Эксперимент: Positive-cycle Jacobian penalty (#439)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a positive-cycle Jacobian penalty MVP for a two-state recurrent cell. The mechanism manifested: tr(K²)=2ab exactly, the growth transition occurred at the predicted gamma*=1/rho=0.833 and was bracketed between 0.76 and 0.90, measured log-growth slopes matched theory exactly, and temperature scaling followed the predicted tau^-2 law. In the mini-experiment, the cycle penalty reduced mean closed-walk gain to 0.0396 versus 0.6008 unregularized and 0.0956 for the spectral proxy, but it did not improve mean task MSE and required about 1.5x the runtime.", "metrics": { "baseline": "No regularizer: mean MSE 0.05242 ± 0.03590; mean closed-walk trace2 0.60075; mean runtime 4.40 s", "idea": "Cycle penalty: mean MSE 0.05649 ± 0.03337; mean closed-walk trace2 0.03958; mean runtime 7.22 s. Single-seed MSE was 0.02342 versus baseline 0.02345." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "multiseed.json" ], "limitations": "This is a tiny two-state synthetic regression experiment, not a transformer, attention model, MoE, or deep-equilibrium system. The Jacobian estimate is exact for the toy block structure but uses detached activations, only r=2, three random seeds, and no matched-FLOP larger-scale validation." }