Эксперимент: Continuation Maps for Training-Mode Transitions (#879)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a continuation-map MVP for a diagonal quadratic training dynamical system. The measured instability boundary matched eta*(4+lambda)=2 with 0.054% mean relative error, the local normal sweep switched feature sign, and secant prediction plus scalar bisection tracked the boundary with 1.13e-7 mean relative error. Continuation used 16 trajectory evaluations versus 400 for the 20x20 grid, confirming the mechanism in this toy system but not yet in a neural-network trainer.", "metrics": { "baseline": "20x20 dense grid: 400 runs, mean relative boundary error 0.04044", "idea": "Secant continuation plus 1D bisection: 16 runs, mean relative boundary error 1.13e-7; direct sweep mean error 5.42e-4; scaling mean eta_boundary*(4+lambda)=2.00108" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a deterministic 2D diagonal quadratic was tested; no MLP, minibatch noise, validation loss, real optimizer, checkpoint reuse, schedule-following test, or noisy/multiregime boundary was evaluated. The toy feature is asymptotic log-norm growth rather than the exact proposed loss coefficient of variation." }