Эксперимент: Patch-Consensus Weak Residual Training (#873)

{ "worked": true, "confidence": 8, "verdict": "Built a readable MVP implementing weak patch integration, local LASSO support estimation, and modal support consensus. The mechanism manifested: weak-integration noise scaled with log-log slope -0.481 versus the predicted -0.5, majority error decreased with patch count for p>0.5, and increased toward certainty of the wrong decision for p<0.5. In the synthetic sparse-regression check, exact local support accuracy was 0.997 for individual patches and 1.000 for modal consensus, although this secondary setup was relatively easy.", "metrics": { "baseline": "Individual patch exact support accuracy: 0.9971 mean over 100 trials. Weak-integration standard deviations for n=[8,16,32,64,128,256] were [0.4245, 0.3385, 0.2174, 0.1623, 0.1191, 0.0816].", "idea": "Modal consensus exact support accuracy: 1.000 over 100 trials. For local decision accuracy p=0.7, majority error fell from 0.2181 at m=3 to 0.00783 at m=31, versus Hoeffding bounds 0.7866 and 0.0837. Weak-noise scaling was -0.4811 versus the predicted -0.5." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 weak_consensus_experiment.py", "files": [ "weak_consensus_experiment.py", "results.json", "run_output.txt" ], "limitations": "Did not train or compare a full neural PDE surrogate or PINN, and did not measure field error, FLOPs, runtime, boundary accuracy, gradient variance, or GPU performance. The LASSO and patch regression are synthetic MVP approximations, and the consensus theorem test assumes independent binary local decisions rather than correlated neural patches." }