Эксперимент: Fisher-Geodesic Finite-Step Annealing (#1082)

{ "worked": true, "confidence": 9, "verdict": "The Fisher identity matched Monte Carlo within 0.066%. Equal-Fisher spacing reduced local-KL coefficient of variation to approximately zero, versus 0.406 to 4.531 for linear spacing, and the widest-range cumulative KL approached the predicted L^2/(2N) scaling.", "metrics": { "baseline": "Linear variance schedule: widest-range N=32 cumulative KL was 3.90 times the geodesic result; fitted cumulative-KL exponent was -0.478 over N=16..128.", "idea": "Equal-Fisher-arc geometric-variance schedule: local-KL CV below 4e-15; fitted exponent -0.950 over N=16..128; N*KL=8.966 at N=2048 versus predicted 8.974." }, "how_to_run": "python3 fisher_annealing_toy.py && python3 extra_check.py", "files": [ "fisher_annealing_toy.py", "toy_results.json", "toy_results.csv", "extra_check.py" ], "limitations": "Only a one-dimensional exact Gaussian path was tested. No neural diffusion model, Langevin relaxation, FID, runtime, noisy Fisher estimation, or multidimensional learned-energy experiment was tested." }