Эксперимент: Mittag-Leffler second-moment optimizer (#1033)

{ "worked": false, "confidence": 9, "verdict": "Built a NumPy-only Mittag-Leffler EMA-bank optimizer prototype with simplex-constrained fitting and a deterministic toy benchmark. The target tail prediction was confirmed: observed log-log slope -0.4945 versus predicted -0.5. However, the stated normalized mixture could not approximate the target kernel (relative RMSE 0.951; weights collapsed to timescales 1 and 4), and the toy final loss was worse than AdamW, so the claimed long-memory mechanism was not realized.", "metrics": { "baseline": "AdamW toy final loss, seeds 0/1/2: 0.000545, 0.001002, 0.000733; mean 0.000760", "idea": "Mittag-Leffler bank toy final loss, seeds 0/1/2: 0.003656, 0.004101, 0.004674; mean 0.004143. Tail slope: predicted -0.5, observed -0.4945. Bank kernel relative RMSE 0.9509; fitted weights [0.1415, 0.8585, 0, 0, 0, 0]." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json" ], "limitations": "Only alpha=0.5 was implemented because the compact fallback evaluates the half-order Mittag-Leffler function; no CIFAR-10, WikiText, Transformer, sparse embedding, hyperparameter tuning, or GPU experiment was run. The proposed kernel normalization itself appears inconsistent: the EMA mixture has unit total lag mass while the target relaxation values generally do not." }