network,
           invisible to every per-step alignment metric, and traced to response components that finite nudge
           displacement under-reaches. We built a screening instrument that measures this leak in 90 minutes per
-          candidate recipe, mapped its dose&ndash;response law (logarithmic across two decades of displacement
-          amplification), and demonstrated a pure estimator-side treatment that closes 97% of it &mdash; no change to
+          candidate recipe, mapped its dose-response law (logarithmic across two decades of displacement
+          amplification), and demonstrated a pure estimator-side treatment that closes 97% of it: no change to
           the model, its inference path, or the cost budget. The same instruments provide the go/no-go protocol
           for each next rung of the ladder.</p>
         </div>
@@ -289,18 +291,18 @@
         <div class="content">
           <ul>
             <li>Measured energy projection for an integrated weight-stationary realization:
-              <b>0.21&ndash;0.63 pJ/MAC</b> (SPICE-measured analog core + datasheet periphery), against a
-              0.3&ndash;1 pJ/MAC digital INT8 system envelope.</li>
-            <li>Single-column analog prototype: SPICE-modeled, discrete multiplying-DAC parts list &mdash; kept at the
+              <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 &mdash; the
+            <li>Nudge-amplitude operating windows and their evolution over training are mapped: the
               dynamic-range spec an analog implementation must meet.</li>
           </ul>
         </div>
         <h2 class="title is-3">Roadmap</h2>
         <div class="content has-text-justified">
-          <p>Staged scaling with matched BP controls and hardware-relevant ablations at every rung: a 150M&ndash;600M
-          ladder (does the gap grow or shrink with scale &mdash; measured, not assumed), then 1B&ndash;3B; each stage
+          <p>Staged scaling with matched BP controls and hardware-relevant ablations at every rung: a 150M-600M
+          ladder (does the gap grow or shrink with scale: measured, not assumed), then 1B-3B; each stage
           gated on the previous stage&rsquo;s loss, alignment, and throughput numbers. In parallel: the
           algorithm&rarr;regime map across the activity-difference family (contrastive / coupled-learning arms on
           the same harness), and a bounded single-column hardware feasibility study.</p>