Эксперимент: Exponential-Map Stochastic Residual Layer (#436)

{ "worked": true, "confidence": 9, "verdict": "Built a sphere S^2 exponential-map stochastic residual layer with tangent projection, geodesic exponential map, tangent noise, and chart utilities. The mechanism checks succeeded: Exp preserved unit norm to 3.3e-16 versus 3.7e-3 additive drift, global endpoint error had slope 1.01 as predicted by O(h), and parallel-transported geodesic composition error stayed below 6e-16. The coordinate-Euler chart discrepancy decreased with slope 1.08, while tangent-noise covariance matched identity within Monte Carlo error; the geometric signal is clear, although endpoint accuracy improvement over additive Euler was modest.", "metrics": { "baseline": "Unconstrained additive Euler: norm errors [3.67e-3, 1.77e-3, 8.69e-4, 4.31e-4], endpoint error at h=0.1 6.37e-3, convergence slope 1.015.", "idea": "Sphere Exp layer: norm errors <=3.33e-16, endpoint error at h=0.1 5.80e-3, convergence slope 1.011; geodesic composition error <=5.82e-16. Nonlinear-coordinate Euler gap decreased from 8.43e-3 to 8.83e-4 with slope 1.083." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "sphere_exp_residual.py", "run_experiment.py" ], "limitations": "No neural-network training, stochastic transition-loss/Jacobian evaluation, learned diffusion tensor, or wall-clock/FLOP comparison was tested. The chart experiment compares coordinate Euler implementations rather than independently implementing the full stochastic layer in both charts, and covariance verification used finite Monte Carlo sampling." }