Эксперимент: Directional Hölder Step Controller (#514)

{ "worked": true, "confidence": 9, "verdict": "Built and numerically verified the alpha=1 Directional Hölder Step Controller. On quadratic sweeps, estimated directional curvature matched the exact value to approximately 1e-13 relative error, inverse-curvature learning-rate scaling matched eta·lambda=0.9, and the sufficient-decrease acceptance boundary matched the predicted 1.8 threshold. In the small fixed full-batch MLP test, the controller reached loss 0.1407 and 96.3% accuracy versus cosine SGD loss 0.6545 and 72.1%, with all steps accepted; this is promising but not a matched-FLOP or broad benchmark.", "metrics": { "baseline": "Cosine SGD: final loss 0.6545, accuracy 72.1%, loss at steps 10/50 = 0.6695/0.6557, mean learning rate 0.0758, wall time 0.325 s.", "idea": "Directional controller: final loss 0.1407, accuracy 96.3%, loss at steps 10/50 = 0.6487/0.2783, accepted fraction 100%, mean learning rate 1.6610, wall time 0.312 s. Toy curvature relative error ranged from 4.1e-13 to 3.4e-16; observed eta·lambda was 0.9000000000 across lambda 0.1–10; boundary predictions matched all 6 tests." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 directional_controller_experiment.py", "files": [ "directional_controller_experiment.py", "results.json", "REPORT.md" ], "limitations": "Only alpha=1 was tested, using exact full-batch losses on a tiny 2x16 MLP and synthetic data. AdamW, minibatch noise, larger models/datasets, rigorous matched-FLOP accounting, repeated seeds, and wall-clock scaling were not tested." }