Эксперимент: Holonomy-designed recurrent memory (#1123)

{ "worked": true, "confidence": 8, "verdict": "Built a 16-state deterministic two-factor transition system whose individual generators have only fixed-point cycles, while their composition contains a certified joint Z2 two-cycle exchanging states (0,0) and (1,1); monoid closure had 10 transformations. The quantitative predictions manifested: two-leg reliability exactly matched (1-eps)^4 across eps=0..0.4, the composite orbit alternated for 8 steps, and all non-attractor states reset under A within at most 2 steps. Soft exchange fidelity decreased from 1.0 at tau=0 to 0.371 at tau=0.4, verifying the mechanism, but the algebraic cell did not beat the GRU on the fixed toy task.", "metrics": { "baseline": "Small 8-unit GRU, 330 parameters, delayed-copy accuracy 1.000 on the fixed 600-example toy set after 80 epochs; CUDA fell back to CPU after a cuDNN allocation error.", "idea": "16-state holonomy cell with exact q0<->q1 swap, generator cycle lengths [1], composite cycle lengths [1,2], and monoid size 10. Delayed-copy accuracy was 1.000 at noise 0, 0.748 at 0.05, 0.560 at 0.10, 0.303 at 0.20, and 0.171 at 0.30. The noise prediction observed=(1-eps)^4 exactly at every tested point; orbit was [5,0,5,0,5,0,5,0]." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 holonomy_experiment.py", "files": [ "holonomy_experiment.py", "results.json" ], "limitations": "This MVP is a hand-designed finite-state algebraic cell rather than a learned continuous GRU-like module with soft assignments and straight-through discretization. The delayed-copy comparison was not matched training: the finite-state cell was specified analytically, while the GRU was trained on one small fixed dataset. No repeated-seed statistics, FLOP-normalized comparison, variable delays, learned transition robustness, or larger tasks were tested. The corruption model was uniform state replacement, and the temperature sweep used uniform leakage as a proxy for softmax temperature." }