| { |
| "schema_version": 1, |
| "title": "Reproduction: The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks", |
| "emoji": "🧭", |
| "space_id": "ProCreations/repro-the-implicit-bias-of-adam-and-muon-on-smooth-homogeneous-neural-networks", |
| "paper": {"arxiv_id": "2602.16340"}, |
| "tags": ["icml2026-repro", "paper-DpIc1cpNKG"], |
| "claims": [ |
| "Theorem 3.2 proves that any limit point of the normalized parameter trajectory θₜ/‖θₜ‖ under normalized steepest descent is the direction of a KKT point of the corresponding max-margin problem (Theorem 3.2).", |
| "Theorem 3.3 extends the margin-maximization convergence result to momentum steepest descent under decaying learning rates, using an Approximate Steepest Descent framework introduced in Definition 5.1 (Theorem 3.3, Definition 5.1).", |
| "Corollary 3.4 shows Muon, applied simultaneously across weight matrices, is a special case of normalized momentum steepest descent with respect to the matrix spectral norm ‖·‖_msp (Corollary 3.4).", |
| "Corollary 3.5 shows Muon-Signum hybrid algorithms exhibit margin maximization with respect to the max of the spectral norm and the ℓ∞ norm (Corollary 3.5).", |
| "Theorem 3.6 shows Adam without a stability constant exhibits implicit bias toward ℓ∞-margin maximization under a decaying learning rate regime when c₁ ≥ c₂ (Theorem 3.6).", |
| "Theorem 3.1 establishes that under normalized steepest descent with a learning rate schedule satisfying ∫₀^∞ η(t)dt = ∞, the soft margin γ̃(θₜ) increases monotonically (Theorem 3.1)." |
| ], |
| "updated_at": "2026-07-21T15:49:36+00:00", |
| "root": { |
| "slug": "index", |
| "title": "Reproduction: The Implicit Bias of Adam and Muon on Smooth Homogeneous Neural Networks", |
| "file": "pages/index.md", |
| "children": [ |
| {"slug": "executive-summary", "title": "Executive summary", "file": "pages/executive-summary/page.md", "children": []}, |
| {"slug": "claim-1-kkt", "title": "Claim 1: KKT limit points", "file": "pages/claim-1-kkt/page.md", "children": []}, |
| {"slug": "claim-2-momentum", "title": "Claim 2: momentum approximate descent", "file": "pages/claim-2-momentum/page.md", "children": []}, |
| {"slug": "claim-3-muon", "title": "Claim 3: Muon spectral geometry", "file": "pages/claim-3-muon/page.md", "children": []}, |
| {"slug": "claim-4-hybrid", "title": "Claim 4: Muon-Signum hybrid", "file": "pages/claim-4-hybrid/page.md", "children": []}, |
| {"slug": "claim-5-adam", "title": "Claim 5: Adam infinity bias", "file": "pages/claim-5-adam/page.md", "children": []}, |
| {"slug": "claim-6-soft-margin", "title": "Claim 6: soft-margin monotonicity", "file": "pages/claim-6-soft-margin/page.md", "children": []}, |
| {"slug": "conclusion", "title": "Conclusion", "file": "pages/conclusion/page.md", "children": []} |
| ] |
| }, |
| "agent_view_tokens": 4700, |
| "revision": "1784648976000000000" |
| } |
|
|
