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| <header><h1>Can training beat Lloyd?</h1><p class="sub">2jw5U060C4 路 three trained seeds 路 paired held-out and OOD controls</p></header> | |
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| <article class="card"><h2>Training worked</h2><div class="metric">3 / 3 seeds</div><p>Validation improved, parameters moved, and every checkpoint stayed within 2.6% of Lloyd-10.</p></article> | |
| <article class="card"><h2>Held-out superiority</h2><div class="metric negative">Not detected</div><p>Normalized costs: trained <code>0.64676</code>, Lloyd-10 <code>0.64306</code>; paired CI crosses zero.</p></article> | |
| <article class="card"><h2>OOD generalization</h2><div class="metric negative">Significantly worse</div><p>Trained <code>1.03585</code> vs Lloyd-10 <code>1.01574</code>; 95% CI <code>[0.01119, 0.03040]</code>.</p></article> | |
| <article class="card"><h2>Paper source</h2><div class="metric">Question left open</div><p>The paper uses chosen parameters without training and expressly leaves learnability to future work.</p></article> | |
| <article class="card wide"><h2>Bounded conclusion</h2><p>The challenge claim is falsified in this executed protocol: successful optimization does not produce superior clustering or OOD generalization. This does not prove impossibility for every conceivable learning environment.</p></article> | |
| </section><footer>C1 preserved at 10,000-point paper scale 路 C2: 200 ID + 100 OOD tasks 路 14/14 tests pass 路 no paid compute</footer> | |
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