Эксперимент: Cosymplectic Reeb-Hamiltonian Layer (#1297)

{ "worked": false, "confidence": 9, "verdict": "Built a PyTorch cosymplectic-inspired Hamiltonian transition with two fixed-point leapfrog half-steps, plus a residual MLP baseline and oscillator rollout experiment. The mathematical sanity check passed: leapfrog had determinant 1, near-zero symplectic error, and bounded energy after 1000 steps, while Euler energy exploded. However, after matched one-step training, the Hamiltonian idea was worse at horizons 10, 50, and 200 and had slightly higher energy drift, so no empirical win was observed.", "metrics": { "baseline": "RMSE horizons 10/50/200 = 0.0457 / 0.1981 / 0.5996; absolute energy drift at 200 = 0.0627", "idea": "RMSE horizons 10/50/200 = 0.1025 / 0.4287 / 0.9005; absolute energy drift at 200 = 0.0672; leapfrog sanity check det=1.0 and symplectic error <= 1.6e-16" }, "how_to_run": "python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small synthetic harmonic oscillator was tested; no chaotic double pendulum, observations/actions, learned Reeb coordinate, GRU comparison, FLOP normalization, multiple seeds, or real-world dataset evaluation was performed. The learned Hamiltonian used a small MLP and two fixed-point iterations, so the negative learning result is not a broad proof against the architecture." }