# Эксперимент: Free-Loss Jacobian Spectral Target (#1305)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a reproducible free-loss moment calculator, Haar projection-product verification, and MLP spectral-regularization experiment. The product check closely matched m1-m3 and reproduced the atom masses: empirical versus target moment errors were below 0.005 for tau in {0.25, 0.5, 1, 2}. In the MLP, spectral regularization reduced final log-moment RMSE from 4.15 to 2.82 and reduced both moments substantially toward target, but final task MSE worsened from 0.767 to 0.922 and optimization was slower; therefore this is a genuine spectral-control signal, not evidence of an end-to-end task-performance win.",
  "metrics": {
    "baseline": "Haar check: target/empirical moment absolute errors for tau=.25,.5,1,2 were respectively [0.00095,0.00039,0.00019], [0.00497,0.00378,0.00291], [0.00463,0.00380,0.00339], [0.00338,0.00194,0.00126]. MLP final MSE=0.7673; final moments=[5.3055,234.4828]; log-moment RMSE=4.151.",
    "idea": "Haar check reproduced atom targets 0.75,0.5,0,0. MLP final MSE=0.9215; final moments=[2.1802,42.7845]; log-moment RMSE=2.8229, a 32% reduction versus baseline, but with worse task loss."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run.log"
  ],
  "limitations": "The MLP experiment used exact per-example Jacobians rather than memory-efficient JVP/VJP probes, only one seed and one tiny regression task, 120 steps, K=2, and no CIFAR/transformer benchmark. The implementation did not test GPU execution, multiple regularizer weights, equal-FLOP comparisons, gradient variance, or trained-network singular-value histograms."
}