Эксперимент: Finite-horizon Lyapunov regularization for neural updates (#696)

{ "worked": true, "confidence": 8, "verdict": "Built a finite-horizon Lyapunov toy verifier and an online gradient-based MLP proxy. The mechanism manifested: predicted contraction boundaries for M=2,4,8 matched grid observations within 0.001; stochastic mismatch scaled quadratically with noise; and EMA violations transitioned from 0% for a=0.98 to 100% at a>=1.0, consistent with instability. The tiny MLP comparison did not show a practical win: the regularized run reached 26.7% accuracy versus 83.1% baseline and had higher tail loss and gradient variance, so the claim is supported only as a toy mechanism, not as an effective training method here.", "metrics": { "baseline": "MLP accuracy 0.8311; final tail loss 0.1600; tail loss std 0.0842; gradient std 0.3407.", "idea": "MLP accuracy 0.2667; final tail loss 0.5933; tail loss std 0.9117; gradient std 0.8450. Toy contraction boundaries predicted/observed: M=2, 0.974004/0.974000; M=4, 0.986916/0.986000; M=8, 0.993437/0.993000. Noise mismatch normalization was 0.606-0.618; EMA violation rate was 0% at a=0.98 and 100% at a>=1.0." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only one fixed seed and a tiny sklearn digits MLP were used. CIFAR-10, multi-seed evaluation, optimizer meta-loss, recurrent modules, FLOP-matched hyperparameter search, and systematic lambda/M tuning were not tested. The gradient certificate is a practical delayed-minibatch-gradient proxy rather than a full unrolled optimizer-state Lyapunov implementation." }