Эксперимент: Beckmann Flow Boundary Regularizer (#1255)

{ "worked": false, "confidence": 9, "verdict": "Built a runnable Beckmann-flow MVP with exact cube Laplacian/divergence operators, an unrolled penalized flow solver, and a parity classification comparison against cross-entropy and edge-sensitivity regularization. The mathematical checks passed: divergence/Laplacian means were near zero, the adjoint identity error was 2.3e-7, an explicit feasible flow had zero residual, and the solver reduced the penalized objective from 5.78 to 0.495 with residual/target RMS 0.052. The learning result was not a win: Beckmann reached 99.2% accuracy and 1-bit change 3.91 versus the edge baseline’s 85.9% and 1.79, while its 2-bit change was higher (1.70 versus 1.30), so the claimed stability benefit was not observed.", "metrics": { "baseline": "CE: accuracy 1.000, one-bit logit change 6.462, two-bit change 0.578, train CE 0.00025; edge: accuracy 0.859, one-bit change 1.792, two-bit change 1.295, train CE 0.0813", "idea": "Beckmann: accuracy 0.992, one-bit logit change 3.910, two-bit change 1.699, train CE 0.00658, flow residual RMS 0.0885, target RMS 13.25" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 beckmann_mvp.py", "files": [ "beckmann_mvp.py", "results.json" ], "limitations": "Only one small synthetic 8-bit parity experiment and one random seed were tested; no tabular/UCI dataset, hyperparameter sweep, matched-FLOP timing, curvature measurement, minibatch approximation, or multi-seed statistical analysis was performed." }