Multiplicity-balanced symmetric interaction layer / report_bench_2026-09-01T135320.md
Mechanism confirmed, baseline not beaten
Стенд-проверка (stage-2) · промт оператора:
(универсальный)
Ответ агента:
{ "worked": false, "confidence": 9, "verdict": "Built and evaluated a custom permutation-invariant degree-4 polynomial regression track because no built-in track had the required symmetric interaction structure. The exact sqrt(multinomial) feature scaling matched observed feature-variance ratios extremely closely, confirming the mechanism signature, but the idea's best test MSE was worse than the tuned dense ordered baseline (182.48 vs 167.83; paired delta +14.65; permutation p=0.1557). Therefore the mechanism works arithmetically, but the promised neural-network task-level win was not observed.", "metrics": { "baseline": "Tuned dense ordered interaction layer, lr=0.01, 20 epochs: test MSE 167.82897 +/- 48.00323 across 8 seeds; 4096 ordered parameters.", "idea": "Multiplicity-weighted orbit interaction layer, lr=0.01, 20 epochs: test MSE 182.48091 +/- 44.26628 across 8 seeds; 330 orbit parameters.", "parameter_reduction": "4096 -> 330, approximately 12.41x fewer parameters.", "paired_delta": "idea - baseline = +14.65195 MSE; lower is better.", "permutation_p_value": 0.1557 }, "bench_report": { "bench_version": 1, "track": "custom_symmetric_polynomial_regression", "model": "interaction_layer", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.01, "epochs": 20 }, "sweep": [ { "cfg": { "lr": 0.001, "epochs": 20 }, "mean": 288.5231819152832 }, { "cfg": { "lr": 0.003, "epochs": 20 }, "mean": 186.22671699523926 }, { "cfg": { "lr": 0.01, "epochs": 20 }, "mean": 147.9050407409668 } ], "full": { "mean": 167.82896614074707, "std": 48.00322837292885, "per_seed": [ 141.9176483154297, 198.45465087890625, 160.6289825439453, 90.61888122558594, 214.09580993652344, 127.07957458496094, 158.7684783935547, 251.0677032470703 ], "n": 8 } }, "idea": { "mean": 182.48091316223145, "std": 44.266280792836994, "per_seed": [ 149.2514190673828, 157.55279541015625, 199.7967529296875, 138.394287109375, 229.0579833984375, 128.88735961914062, 193.53683471679688, 263.369873046875 ], "n": 8 }, "comparison": { "delta_mean": 14.651947021484375, "idea_wins": 1, "n_pairs": 8, "per_seed_diffs": [ 7.333770751953125, -40.90185546875, 39.16777038574219, 47.77540588378906, 14.962173461914062, 1.8077850341796875, 34.76835632324219, 12.302169799804688 ], "p_value": 0.1557, "mde": 23.25227057624662, "mde_rel_pct": 13.854742188393438, "verdict": "no significant win", "system_worked": false }, "mechanism_signature": { "prediction": "weighted feature variance ratio equals multinomial multiplicity N_alpha", "predicted_mean_ratio": 12.412121212121212, "observed_mean_ratio": 12.412121438416662, "median_relative_error": 3.4938962389929884e-08, "max_relative_error": 1.6764265427700783e-07, "n_feature_supports": 330, "confirmed": true }, "idea_sweep": [ { "cfg": { "lr": 0.001, "epochs": 20 }, "mean": 408.1041793823242 }, { "cfg": { "lr": 0.003, "epochs": 20 }, "mean": 300.2734432220459 }, { "cfg": { "lr": 0.01, "epochs": 20 }, "mean": 182.48091316223145 } ], "custom_track": { "name": "symmetric_polynomial_regression", "file": "custom_symmetric_poly.py", "domain": "symmetric_interactions" } }, "how_to_run": "/home/maxwelhelp/main/bin/python3 bench_run.py", "files": [ "custom_symmetric_poly.py", "bench_run.py", "bench_report.json" ], "limitations": "Only the custom regression track was tested; the built-in tracks were structurally mismatched. The baseline is a fully independent ordered-tuple parameterization and therefore has substantially more parameters than the orbit model; no matched-parameter MLP, larger datasets, degrees beyond m=4, longer training, or broader architecture study was tested. The mechanism signature measures the trained idea model's feature behavior, while the task comparison remains the primary metric.", "system_verdict": "partial", "practical_verdict": "inconclusive", "mechanism_ok": 1, "system_judged": true }