Exact Neural de Rham Backbone / report_bench_2026-08-31T163351.md
Mechanism confirmed, baseline not beaten
Стенд-проверка (stage-2) · промт оператора:
(универсальный)
Ответ агента:
{
"worked": false,
"confidence": 10,
"verdict": "The registered PDE benchmark completed successfully on poisson_boundary with 8 paired seeds. The exact ReLU-power potential mechanism was confirmed by trained-model behavior (observed curl RMS 1.15e-7 versus predicted 0), but the idea was significantly worse on the independent task metric: MSE delta +0.02630 and permutation p=0.0081.",
"metrics": {
"baseline": "Best lr=0.03; test MSE mean 0.0109364952",
"idea": "Best lr=0.03; test MSE mean 0.0372408738; paired delta +0.0263043786; permutation p=0.0081"
},
"bench_report": {
"bench_version": 1,
"track": "poisson_boundary",
"model": "scalar_potential_backbone",
"metric_direction": "lower is better",
"n_seeds": 8,
"baseline": {
"best_cfg": {
"lr": 0.03
},
"sweep": [
{
"cfg": {
"lr": 0.003
},
"mean": 0.12233347818255424
},
{
"cfg": {
"lr": 0.01
},
"mean": 0.05105730285868049
},
{
"cfg": {
"lr": 0.03
},
"mean": 0.009451728663407266
}
],
"full": {
"mean": 0.01093649520771578,
"std": 0.003025037049171694,
"per_seed": [
0.00799343828111887,
0.006817351561039686,
0.010449049063026905,
0.012547075748443604,
0.008240480907261372,
0.011241904459893703,
0.01626167818903923,
0.013940983451902866
],
"n": 8
}
},
"idea": {
"mean": 0.03724087378941476,
"std": 0.012178382868521676,
"per_seed": [
0.030537452548742294,
0.06148594617843628,
0.022630251944065094,
0.05179433524608612,
0.032382115721702576,
0.02730206958949566,
0.03700961917638779,
0.0347851999104023
],
"n": 8
},
"comparison": {
"delta_mean": 0.026304378581698984,
"idea_wins": 0,
"n_pairs": 8,
"per_seed_diffs": [
0.022544014267623425,
0.05466859461739659,
0.012181202881038189,
0.03924725949764252,
0.024141634814441204,
0.016060165129601955,
0.020747940987348557,
0.02084421645849943
],
"p_value": 0.0081,
"mde": 0.01163752387239483,
"mde_rel_pct": 106.40999379933409,
"verdict": "idea worse (significant)",
"system_worked": false
},
"mechanism_signature": {
"stage1_prediction": "d squared equals zero for the learned potential gradient",
"baseline_gradient_curl_rms": 1.36577753551137e-07,
"predicted_gradient_curl_rms": 0.0,
"observed_gradient_curl_rms": 1.154990201257533e-07,
"n_probe": 128,
"confirmed": true,
"idea_sweep": [
{
"cfg": {
"lr": 0.003
},
"result": {
"mean": 0.11393675301223993,
"std": 0.01067011604185375,
"per_seed": [
0.11674976348876953,
0.11242678761482239,
0.09828850626945496,
0.12337931990623474,
0.13426120579242706,
0.11549603939056396,
0.10730288922786713,
0.1035895124077797
],
"n": 8
}
},
{
"cfg": {
"lr": 0.01
},
"result": {
"mean": 0.08499461971223354,
"std": 0.00870385202148945,
"per_seed": [
0.07853147387504578,
0.0928913876414299,
0.07291875034570694,
0.09869463741779327,
0.09521957486867905,
0.08183202892541885,
0.08108515292406082,
0.07878395169973373
],
"n": 8
}
},
{
"cfg": {
"lr": 0.03
},
"result": {
"mean": 0.03724087378941476,
"std": 0.012178382868521676,
"per_seed": [
0.030537452548742294,
0.06148594617843628,
0.022630251944065094,
0.05179433524608612,
0.032382115721702576,
0.02730206958949566,
0.009091251529753208,
0.0013353731483221054
],
"n": 8
}
}
],
"math_check": {
"nilpotence_max_abs": 0.0,
"derivative_identity_max_abs": 0.0
}
},
"custom_track": {
"name": "poisson_boundary",
"domain": "pde",
"file": "bench/custom_tracks/poisson_boundary.py"
}
},
"how_to_run": "/home/maxwelhelp/main/bin/python3 run_bench_registered.py",
"files": [
"run_bench_registered.py",
"bench_report_registered.json",
"custom_exact_gradient_track.py"
],
"limitations": "The registered task is supervised Poisson boundary-value regression rather than explicit PDE collocation with separate interior and boundary residual losses. Higher-form divergence-free experiments, conditioning/eigenmode counts, broader feature-count sweeps, and larger datasets were not tested.",
"system_verdict": "partial",
"practical_verdict": "harms",
"mechanism_ok": 1,
"system_judged": true
}