Эксперимент: Differentiable Simulation-Regularized Neural Dynamics (#934)

{ "worked": false, "confidence": 9, "verdict": "Built and numerically verified the differentiable softmin/softmax simulation surrogate on a 1D nonlinear dynamics toy problem. The finite-set approximation error obeyed the claimed O(tau log n) bound, and the smooth loss strongly correlated with the independent hard residual (Spearman 0.967), but regularization did not produce a soundness-preserving win: beta=0.15 reduced hard residual from 0.0707 to -0.0365 and successor count from 1.331 to 0.650, while prediction MSE worsened from 0.00063 to 0.00262 and epsilon coverage fell from 0.993 to 0.090. Higher beta was worse, so the claimed practical effect was not demonstrated.", "metrics": { "baseline": "beta=0: prediction MSE 0.00063, hard max residual 0.07067, epsilon coverage 0.993, average successors 1.331", "idea": "beta=0.15: prediction MSE 0.00262, hard max residual -0.03649, epsilon coverage 0.090, average successors 0.650; beta=0.5: prediction MSE 0.02650, coverage 0.039", "math_check": "Across n=2..32 and tau=0.2..0.02, observed softmin/softmax errors stayed below tau*log(n), with maximum error/bound ratios 0.9914 and 0.9914", "correlation": "Spearman correlation between smooth simulation loss and hard max residual was 0.967 across 9 runs" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small 1D learned-map toy system was tested, not a pendulum, Dubins car, neural ODE, or controller. Cell assignments and successor topology were fixed rather than jointly optimized, and no independent interval/Taylor reachable-set containment projection or rejection step was implemented; epsilon coverage was measured but not enforced. The observed correlations pool beta settings and only 9 final checkpoints rather than a long checkpoint trajectory." }