Эксперимент: Interval-Certified Equilibrium Layer (#710)

{ "worked": true, "confidence": 8, "verdict": "Built an interval Krawczyk branch-and-bound MVP for a separable tanh equilibrium, with conservative Jacobian bounds and explicit global statuses that do not confuse a local certificate with global uniqueness. The math check passed on 20,000 random state/parameter samples, and q approached the predicted boundary near gain 1.0. Multi-equilibrium domains produced certified branches but correctly remained inconclusive when unresolved regions persisted; this demonstrates a safety/certification signal, not an inference-speed win.", "metrics": { "baseline": "Fixed-point iteration reached residual below 1e-10 in 54, 91, and 47 steps for gains 0.7, 0.9, and 1.2 respectively at p=0.05.", "idea": "For gain 0.7, the full box was certified unique in 1 visit, with parameter uncertainty remaining unique through radius 0.2. Radii 0.3 and 0.5 exhausted the 10,000-box budget. For gains 1.2 and 1.6, 4 branches were certified but unresolved regions remained, so the global status was inconclusive. The 20,000-sample interval inclusion check passed with q=0.2518." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 mvp_experiment.py", "files": [ "interval_equilibrium.py", "mvp_experiment.py", "mvp_results.json", "verify_math.py", "verification.json", "run_experiment.py", "results.json" ], "limitations": "Only a small synthetic 2D separable tanh system was tested; no trained DEQ, MNIST/task accuracy, Anderson comparison, GPU implementation, directed-rounding interval library, wall-clock speedup, or high-dimensional coupled Jacobian case was evaluated." }