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

(универсальный)

Ответ агента:

{ "worked": true, "confidence": 7, "verdict": "Built a local symmetric periodic Poisson PDE track and a matched end-to-end MLP pair differing only in the final linear solve: original-basis dense solve versus FFT symmetry-basis solve. Across 8 paired seeds, the idea had lower test MSE, with delta_mean=-1542.8097 and permutation p=0.0081, satisfying the benchmark's significant-win criterion. The mechanism signature was not confirmed: trained-model translation-equivariance error was 0.4863 and the recorded commutator check was 8.0, so the result supports a strong task-performance signal but not full learned symmetry preservation.", "metrics": { "baseline": "Best lr=0.003; mean test MSE 1542.9739, std 881.7730; sweep means lr=0.001: 3678.5545, lr=0.003: 1542.9739, lr=0.01: 61191.1179.", "idea": "Best shared lr=0.01; mean test MSE 0.16419, std 0.00518; sweep means lr=0.001: 0.33431, lr=0.003: 0.22666, lr=0.01: 0.16419. All 8 paired seeds favored the idea; delta_mean=-1542.8097, permutation p=0.0081." }, "bench_report": { "bench_version": 1, "track": "symmetric_periodic_poisson", "model": "matched_mlp_implicit_poisson", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.003 }, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 3678.5545349121094 }, { "cfg": { "lr": 0.003 }, "mean": 1542.9738693237305 }, { "cfg": { "lr": 0.01 }, "mean": 61191.117919921875 } ], "full": { "mean": 1542.9738693237305, "std": 881.7730243013423, "per_seed": [ 551.7968139648438, 1715.5308837890625, 1606.8431396484375, 3546.521728515625, 896.7335205078125, 1585.5440673828125, 690.23828125, 1750.58251953125 ], "n": 8 } }, "idea": { "lr": 0.01, "mean": 0.16419056802988052, "std": 0.005184735120563237, "per_seed": [ 0.16288402676582336, 0.16800929605960846, 0.17022863030433655, 0.15940041840076447, 0.1558334082365036, 0.16848696768283844, 0.16939124464988708, 0.15929055213928223 ], "n": 8, "sweep": [ { "lr": 0.001, "mean": 0.3343125320971012, "std": 0.009810974440563, "per_seed": [ 0.3338050842285156, 0.3555314540863037, 0.33778291940689087, 0.3278142511844635, 0.3225341737270355, 0.33397650718688965, 0.33897507190704346, 0.32408079504966736 ], "n": 8 }, { "lr": 0.003, "mean": 0.22666289284825325, "std": 0.0031595270674267305, "per_seed": [ 0.22902223467826843, 0.23013357818126678, 0.22756972908973694, 0.22086501121520996, 0.2224116325378418, 0.22880665957927704, 0.22874034941196442, 0.22575394809246063 ], "n": 8 }, { "lr": 0.01, "mean": 0.16419056802988052, "std": 0.005184735120563237, "per_seed": [ 0.16288402676582336, 0.16800929605960846, 0.17022863030433655, 0.15940041840076447, 0.1558334082365036, 0.16848696768283844, 0.16939124464988708, 0.15929055213928223 ], "n": 8 } ], "cfg": { "lr": 0.01, "nearby_tested": [ 0.001, 0.003, 0.01 ] } }, "comparison": { "delta_mean": -1542.8096787557006, "idea_wins": 8, "n_pairs": 8, "per_seed_diffs": [ -551.6339299380779, -1715.362874493003, -1606.6729110181332, -3546.3623280972242, -896.577687099576, -1585.3755804151297, -690.0688900053501, -1750.4232289791107 ], "p_value": 0.0081, "mde": 788.2054458068113, "mde_rel_pct": 51.08352522860764, "verdict": "idea better (significant)", "system_worked": true }, "mechanism_signature": { "prediction": "symmetry-basis implicit solve preserves the discretized solution and commutes with translations", "trained_model_observed_max_relative_solve_residual": 0.0692358985543251, "trained_model_observed_max_translation_equivariance_error": 0.4862891137599945, "operator_commutator_frobenius": 8.0, "predicted_residual_and_equivariance": 0.0, "confirmed": false }, "custom_track": { "name": "symmetric_periodic_poisson", "file": "poisson_symmetry_track.py", "domain": "pde" }, "stage2_config": { "epochs": 16, "batch": 64, "seeds": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "lr_union": [ 0.001, 0.003, 0.01 ], "track_reason": "PDE inverse problem with periodic Poisson operator; no built-in track had this structure" } }, "how_to_run": "/home/maxwelhelp/main/bin/python3 bench_symmetry_pde.py", "files": [ "poisson_symmetry_track.py", "bench_symmetry_pde.py", "bench_report.json" ], "limitations": "The custom task is a small 8x8 periodic Poisson regression rather than a 2-D/3-D simplicial mesh or large neural PDE operator. No wall-clock speedup, peak memory, GPU occupancy, distributed block solves, Maxwell/DEC face or edge cochains, or scaling to 10k vertices was measured. The signature's failed equivariance check also means the benchmark does not establish that the unconstrained neural trunk learns the claimed group symmetry.", "system_verdict": "worked", "practical_verdict": "helps", "mechanism_ok": 0, "system_judged": true }