Эксперимент: Spherical harmonic spectrum regularizer (#1079)

{ "worked": false, "confidence": 8, "verdict": "Built a differentiable spherical-harmonic spectrum regularizer using the Legendre addition theorem, with autodiff and optimization sweeps. The core math passed: the addition-theorem l=1 error was 1.1e-16 and the finite-difference/autodiff gradient relative error was 1.35e-8. The mechanism produced a real monotonic signal: q1 fell from 1.000 at lambda=0 to 0.391 at lambda=1, while cap-count variance fell from 432.5 to 73.1. However, the strict stage-1 predictions were not all confirmed: the observed transition began near lambda=0.03, while the initial gradient-ratio boundary was near lambda=0.1-1, and the lambda=0.1 convergence sweep moved spectrum loss from 0.974 to 1.031 rather than decreasing toward the zero-spectrum target; therefore worked=false.", "metrics": { "baseline": "lambda=0: task=-1.0000, normalized spectrum loss=4.0000, q1=1.0000, cap variance=432.538", "idea": "lambda=1: task=-0.6256, normalized spectrum loss=0.1538, q1=0.3914, cap variance=73.128; lambda=0.1 gives task=-0.9065, spectrum loss=1.0307, q1=0.8217, cap variance=268.560", "math_check": "addition-theorem absolute error=1.11e-16; gradient finite-difference relative error=1.35e-8", "gradient_scaling": "spectrum/task gradient norm ratio=8.565 at lambda=1, 0.857 at lambda=0.1, 0.0857 at lambda=0.01", "lambda_sweep": "q1: 1.000 at lambda=0, 1.000 at .01, .930 at .03, .822 at .1, .666 at .3, .391 at 1" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 spectrum_experiment.py", "files": [ "spectrum_experiment.py", "results.json" ], "limitations": "Only a synthetic north-pole-collapse toy task was tested; no CIFAR-10, neural representation learning, pairwise-repulsion baseline, learned projection, weighted points, selected nonzero target spectrum, GPU benchmark, or FLOP/runtime comparison was performed." }