Эксперимент: Kurtosis-calibrated gradient clipping (#1296)

{ "worked": true, "confidence": 7, "verdict": "Built kurtosis-calibrated clipping with transition-regime protection, EMA moment estimation, and a safety factor. The inversion and transition polynomial were verified to near machine precision, and Student-t trials stayed below the requested tail probabilities. In the noisy quadratic, calibrated clipping reduced threshold-exceeding spike steps from 238.2 to 6.9 versus no clipping, but final loss was unchanged, so the demonstrated benefit is stability rather than faster optimization.", "metrics": { "baseline": "No clipping: final loss 0.001323, mean last-50 loss 0.001370, max loss 27.04, 238.2 spike steps.", "idea": "Kurtosis-calibrated clipping: final loss 0.001323, mean last-50 loss 0.001370, max loss 27.05, 6.9 spike steps, mean empirical tail above threshold 0.000656. Formula inversion error was 1.4e-17; Student-t observed tails were 0.00019-0.00377 for targets 0.01/0.05." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "article.md", "idea_context.json" ], "limitations": "Only a scalar noisy-quadratic toy optimizer was tested; no MLP, Transformer, CIFAR-10, WikiText-2, AdamW/SGD comparison, FLOP accounting, validation accuracy, online kurtosis-estimation calibration study, or adversarial extremal distribution was evaluated." }