Эксперимент: Weighted Resolvent-Equivariant Attention (#921)

{ "worked": true, "confidence": 8, "verdict": "Implemented weighted reflection commutator regularization for a toy attention head and verified the core mechanism numerically. Perturbation scaling was exact, commuting operators preserved powers and resolvents to floating-point precision, and resolvent incompatibility vanished at gamma=1 with the predicted near-one damping behavior. The pilot reduced commutator RMS 8.6x and improved mean accuracy from 0.6994 to 0.7351, but did not meet the requested 10x empirical threshold and is not sufficient evidence for a broad ML win.", "metrics": { "baseline": "lambda=0: accuracy 0.6994, validation loss 0.6377, commutator RMS 3.3943", "idea": "lambda=1: accuracy 0.7351, validation loss 0.5181, commutator RMS 0.3932; math checks: perturbation slope predicted/fitted 1.9490096903/1.9490096903, max power commutator 6.34e-16, resolvent identity relative error <1.2e-13" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "REPORT.md" ], "limitations": "Only a tiny single-head attention task and two seeds were tested. No 4-layer/8-head transformer, graph benchmark, reversal-augmentation baseline, learned kappa, sample-complexity curve, FLOP-matched analysis, or direct function-level equivariance evaluation was performed; the toy resolvent matrix was also not constrained to be a well-conditioned Markov transition matrix." }