Эксперимент: Graph-Certified Switching SSM (#401)

{ "worked": true, "confidence": 8, "verdict": "Built a graph-certified switching scalar SSM with quadratic certificate V(z)=z², all-mode self-edges, softplus contraction penalty, CUDA execution with fallback, and a reproducible mini-experiment. The mechanism checks passed: the observed contraction boundary was |a|=0.901 versus predicted sqrt(0.81)=0.900, worst-switching log norm matched the product prediction to numerical precision, and the quadratic violation slope was within 10.6% of the predicted boundary slope. In the tiny learning comparison, regularization reduced max mode magnitude from 0.495 to 0.391 and improved MSE negligibly (2.32133 to 2.32117); this is a stability signal, not a meaningful task-performance win.", "metrics": { "baseline": "MSE 2.321325; max |a| 0.494540; edge violation rate 0; worst 1000-step log norm -704.127", "idea": "MSE 2.321170; max |a| 0.390664; edge violation rate 0; worst 1000-step log norm -939.909", "verification": "Boundary predicted 0.900 vs observed grid 0.901; worst-switching log norm predicted and observed 2.364704; boundary-slope relative error 10.6%" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a scalar linear recurrence and one-node graph were tested, rather than a multi-node reachability envelope or neural/quadratic matrix certificates. The task experiment was very small and both models learned stable modes, so long-horizon adversarial switching, accuracy generalization, parameter-matched GRU comparison, and statistically repeated runs were not tested." }