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

(универсальный)

Ответ агента:

{ "worked": true, "confidence": 8, "verdict": "Implemented the Kolmogorov-Lie unitary recurrent layer as a matched modification of a small dynamics RNN, using four input-conditioned anti-symmetric exponential factors and the benchmark train_model path. On the structurally appropriate pendulum-control dynamics track, it achieved lower test MSE than the dense recurrent baseline across 7/8 paired seeds: 0.005406 versus 0.011876, paired delta -0.006470, permutation p=0.0156. The trained-model mechanism signature confirmed near-unitarity with residual 1.82e-6, so both the predicted stability property and a significant task-metric improvement were observed.", "metrics": { "baseline": "Dense recurrent baseline, best lr=0.01, 8-seed mean test MSE 0.0118761, std 0.0048702.", "idea": "KLU recurrent layer, best lr=0.01, 8-seed mean test MSE 0.00540594, std 0.00174744; 7/8 paired wins; permutation p=0.0156; observed unitarity residual 1.8216e-6." }, "bench_report": { "bench_version": 1, "track": "dynamics", "model": "rnn_small", "metric_direction": "lower is better", "n_seeds": 8, "baseline": { "best_cfg": { "lr": 0.01 }, "sweep": [ { "cfg": { "lr": 0.001 }, "mean": 0.4970664903521538 }, { "cfg": { "lr": 0.003 }, "mean": 0.06318101449869573 }, { "cfg": { "lr": 0.01 }, "mean": 0.011876139731612056 } ], "full": { "mean": 0.011876139731612056, "std": 0.00487020680273246, "per_seed": [ 0.010697474703192711, 0.011668417602777481, 0.012986297719180584, 0.019935088232159615, 0.005051083862781525, 0.009833427146077156, 0.018368331715464592, 0.006468996871262789 ], "n": 8 } }, "idea": { "mean": 0.0054059389512985945, "std": 0.001747436411673786, "per_seed": [ 0.007179650943726301, 0.003484317334368825, 0.006277043838053942, 0.004052966833114624, 0.004533923696726561, 0.0029652707744389772, 0.007882867939770222, 0.006871470250189304 ], "n": 8, "best_cfg": { "lr": 0.01 } }, "comparison": { "delta_mean": -0.006470200780313462, "idea_wins": 7, "n_pairs": 8, "per_seed_diffs": [ -0.0035178237594664097, -0.008184100268408656, -0.006709253881126642, -0.01588212139904499, -0.0005171601660549641, -0.006868156371638179, -0.01048546377569437, 0.0004024733789265156 ], "p_value": 0.0156, "mde": 0.004461024219396654, "mde_rel_pct": 37.56291455145348, "verdict": "idea better (significant)", "system_worked": true }, "baseline_grid": [ { "lr": 0.001 }, { "lr": 0.003 }, { "lr": 0.01 } ], "idea_grid": [ { "cfg": { "lr": 0.001 }, "mean": 0.1896328409202397 }, { "cfg": { "lr": 0.003 }, "mean": 0.02868673810735345 }, { "cfg": { "lr": 0.01 }, "mean": 0.0054059389512985945 } ], "math_check_exponential_residual": 1.9421449906076305e-06, "mechanism_signature": { "prediction": "The KLU recurrent map preserves the norm of incoming hidden states while dense recurrence need not.", "observed_idea_recurrent_norm": 2.192119225859642, "observed_baseline_recurrent_output_norm": 1.5108804553747177, "observed_idea_unitarity_residual": 1.8216120736269659e-06, "confirmed": true }, "protocol_note": "The dynamics track was selected because the idea targets stability and control through norm-preserving recurrent transformations." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 stage2_bench.py", "files": [ "stage2_bench.py", "bench_report.json" ], "limitations": "Only the built-in dynamics track was tested; CIFAR-10, sequence, tabular, Householder layers, Cayley approximations, FLOP-normalized timing, and larger hidden sizes were not evaluated. The prototype uses real anti-symmetric generators as the real-valued analogue of anti-Hermitian complex generators.", "system_verdict": "worked", "practical_verdict": "helps", "mechanism_ok": 1, "system_judged": true }