Эксперимент: Oracle symmetry-level selection (#45)

{ "worked": false, "confidence": 9, "verdict": "Built a NumPy MVP for cyclic orbit averaging, ridge fitting, the displayed A_hat_q and D_q diagnostics, oracle scoring, and synthetic periodic regression. The math sanity check passed: the variance proxy decreases with q, the constructed bias is non-decreasing, and their sum has the expected interior minimizer; full-group averaging was also numerically shift-invariant. In the benchmark, oracle selection did not produce a win: across 12 seeds per asymmetry, it never beat both q=1 and q=8, and at asymmetry 0.15 its mean test MSE was 1.0888 versus 1.1077 for q=1 and 1.0461 for q=8; at asymmetry 0.5 it was 1.1135 versus 1.1077 and 1.1660. Therefore the proposed effect was not demonstrated.", "metrics": { "baseline": "Mean test MSE over 12 seeds: q=1 = 1.1077 for every asymmetry condition; q=8 = 1.0420 (asymmetry 0), 1.0461 (0.15), 1.1660 (0.5), 1.6050 (1.0).", "idea": "Mean selected test MSE: 1.0599 (asymmetry 0), 1.0888 (0.15), 1.1135 (0.5), 1.1077 (1.0); selected q counts over 12 seeds: {1:3,2:1,4:1,8:7}, {1:4,2:1,4:2,8:5}, {1:9,2:1,4:2,8:0}, {1:12,2:0,4:0,8:0}, respectively. It never beat both fixed baselines in any trial." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py", "results.json", "run.log", "idea_context.json" ], "limitations": "This is a small linear ridge-regression proxy rather than a sparse functional neural network; q candidates are cyclic shifts of synthetic vectors, not learned transformations. The validation A_hat_q uses a model trained on unaveraged inputs and clips negative discrepancies, is not standard-error corrected, and does not implement the requested beta pilot, bandwidth-derived q_sharp, or one-standard-error rule. Only one synthetic data family, fixed q_sharp=8, one validation split, and 12 repeated seeds were tested; no GPU or neural-training comparison was needed." }