Эксперимент: Bilinear Input-Conditioned Koopman Cell (#1371)

{ "worked": true, "confidence": 9, "verdict": "Built a deterministic bilinear Koopman-style controlled predictor and compared it with an additive linear transition on a system containing an action-state interaction. The paper matrix identity held to 3.6e-15 maximum absolute error; the bilinear model recovered the planted coefficients and achieved essentially zero held-out 24-step rollout error, versus additive RMSE 0.0564. This clearly demonstrates the claimed multiplicative-effect advantage on the toy system, though it does not establish performance on noisy high-dimensional world models.", "metrics": { "baseline": "Additive linear: one-step MSE 0.0054615; 24-step held-out rollout MSE 0.00318596, RMSE 0.05644; 3 parameters.", "idea": "Bilinear feature model: one-step MSE 4.04e-32; 24-step held-out rollout MSE 3.48e-32, RMSE 1.86e-16; 4 parameters. Matrix identity maximum error 3.55e-15." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run_output.txt" ], "limitations": "Only a scalar, noiseless synthetic plant was tested, with offline least-squares fitting and one action dimension. No neural encoder/decoder, rank-constrained latent implementation, stability constraint, training-cost comparison, MPC reward, noise robustness, or CartPole/pendulum benchmark was evaluated." }