{ "baseline": { "best_cfg": { "lr": 0.01 }, "full": { "mean": 0.0575008038431406, "n": 8, "per_seed": [ 0.06365571171045303, 0.0492621511220932, 0.07721881568431854, 0.05750827118754387, 0.04907004162669182, 0.06700301915407181, 0.03857070580124855, 0.057717714458703995 ], "std": 0.011260127917232875 }, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 0.08882061671465635 }, { "cfg": { "lr": 0.003 }, "mean": 0.09223039448261261 }, { "cfg": { "lr": 0.01 }, "mean": 0.0575008038431406 } ] }, "bench_version": 1, "comparison": { "delta_mean": -0.05702371649658744, "idea_wins": 8, "mde": 0.010041533799026574, "mde_rel_pct": 17.46329290703377, "n_pairs": 8, "p_value": 0.0081, "per_seed_diffs": [ -0.06314983440097421, -0.048904426948865876, -0.07662046700716019, -0.05741136383585399, -0.048732060997281224, -0.06664702549460344, -0.038038548082113266, -0.05668600520584732 ], "system_worked": true, "verdict": "idea better (significant)" }, "custom_track": { "domain": "graph-positional-encoding", "file": "cayley_graph_track.py", "name": "cayley_cycle_distance" }, "idea": { "best_cfg": { "lr": 0.01 }, "mean": 0.0004770873465531622, "n": 8, "per_seed": [ 0.0005058773094788194, 0.0003577241732273251, 0.0005983486771583557, 9.690735168987885e-05, 0.0003379806294105947, 0.0003559936594683677, 0.0005321577191352844, 0.0010317092528566718 ], "std": 0.0002546983835343552, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 0.02106541721150279 }, { "cfg": { "lr": 0.003 }, "mean": 0.0008379632126889192 }, { "cfg": { "lr": 0.01 }, "mean": 0.0004770873465531622 } ] }, "math_check": { "cycle_sum_mod_n": 0, "group": "Z_32", "max_edge_increment_error": 0, "path_independence": true }, "mechanism_signature": { "baseline_mean_output_change": 0.2193981111049652, "confirmed": true, "idea_mean_output_change": 0.0, "predicted_idea_change": 0.0, "prediction": "relative group differences are invariant to simultaneous vertex translation" }, "metric_direction": "lower is better", "model": "mlp_tiny", "n_seeds": 8, "protocol_notes": { "batch": 128, "epochs": 18, "grid_union": [ { "lr": 0.001 }, { "lr": 0.003 }, { "lr": 0.01 } ], "paired_seeds": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "structure_justification": "The custom task is a cyclic Cayley graph distance prediction problem, directly containing generator increments, cycle constraints, and relative group displacements." }, "track": "cayley_cycle_distance" }