Fractional Mahalanobis radial head / report_bench_2026-09-04T134853.md

Mechanism confirmed, baseline not beaten

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Стенд-проверка (stage-2) · промт оператора:

(универсальный)

Ответ агента:

{ "worked": false, "confidence": 9, "verdict": "Built a local heavy-tailed binary-classification track and compared end-to-end matched systems using the same encoder, training budget, and shared learning-rate sweep. The fractional radial head showed strong trained-model nonlinear curvature beyond an affine radius difference, but its test error was significantly worse: mean 0.1850 versus baseline 0.17875, paired delta +0.00625, permutation p=0.01485. Therefore the mechanism is present, but it did not transfer into a benchmark win.", "metrics": { "baseline": "8-seed test error mean 0.17875, std 0.01447; baseline sweep best lr=0.003 (4-seed sweep mean 0.174375). Per-seed: [0.1675, 0.1800, 0.1825, 0.1675, 0.1725, 0.1925, 0.1600, 0.2075].", "idea": "8-seed test error mean 0.18500, std 0.01500; best idea lr=0.003 from shared grid. Per-seed: [0.1675, 0.1950, 0.1850, 0.1775, 0.1750, 0.2025, 0.1675, 0.2100]. Paired delta +0.00625; idea wins 0/8; p=0.01485; verdict idea worse (significant)." }, "bench_report": { "bench_version": 1, "track": "custom:heavy_tailed_binary_radial", "model": "mlp_tiny", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.003 }, "sweep": [ { "cfg": { "lr": 0.003 }, "mean": 0.1743749901652336 }, { "cfg": { "lr": 0.01 }, "mean": 0.17874999344348907 }, { "cfg": { "lr": 0.03 }, "mean": 0.18687499687075615 } ], "full": { "mean": 0.17874999344348907, "std": 0.014469796810738268, "per_seed": [ 0.16749998927116394, 0.17999999225139618, 0.1824999898672104, 0.16749998927116394, 0.17249999940395355, 0.19249999523162842, 0.1599999964237213, 0.20749999582767487 ], "n": 8 } }, "idea": { "mean": 0.1849999949336052, "std": 0.015000001837810447, "per_seed": [ 0.16749998927116394, 0.19499999284744263, 0.1850000023841858, 0.17749999463558197, 0.17499999701976776, 0.20250000059604645, 0.16749998927116394, 0.20999999344348907 ], "n": 8 }, "comparison": { "delta_mean": 0.006250001490116119, "idea_wins": 0, "n_pairs": 8, "per_seed_diffs": [ 0.0, 0.015000000596046448, 0.002500012516975403, 0.01000000536441803, 0.002499997615814209, 0.01000000536441803, 0.007499992847442627, 0.002499997615814209 ], "p_value": 0.01485, "mde": 0.004327507057943815, "mde_rel_pct": 2.4209830582801866, "verdict": "idea worse (significant)", "system_worked": false }, "custom_track": { "name": "heavy_tailed_binary_radial", "file": "bench_experiment.py", "domain": "binary_classification" }, "math_check": { "max_abs_radius_error": 2.6645352591003757e-15, "finite": true }, "idea_sweep": [ { "cfg": { "lr": 0.003 }, "mean": 0.18124999478459358 }, { "cfg": { "lr": 0.01 }, "mean": 0.18312499672174454 }, { "cfg": { "lr": 0.03 }, "mean": 0.1899999938905239 } ], "selection": { "best_idea_cfg": { "lr": 0.003 }, "shared_lr_grid": [ 0.003, 0.01, 0.03 ] }, "mechanism_signature": { "prediction": "fractional radial readout produces measurable nonlinear curvature beyond affine radius difference on trained heavy-tailed systems", "affine_logit_rmse_mean": 0.12869403761578724, "fractional_basis_logit_rmse_mean": 3.302959132867045e-07, "tail_abs_logit_mean": 3.0879115611314774, "confirmed": true } }, "how_to_run": "/home/maxwelhelp/main/bin/python3 bench_experiment.py", "files": [ "bench_experiment.py", "bench_report.json" ], "limitations": "Only the custom heavy-tailed binary classification track was tested because the four built-in tracks lack the idea's binary class-conditional radial likelihood structure. The custom dataset uses 400 training and 400 test samples, one tiny MLP encoder, 28 epochs, and three shared learning rates; no CIFAR/UCI benchmark, calibration analysis, parameter/FLOP audit, covariance condition-number report, or broader architecture sweep was run.", "system_verdict": "partial", "practical_verdict": "harms", "mechanism_ok": 1, "system_judged": true }