Claude's Muon optimizer theorem checks out numerically to 4 decimal places
vxnuaj · x · 2026-10-31
Follow-up from vxnuaj: the theory he couldn't evaluate turns out to be a formal proof that Muon removes spectral bias keeping networks insensitive off the data manifold.
- Theorem 3.1 compares gradient flow vs. polar descent on a linear layer, with closed-form solutions and error bounds for GD and polar flow
- Marked "[proved; verified numerically]" — GD columns match the formula to 4 decimals
- Includes subtle details like floating-point round-off promoting zero singular values to unit steps, coupling columns
From "I need a mathematician" to "actually this isn't that bad" — a notable datapoint on model-generated research math surviving verification.
More from Models
- LiquidAI's LFM3-VL d1-2B edge vision-language model trends on Hugging Face — LiquidAI · 2026-10-31
- OpenAI's new API credits make ChatGPT Pro tiers a no-brainer for API users — Quiet-Recording-9269 · 2026-10-31
- Qwen4 Spotted in Alibaba's Own Code: 1M-Token Default Context and a qwen4-omni-120b-think Variant — mark_k · 2026-10-31
- EdgeRock-4B open-sourced with fixed 72MiB KV cache, 99.1% less memory than base — testingcatalog · 2026-10-31
- Dev asks for a mathematician: Claude's Muon optimizer theory is too deep to verify — vxnuaj · 2026-10-31
- KOL jokes Codex is great — if you're a rich American — lxfater · 2026-10-31