{ "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": 0.009810974440287518, "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, "note": "signature is measured from the trained idea model on held-out benchmark inputs" }, "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" } }