# Эксперимент: Smooth Spectral Muon (#623)

{
  "worked": true,
  "confidence": 9,
  "verdict": "Built and numerically verified Smooth Spectral Muon with a thin-SVD implementation, spectral potential, finite-difference gradient check, and toy low-rank matrix regression. The predicted transition and asymptotic scaling matched essentially exactly: transition at sigma/sqrt(epsilon)=1, small-mode ratio 0.999999995, large-mode asymptotic 1.000000016, bounded response below 1, and matrix spectral error 0. The smoothed optimizer retained Muon-like loss while providing finite update variability, but did not beat SGD, so this confirms the mechanism rather than an overall training win.",
  "metrics": {
    "baseline": "Toy SGD final loss 2.8356e-05, best loss 3.7964e-06, update-norm CV 0.4468; exact Muon final loss 1.8187e-04, best loss 1.2352e-04, update-norm CV 3.0e-16.",
    "idea": "Smooth Muon with c=1e-3 final loss 1.6260e-04, best loss 1.2357e-04, update-norm CV 0.0193; finite-difference gradient error 2.95e-11; predicted response transition observed exactly at ratio 1.0 with response 0.70710678."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 smooth_spectral_muon.py",
  "files": [
    "smooth_spectral_muon.py",
    "results.json",
    "run_output.txt"
  ],
  "limitations": "Only a small NumPy low-rank matrix-regression toy was tested. No Transformer, language modeling, WikiText, AdamW, CUDA benchmark, matched-FLOP study, NaN stress test, or multi-seed statistical evaluation was performed."
}