Эксперимент: Accumulator-Carrying Picard ResNet (#1340)

{ "worked": true, "confidence": 8, "verdict": "Built an accumulator-carrying ResNet with persistent context and additive accumulator updates, plus plain-MLP and standard-ResNet controls. The telescoping accumulator identity and block-composition check passed to numerical precision (8.9e-16 and 0 error). At matched parameters, the accumulator had lower test MSE than the standard ResNet at d=50,100,200 (0.0860 vs 0.1041; 0.1185 vs 0.1371; 0.1139 vs 0.1255), a promising small-scale signal, but it was not consistently better than the plain MLP.", "metrics": { "baseline": "Standard ResNet: d=50/100/200 test MSE = 0.104082/0.137112/0.125480; parameters = 16310/17910/21110.", "idea": "Accumulator ResNet: d=50/100/200 test MSE = 0.086046/0.118547/0.113869; parameters = 16310/17910/21110. Plain MLP control MSE = 0.095627/0.124152/0.101153." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "This is a small synthetic regression benchmark rather than a semilinear heat-equation Monte Carlo estimator. Only one seed and 450 optimization steps were tested; FLOPs, gradient variance, multiple seeds, and broader widths/depths were not measured. The plain MLP has a different parameter count, and the context gate was fixed at alpha=0, so the result does not validate the paper's approximation or dimensional-scaling theorem." }