Эксперимент: Cyclic Lie-Bracket Residual Block (#699)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified a cyclic two-field residual composition. The mechanism manifested clearly: order-gap scaling with epsilon was 0.9995 versus predicted 1.0, joint field scaling was 1.9997 versus predicted 2.0, normalized gap matched the bracket norm (0.61108 vs 0.61098), and the commuting control was essentially zero (5.0e-17). In the secondary toy regression, cyclic training did not beat the baseline: test MSE was 0.00315 versus 0.000224 and it used 2274 versus 1170 parameters and about twice the runtime, so no practical win was established.", "metrics": { "baseline": "Toy regression: train MSE 0.0002188, test MSE 0.0002243, loss at step 50 0.07765, loss at step 350 0.0002203, 1170 parameters, 1.70 s.", "idea": "Toy regression: train MSE 0.002853, test MSE 0.003149, loss at step 50 0.09836, loss at step 350 0.002886, 2274 parameters, 3.44 s, learned order signal 4.74e-05. Math: epsilon exponent 0.9995, field-scale exponent 1.9997, normalized gap 0.61108 versus bracket prediction 0.61098, commuting gap 5.02e-17." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py && /home/maxwelhelp/main/bin/python3 train_toy.py", "files": [ "run_experiment.py", "train_toy.py", "results.json", "toy_results.json" ], "limitations": "The learning comparison is a tiny synthetic regression, not CIFAR-10/ViT or a parameter/FLOP-matched benchmark. The cyclic model uses stochastic scalar run times and was not tuned across schedules; robustness, gradient variance, larger architectures, and diffusion-limit behavior were not tested. The secondary model has more parameters than the baseline, so its poorer result is not a controlled efficiency comparison." }