| <html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><style>body{margin:0;background:#faf7ff;color:#221a31;font-family:Inter,system-ui,sans-serif}.wrap{max-width:1050px;margin:auto;padding:30px}.hero{background:linear-gradient(135deg,#581c87,#7e22ce 58%,#ea580c);color:white;border-radius:24px;padding:30px}.hero h1{font-size:34px;margin:0 0 8px}.grid{display:grid;grid-template-columns:repeat(4,1fr);gap:12px;margin:18px 0}.card{background:white;border:1px solid #e5d8f2;border-radius:16px;padding:18px}.num{font-size:28px;font-weight:800;color:#7e22ce}.figure{width:100%;border-radius:16px;border:1px solid #e5d8f2;background:white}@media(max-width:760px){.grid{grid-template-columns:1fr 1fr}}</style></head><body><div class="wrap"><section class="hero"><h1>Implicit Bias of Adam and Muon</h1><p>KKT limits, spectral duality, hybrid norms, and infinity margins</p></section><div class="grid"><div class="card"><div class="num">18/18</div><div>scientific gates</div></div><div class="card"><div class="num">370</div><div>exact Muon identities</div></div><div class="card"><div class="num">96.4%</div><div>worst momentum/optimal margin</div></div><div class="card"><div class="num">2×</div><div>byte-identical strict runs</div></div></div><img class="figure" src="outputs/implicit_bias_adam_muon_audit.png" alt="Four-panel optimizer audit"><p>Version-locked to arXiv v1. Finite smooth homogeneous flows audit mechanisms; source proofs retain general nonlinear asymptotic scope.</p></div></body></html> | |