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

(универсальный)

Ответ агента:

{ "worked": false, "confidence": 9, "verdict": "Implemented a local binary_symmetric_power_regression track and an end-to-end degree-4 symmetric-power model using the canonical train_model loop, with matched MLP heads and parity-preserving learning-rate sweeps. Polynomial substitution, representation composition, and the trained feature-map rotation check were near machine precision, confirming the mechanism numerically. However, the idea's mean test MSE was 0.00797 versus 0.00457 for the tuned baseline; paired delta was +0.00340 with permutation p=0.3091, so there was no significant win.", "metrics": { "baseline": "mean test MSE 0.0045715 ± 0.0009398 over 8 seeds; best lr=0.01", "idea": "mean test MSE 0.0079724 ± 0.0076998 over 8 seeds; lr=0.01", "paired_delta": "+0.0034009 idea minus baseline; 3/8 idea wins; permutation p=0.3091", "math_check": "max polynomial error 4.26e-14; max composition error 1.14e-13; max rotation-invariant feature error 2.18e-11" }, "bench_report": { "bench_version": 1, "track": "binary_symmetric_power_regression", "model": "local_mlp_head", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.01 }, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 0.1037276852875948 }, { "cfg": { "lr": 0.003 }, "mean": 0.007304377853870392 }, { "cfg": { "lr": 0.01 }, "mean": 0.004617542843334377 } ], "full": { "mean": 0.004571487399516627, "std": 0.0009398261599528283, "per_seed": [ 0.004156868439167738, 0.006239068228751421, 0.0032845954410731792, 0.004789639264345169, 0.004069721791893244, 0.00436969893053174, 0.0038355558644980192, 0.005826751235872507 ], "n": 8 } }, "idea": { "best_config": { "lr": 0.01 }, "per_seed": [ 0.0036381708923727274, 0.0029435837641358376, 0.004084695130586624, 0.009996835142374039, 0.004572708159685135, 0.02756613865494728, 0.006751858629286289, 0.004224956501275301 ], "mean": 0.007972368359332904, "std": 0.007699778199581965 }, "comparison": { "delta_mean": 0.003400880959816277, "idea_wins": 3, "n_pairs": 8, "per_seed_diffs": [ -0.0005186975467950106, -0.0032954844646155834, 0.0008000996895134449, 0.00520719587802887, 0.0005029863677918911, 0.02319643972441554, 0.00291630276478827, -0.0016017947345972061 ], "p_value": 0.3091, "mde": 0.007036725002667524, "mde_rel_pct": 153.92637860954318, "verdict": "no significant win", "system_worked": false }, "mechanism_signature": { "predicted_equivariance_error": 0.0, "observed_trained_feature_equivariance_error": 2.1827872842550278e-11, "predicted_composition_error": 0.0, "observed_representation_composition_error": 1.1368683772161603e-13, "confirmed": true } }, "how_to_run": "cd /home/maxwelhelp/all/math2nn/experiments/exp512_binary-form-symmetric-power-equivariant- && /home/maxwelhelp/main/bin/python3 bench_symmetric_power.py", "files": [ "bench_symmetric_power.py", "bench_results.json" ], "limitations": "The benchmark uses a custom planar radial regression task rather than a built-in track because the built-ins lack the required planar-coordinate representation structure. The current intervention compresses the V4 block to a scalar invariant before the MLP head, rather than benchmarking multiple learned V4 representation copies with equivariant nonlinear gates. The mechanism signature numerically checks the trained model's feature computation, but does not test a full transformed-input prediction relation under arbitrary GL2 shears because the task target is only rotation invariant.", "system_verdict": "partial", "practical_verdict": "inconclusive", "mechanism_ok": 1, "system_judged": true }