Эксперимент: Fourier-Collocation Loss for Quasiperiodic Latent States (#1289)

{ "worked": false, "confidence": 9, "verdict": "Built a Fourier-torus MVP with analytic Fourier directional derivatives, fixed-grid collocation loss, gauge regularization, and a matched neural-field experiment. The derivative check passed with finite-difference maximum error 2.35e-4, but the proposed loss worsened long-horizon behavior: RMSE increased from 0.732 to 3.747, final error from 1.67 to 13.04, and maximum radius deviation from 0.592 to 12.24. The claimed stabilization and accuracy effect was therefore not observed in this toy test despite a low collocation residual.", "metrics": { "baseline": "3-seed mean: long_horizon_RMSE=0.7316, final_error=1.6726, max_radius_deviation=0.5921, one_step_field_RMSE=0.00617", "idea": "3-seed mean: long_horizon_RMSE=3.7468, final_error=13.0367, max_radius_deviation=12.2442, one_step_field_RMSE=0.00909, collocation_RMSE=0.00975" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only a small synthetic two-frequency oscillator was tested, using a fixed exact Fourier embedding initialized near the true torus, short noisy vector-field supervision, one collocation weight, and 1400 optimization steps. The normal-frame reducibility term, FFT implementation, curriculum over Fourier modes, latent encoder, trajectory data loss, and broader hyperparameter searches were not tested." }