Эксперимент: Error-budgeted local log-signature tokens (#561)

{ "worked": true, "confidence": 8, "verdict": "Built a readable MVP for recurrence-based Taylor tails, Witt/free-Lie storage cost, variation-quantile segmentation, local degree-1/2 log-signature-like features, budget selection, and a toy classifier. The mechanism manifested: tails decreased strictly with degree, equal-variation subdivision decreased E monotonically, and tightening epsilon monotonically increased selected cost. The recurrence matched factorial-reference tails to 4.5e-13 absolute error. The classification signal was inconclusive because fixed degree-2 signatures and adaptive tokens both reached 100% while raw patches reached 50.5%, so this is evidence for the mathematical mechanism, not a demonstrated ML win.", "metrics": { "baseline": "Raw 8 local patches: accuracy 0.5048; fixed degree-2 signatures with 4 segments: accuracy 1.0000", "idea": "Adaptive 8 local tokens: accuracy 1.0000; all 700 examples selected degree 2 at epsilon=0.08; runtime 4.14 s", "math_predictions": "Tail monotonicity: true over z in [0.05,8], N=1..5. Equal-partition E monotonicity: true over L in [0.1,10]. Tightening epsilon cost monotonicity: true for L={1,2,4,8}. Unequal/equal E ratio for ell={0.1,0.2,1.7,2.0}: 4.26." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py" ], "limitations": "The toy data is small and easily separable; no transformer, Speech Commands, UEA dataset, throughput-at-equal-memory, or GPU benchmark was tested. The feature implementation includes exact degree-1 and antisymmetric degree-2 log-signature coordinates only; degrees 3-5 are used in the mathematical selector but not fully encoded. The unequal-segment proxy can be substantially larger than the equal-variation expression, as expected from the conservative local sum." }