Эксперимент: Multiplicity-balanced symmetric interaction layer (#892)

{ "worked": true, "confidence": 9, "verdict": "Built a compact symmetric orbit interaction experiment with composition enumeration, exact multinomial multiplicities, weighted features, BH orbit norms, and regression comparison. The quantitative predictions were confirmed: parameter reduction matched d^m/C(d+m-1,m), diagonal reconstruction and BH orbit sums had numerical error below 7e-10, and weighted feature second moments scaled by exactly N_alpha. The proposed sqrt(N_alpha) factor preserves ordered-tensor contributions but does not equalize raw activation variance; it amplifies high-multiplicity supports, so the 'balanced' label should be interpreted as coefficient/orbit normalization rather than raw feature-variance balancing.", "metrics": { "baseline": "Unweighted orbit regression: validation MSE 9.20039 after 500 updates; 330 parameters; d=8,m=4.", "idea": "Multiplicity-weighted orbit regression: validation MSE 8.94852 after 500 updates; 330 parameters; ordered reference would use 4096 parameters. Exact identity errors ranged from 0 to 2.33e-12; BH-sum errors ranged from 8.88e-16 to 6.99e-10; observed variance ratios matched N_alpha for tested multiplicities 1, 2, 6, 12, 24, 30, and 180." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py", "files": [ "experiment.py" ], "limitations": "Only a small synthetic polynomial regression was tested, not a DeepSets task or dense learned ordered-tensor baseline. Regression optimization was not tuned extensively, timings are implementation-dependent, and the asymptotic Bohnenblust–Hille theorem bound was not independently reproduced." }