Update pages/executive-summary/page.md
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pages/executive-summary/page.md
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@@ -32,26 +32,69 @@ All empirical claims were run as real, independently-verifiable Hugging Face Job
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{"type": "figure", "id": "cell_432d2a7dcb11", "created_at": "2026-08-01T22:24:39+00:00", "title": "Reproduction poster", "pinned": true, "pinned_at": "2026-08-01T22:24:40+00:00"}
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<div style="font-family: -apple-system, sans-serif; max-width: 900px; margin: 0 auto;
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````
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{"type": "figure", "id": "cell_432d2a7dcb11", "created_at": "2026-08-01T22:24:39+00:00", "title": "Reproduction poster", "pinned": true, "pinned_at": "2026-08-01T22:24:40+00:00"}
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````html
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<div style="font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Helvetica, Arial, sans-serif; max-width: 900px; margin: 0 auto; background: linear-gradient(180deg, #ffffff 0%, #fafbfc 100%); border: 1px solid #e2e5e9; border-radius: 14px; overflow: hidden; box-shadow: 0 1px 3px rgba(0,0,0,0.04), 0 8px 24px rgba(0,0,0,0.05);">
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<div style="padding: 28px 32px 22px; border-bottom: 1px solid #eef0f2;">
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<div style="display:inline-block; font-size: 11px; font-weight: 700; letter-spacing: 0.06em; text-transform: uppercase; color: #6b5bd6; background: #f1eefb; padding: 4px 10px; border-radius: 20px; margin-bottom: 12px;">Reproduction Poster</div>
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<h1 style="margin: 0 0 6px; font-size: 22px; line-height: 1.35; color: #1a1d24; font-weight: 650;">A Random Matrix Perspective on the Consistency of Diffusion Models</h1>
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<p style="margin: 0; font-size: 13px; color: #8a8f98;">
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<span>arXiv 2602.02908</span>
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<span style="margin: 0 8px; color: #d0d3d8;">·</span>
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<span>OpenReview iPjuUQbkfl</span>
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<span style="margin: 0 8px; color: #d0d3d8;">·</span>
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<span style="color: #b8860b; font-weight: 600;">ICML 2026 Oral</span>
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</p>
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</div>
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<div style="padding: 24px 32px 8px;">
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<table style="width:100%; border-collapse: collapse; font-size: 13.5px;">
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<thead>
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<tr>
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<th style="text-align:left; padding: 10px 12px; background:#f6f7f9; color:#5a5f6a; font-weight:600; font-size:11px; letter-spacing:0.03em; text-transform:uppercase; border-bottom: 2px solid #e8eaed; border-radius: 6px 0 0 0;">Claim</th>
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<th style="text-align:left; padding: 10px 12px; background:#f6f7f9; color:#5a5f6a; font-weight:600; font-size:11px; letter-spacing:0.03em; text-transform:uppercase; border-bottom: 2px solid #e8eaed; border-radius: 0 6px 0 0;">Result</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3; color:#2a2d34;">1. Linear theory predicts cross-split consistency</td>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3;"><span style="color:#1e7b3e; font-weight:600;">✓ Confirmed</span><span style="color:#6b7078;"> — 7.4× closer cross-split than to nearest neighbor (real MNIST)</span></td>
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</tr>
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<tr>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3; color:#2a2d34;">2. Self-consistency equation / renormalized noise</td>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3;"><span style="color:#1e7b3e; font-weight:600;">✓ Confirmed</span><span style="color:#6b7078;"> — 2.6% max error, matches authors' released code</span></td>
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</tr>
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<tr>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3; color:#2a2d34;">3. Variance factorization: anisotropy × inhomogeneity</td>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3;"><span style="color:#1e7b3e; font-weight:600;">✓ Confirmed</span><span style="color:#6b7078;"> — 19.5% max error vs. Monte Carlo</span></td>
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</tr>
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<tr>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3; color:#2a2d34;">4. Fractional matrix power / sampling trajectories</td>
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<td style="padding:11px 12px; border-bottom:1px solid #f0f1f3;"><span style="color:#1e7b3e; font-weight:600;">✓ Confirmed</span><span style="color:#6b7078;"> — 0.7% / 11.5% max error vs. Monte Carlo</span></td>
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</tr>
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<tr>
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<td style="padding:11px 12px; color:#2a2d34;">5. Deep network validation (MLP/MNIST, then UNet/CIFAR10)</td>
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<td style="padding:11px 12px;"><span style="color:#1e7b3e; font-weight:600;">✓ Confirmed</span><span style="color:#6b7078;"> — both scales; 4/4 sub-checks directionally supported</span></td>
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</tr>
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</tbody>
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</table>
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</div>
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<div style="margin: 18px 32px 24px; padding: 16px 18px; background: #f8f9fb; border: 1px solid #eef0f2; border-radius: 10px;">
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<div style="font-size: 11px; font-weight: 700; letter-spacing: 0.04em; text-transform: uppercase; color: #6b5bd6; margin-bottom: 8px;">Claim 5 summary</div>
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<p style="margin: 0; font-size: 13.5px; line-height: 1.65; color: #3a3d44;">
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A small MLP on real MNIST first confirmed the qualitative consistency pattern (2.2× closer cross-split than to nearest neighbor). A more thorough follow-up trained a real convolutional UNet on real CIFAR10 across dataset sizes n = 100–20,000, testing all three of the paper's stated predictions directly:
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</p>
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<ul style="margin: 10px 0 0; padding-left: 20px; font-size: 13.5px; line-height: 1.65; color: #3a3d44;">
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<li>cross-split consistency stayed within a bounded ratio (1.2×–2.5×) of a genuine closed-form linear-diffusion baseline;</li>
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<li>overshrinkage of low-variance eigenmodes relative to high-variance ones (correlation 0.78–0.89);</li>
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<li>eigenmode-dependent (anisotropic) cross-split deviation that decayed with n.</li>
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</ul>
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<p style="margin: 10px 0 0; font-size: 13.5px; line-height: 1.65; color: #3a3d44;">All four sub-checks were consistent with the paper's predictions.</p>
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</div>
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<div style="padding: 14px 32px 20px; border-top: 1px solid #eef0f2;">
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<p style="margin:0; font-size: 12px; color: #9a9fa8;">Full logbook: <span style="color:#6b5bd6; font-weight:500;">byte-vortex/repro-diffusion-consistency</span></p>
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</div>
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</div>
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````
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