# Эксперимент: Spectral-Band Dual-Timescale Network (#431)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built and numerically verified a compact dual-timescale linear network with dissipative fast/slow branches and explicit cross-band exchange. The stability boundary matched k_crit=sqrt(gamma_f gamma_s) to 1.4e-16 relative error, measured decay-rate ratios tracked imposed spectral gaps within about 0.3%, and slow-only frequency-response error increased 3.25x near the fast relaxation rate. The dual-band representation reduced toy two-frequency reconstruction MSE by 79%, although speedup and broad task-level superiority were not tested.",
  "metrics": {
    "baseline": "Single slow-timescale filter: MSE 0.6988269",
    "idea": "Dual spectral-band filter with exchange: MSE 0.1467527, 79.0% lower; observed stability boundary 3.16227766 versus predicted 3.16227766; fitted rate ratios for imposed gaps 2, 5, 10, 20, 40 were 2.015, 5.019, 10.031, 20.055, and 40.105; slow-only relative transfer error was 0.117 at low frequency versus 0.381 near the fast rate"
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 spectral_band_experiment.py",
  "files": [
    "spectral_band_experiment.py",
    "results.json",
    "run_output.txt",
    "REPORT.txt"
  ],
  "limitations": "This was a small linear NumPy toy experiment rather than a trained nonlinear RNN or SSM. GRU, S4, Copy Memory, sequential CIFAR-10, inference speed, learned spectral projection, and larger-dimensional robustness were not tested; high-frequency reduction error continued rising beyond the fast-rate transition, so no sharp error peak exactly at gamma_f was established."
}