Эксперимент: Parabolic Riesz Feature Preconditioner (#1295)

{ "worked": true, "confidence": 8, "verdict": "Built a compact Parabolic Riesz Feature Preconditioner MVP using a ring-graph Laplacian and the resolvent operator lambdaD(I+lambda^2 H)^-1, with RMS normalization and a learned residual gate. The numerical check reproduced the claimed smoothing effect: at n=32/64/128, the Riesz operator norms were about 0.50 versus 2.00 for direct differences, and measured noise amplification was roughly 0.41 versus 1.22–1.54. The toy classifier did not show an accuracy win: all variants reached 1.0 accuracy and the Riesz branch had the highest validation loss, so the result supports stability/noise suppression but not improved task performance.", "metrics": { "baseline": "Direct difference: operator norm 2.000; noise amplification 1.224, 1.368, 1.536 for n=32,64,128; toy validation loss 0.17395, accuracy 1.000, perturbed accuracy 1.000.", "idea": "Resolvent Riesz: operator norm 0.499, 0.500, 0.500; noise amplification 0.400, 0.419, 0.415 for n=32,64,128; toy validation loss 0.22344, accuracy 1.000, perturbed accuracy 1.000." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run.txt" ], "limitations": "Only a 1-D periodic graph and a small synthetic frequency-classification task were tested. No real video, traffic, graph benchmark, FLOP accounting, multi-scale branch, causal temporal operator, conjugate-gradient approximation, or statistically repeated training runs were evaluated." }