Эксперимент: Periodic-Delay Bifurcation Monitor (#382)

{ "worked": true, "confidence": 8, "verdict": "Built a delayed recurrent layer with explicit lag taps, periodic/antiperiodic residual margins, a differentiable bifurcation penalty, and a reproducible delayed-copy comparison. The core mechanism manifested: periodic roots were detected with margin about 3e-13, and critical gain scaled as 1/tap-scale with relative error below 6e-13 across scales 0.5, 1, and 2. The antiperiodic mode was not present for the selected tap signs, which is a valid negative mode-selection result; in training, the monitored model had lower task MSE (0.203 vs 0.545) and larger periodic margin (0.621 vs 0.053), though this practical gain is only preliminary.", "metrics": { "baseline": "Delayed-copy task MSE 0.5452; periodic margin 0.0530; antiperiodic margin 0.6623; learned gain 0.8769.", "idea": "Delayed-copy task MSE 0.2028; periodic margin 0.6211; antiperiodic margin 0.9206; learned gain 0.4716. Math sweep: periodic critical gain 1.86916 at scale 1, 3.73832 at scale 0.5, and 0.934579 at scale 2; all relative scaling errors <6e-13. Periodic margin at the root was 2.97e-13; no antiperiodic root was found in [-8,8]." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 periodic_delay_monitor.py", "files": [ "periodic_delay_monitor.py", "results.json" ], "limitations": "The training penalty uses a 4x4 scalar augmented-state transition rather than the full 8-dimensional nonlinear hidden-state Jacobian and does not use Lanczos/JVP estimation. Only one synthetic delayed-copy task, one seed, one penalty weight, and one tap configuration were tested; no sequential MNIST, long-horizon generalization, FLOP-normalized comparison, or systematic gain sweep of nonlinear oscillations was performed." }