# Эксперимент: Correlation-Exponent-Safe Weight Initialization (#1047)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built row-wise stationary correlated Gaussian initialization with iid, AR(1), and power-law Toeplitz covariance options, plus fourth-moment scaling, spectral, and 100-step MLP checks. The core predictions were observed: gamma=0.3 gave log-log M2 slope 0.485 versus predicted 0.4, gamma=0.5 gave an approximately linear-in-log-width slope 0.995, and gamma=0.7 showed only slow finite-size growth (slope 0.088) consistent with bounded asymptotics. The unsafe gamma=0.3 spectrum grew from max singular value 5.30 to 8.91 and m4 from 13.90 to 28.74 over widths 64 to 256, while safe gamma=0.7 grew from 3.58 to 4.80 and 4.89 to 5.59; this is a clear spectral-risk signal. In the tiny MLP, safe gamma=0.7 reached loss 0.141 versus iid 0.182 and unsafe gamma=0.3 0.161 after 100 updates, but this training improvement is not established as robust.",
  "metrics": {
    "baseline": "iid: max_sv/m4 at width 256 = 1.980/2.028; MLP loss step 100 = 0.1822",
    "idea": "power gamma=0.7: max_sv/m4 at width 256 = 4.804/5.591; MLP loss step 100 = 0.1407. Unsafe gamma=0.3: 8.906/28.743 and loss 0.1610. Scaling slopes: gamma=.3/.5/.7 = .485/.231/.088, with boundary M2-vs-log-width slope .995; predicted subcritical exponent=.4 and boundary logarithmic growth."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json",
    "run.log"
  ],
  "limitations": "Only synthetic data and a small one-hidden-layer MLP were tested; no MNIST, CIFAR-10, attention, convolution, or 512-wide 100-update benchmark was run. The finite width range makes the gamma=0.7 bounded conclusion asymptotic rather than definitive, and the power-law sampler uses finite Toeplitz covariance with small jitter."
}