Эксперимент: Fourier-Calibrated Nonlocal Feature Gradient (#1271)

{ "worked": false, "confidence": 9, "verdict": "Built a readable Fourier-calibrated nonlocal CNN branch with Gaussian neighborhood weights, a numerically computed Fourier multiplier, spectral penalty, and CPU fallback. The multiplier math passed: it was nonnegative, penalized Nyquist frequency about 25x more than a low frequency, and matched the spatial quadratic form with relative error 4.4e-8. However, in the controlled digits experiment the idea reduced accuracy from 70.7% to 53.1%, increased gradient-norm variability from 0.0366 to 0.1175, did not reduce output high-frequency energy (0.469 to 0.474), and took about 5.1x longer; therefore no practical win was observed.", "metrics": { "baseline": "accuracy=0.7067, final_loss=2.1702, grad_norm_std=0.0366, output_high_frequency_energy=0.4691, time=0.440s", "idea": "accuracy=0.5311, final_loss=1.8535, grad_norm_std=0.1175, output_high_frequency_energy=0.4738, time=2.252s; math: multiplier min=0, high/low=25.08, Parseval relative error=4.4e-8" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This was a tiny 8x8 sklearn-digits experiment rather than CIFAR-10/ResNet-18, with one seed and 12 full-batch epochs. CUDA convolution failed in the shared runtime and the script correctly fell back to CPU. The scalar symmetric displacement sum is not a directional gradient and can cancel for ideal periodic linear fields; a proper vector-valued omega/discrete derivative and larger-scale CIFAR ablations were not tested." }