Эксперимент: Energy-Gradient Neural Flow (#1035)

{ "worked": true, "confidence": 9, "verdict": "Built an energy-gradient flow and verified the mechanism on a quadratic energy. The observed Euler transition occurred at gamma=1.00 (etaL=2): energy was monotone for gamma<=1, increased above 1, and strongly diverged for gamma>=1.2; measured contraction factors exactly matched |1-etalambda|, and the normalized descent coefficient was invariant across lambda_max. In the small denoising experiment, the idea preserved monotonic energy and reduced gradient norm, but its 12-step MSE (0.4641) was worse than the residual baseline (0.4081), so the stability mechanism worked without an accuracy win.", "metrics": { "baseline": "12-step denoising MSE 0.4081426; 4-step training loss 0.2311514", "idea": "12-step denoising MSE 0.4640646; 4-step training loss 0.2209387; energy nonincreasing fraction 1.0; gradient norm 1.1651 -> 0.4993; cumulative path length 2.3558; Euler boundary observed gamma=1.00, predicted gamma=1.00; contraction prediction matched exactly" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "The learned-flow comparison used a tiny synthetic fixed-point denoising task rather than MNIST/CIFAR, only one seed, and a fixed step size rather than a full eta/Lhat sweep for the learned neural energy. Łojasiewicz convergence, compact sublevel-set assumptions, wall-clock speed, and large-scale accuracy were not tested." }