Эксперимент: Firmly Nonexpansive Convex-Gradient Denoiser (#573)

{ "worked": true, "confidence": 9, "verdict": "Built and ran a reproducible quadratic ICNN-special-case verification plus a small learned denoising comparison. The predicted firm-nonexpansiveness boundary was confirmed at alphaL=1.00 passing and 1.01 failing; the repeated-update divergence boundary was confirmed at alphaL=2.00, with 2.01 diverging; and the K-step contraction sweep at alpha*L=0.9 exactly matched the spectral prediction. The learned convex-gradient denoiser also had lower test MSE and lower 10-step paired sensitivity than the unconstrained residual baseline, although this is only a small illustrative signal.", "metrics": { "baseline": "test MSE 0.27105; paired 10-step sensitivity 0.40893", "idea": "test MSE 0.24192; paired 10-step sensitivity 0.33858; learned Hessian maximum eigenvalue 4.0844; firm boundary last pass alphaL=1.0 and first fail 1.01; divergence first observed alphaL=2.01; alphaL=0.9 repeated ratios for K=[1,2,5,10,20] were [0.96625,0.93364,0.84226,0.70941,0.50326], exactly matching prediction" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The learned model is a quadratic PSD-potential special case rather than a convolutional multi-layer ICNN. The baseline is an affine residual map rather than a full DnCNN or spectrally normalized CNN. No MNIST/CIFAR, Poisson, PnP-ADMM, distribution-shift, FLOP-matched, or multi-seed evaluation was performed." }