Эксперимент: Gauge-Free Spectral OT Layer (#884)

{ "worked": true, "confidence": 9, "verdict": "Built a gauge-free, covariance-whitened entropic OT MVP with log-domain Sinkhorn and a synthetic matching comparison. The mechanism manifested: gauge perturbations changed the plan by at most 4.8e-15, five near-zero Jacobian singular values were removed leaving rank 3, and whitening condition numbers matched the ridge-aware prediction across all anisotropy levels. The idea also showed a modest optimization improvement, reaching 0.0015565 versus 0.0015634 for the raw baseline at 180 steps, though this is not evidence of a large practical win.", "metrics": { "baseline": "Raw parameterization: final mean matching loss 0.00156339 (std 0.00007242); losses at steps 10/30/60/120/180: 0.00161616/0.00157786/0.00156467/0.00156339/0.00156339.", "idea": "Gauge-free whitened parameterization: final mean matching loss 0.00155647 (std 0.00007205); losses at steps 10/30/60/120/180: 0.00159108/0.00156080/0.00155677/0.00155647/0.00155647. Gauge plan-change sweep: 0, 2.6e-17, 2.8e-17, 2.7e-16, 4.8e-15. Raw Jacobian had 5 near-zero singular values; quotient retained rank 3. Raw covariance condition rose from 1.83 to 1.12e8 as anisotropy alpha decreased from 1 to 0.01, while observed whitened conditions were 1.00, 1.00, 1.014, 2.707, and 139.3, matching the ridge-aware predictions." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json" ], "limitations": "Only a tiny synthetic K=8 experiment was tested, not the proposed K=32 graph benchmark or a multi-layer attention integration. The whitening ridge limits conditioning for extremely small eigenvalues, and the optimization comparison used a single fixed learning rate and six trials rather than a tuned FLOP-matched study." }