Эксперимент: Hessian-Coupled Event-Triggered Preconditioner (#834)

{ "worked": true, "confidence": 8, "verdict": "Built a 2D Hessian-vertex toy implementation with dense and diagonal preconditioners, fixed-K S-procedure LMI margins, trigger simulation, and numerical implication sampling. The dense block increased the certified threshold from 0.416 to 0.697 and reduced communication events at the same sigma by about 30–35% (161 versus 232 events at sigma=0.2) while both methods converged and stayed bounded. This is a clear toy-system signal, but not evidence of a practical neural-network win.", "metrics": { "baseline": "Diagonal K: certified sigma=0.4158; at sigma=0.2, 232/1200 events (19.3%), tail loss=5.94e-33, stable=True.", "idea": "Dense block K: certified sigma=0.6969; at sigma=0.2, 161/1200 events (13.4%), tail loss=1.82e-32, stable=True; maximum sampled LMI quadratic form was -1.23e-7." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "event_triggered_preconditioner.py", "experiment.py", "corrected_results.txt", "verification.txt", "results.txt" ], "limitations": "Only a 2D deterministic quadratic with two alternating Hessian vertices was tested. No neural-network model, stochastic gradients, multi-worker communication overhead, wall-clock or FLOP accounting, optimized SDP over P/lambda/K, or large-block scaling was evaluated; the LMI uses a fixed heuristic P and the discrete switching dynamics are not fully covered by the continuous-time certificate." }