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

(универсальный)

Ответ агента:

{ "worked": true, "confidence": 9, "verdict": "Built a custom cyclic Cayley-graph benchmark because no built-in track contained graph positional-encoding structure. The exact Z_32 quotient check passed with zero cycle-sum and edge-increment errors, and the trained relative-coordinate system achieved substantially lower test MSE than the matched endpoint-coordinate baseline: 0.000477 versus 0.057501, with all 8 paired seeds winning and permutation p=0.0081. The trained-model translation signature confirmed the predicted invariance: idea output change 0.0 versus baseline 0.2194.", "metrics": { "baseline": "test MSE mean 0.0575008038431406, std 0.011260127917232875, best lr=0.01", "idea": "test MSE mean 0.0004770873465531622, std 0.0002546983835343552, best lr=0.01; paired delta=-0.05702371649658744; p=0.0081; 8/8 wins" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 stage2_bench.py", "files": [ "cayley_graph_track.py", "stage2_bench.py", "bench_report.json" ], "limitations": "Tested one synthetic cyclic Cayley graph with a fixed 32-node cycle, one shared tiny MLP architecture, and distance regression only. It did not test general graphs, approximate edge partitions, explicit SNF computation beyond the cyclic quotient, graph transformers/attention, larger-scale memory or speed, or comparisons with Laplacian/random-walk encodings.", "bench_report": { "track": "cayley_cycle_distance", "model": "mlp_tiny", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.01 }, "full": { "mean": 0.0575008038431406, "std": 0.011260127917232875, "n": 8, "per_seed": [ 0.06365571171045303, 0.0492621511220932, 0.07721881568431854, 0.05750827118754387, 0.04907004162669182, 0.06700301915407181, 0.03857070580124855, 0.057717714458703995 ] }, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 0.08882061671465635 }, { "cfg": { "lr": 0.003 }, "mean": 0.09223039448261261 }, { "cfg": { "lr": 0.01 }, "mean": 0.0575008038431406 } ] }, "idea": { "best_cfg": { "lr": 0.01 }, "mean": 0.0004770873465531622, "std": 0.0002546983835343552, "n": 8, "per_seed": [ 0.0005058773094788194, 0.0003577241732273251, 0.0005983486771583557, 9.690735168987885e-05, 0.0003379806294105947, 0.0003559936594683677, 0.0005321577191352844, 0.0010317092528566718 ] }, "comparison": { "delta_mean": -0.05702371649658744, "idea_wins": 8, "n_pairs": 8, "p_value": 0.0081, "mde": 0.010041533799026574, "mde_rel_pct": 17.46329290703377, "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)" }, "mechanism_signature": { "prediction": "relative group differences are invariant to simultaneous vertex translation", "baseline_mean_output_change": 0.2193981111049652, "idea_mean_output_change": 0.0, "predicted_idea_change": 0.0, "confirmed": true }, "math_check": { "group": "Z_32", "cycle_sum_mod_n": 0, "max_edge_increment_error": 0, "path_independence": true }, "custom_track": { "name": "cayley_cycle_distance", "file": "cayley_graph_track.py", "domain": "graph-positional-encoding" }, "protocol_notes": { "epochs": 18, "batch": 128, "paired_seeds": [ 0, 1, 2, 3, 4, 5, 6, 7 ], "grid_union": [ { "lr": 0.001 }, { "lr": 0.003 }, { "lr": 0.01 } ], "structure_justification": "The custom task is a cyclic Cayley graph distance prediction problem, directly containing generator increments, cycle constraints, and relative group displacements." } }, "system_verdict": "worked", "practical_verdict": "helps", "mechanism_ok": 1, "system_judged": true }