Эксперимент: Resolvent Fractional-Power Layer (#1414)

{ "worked": false, "confidence": 7, "verdict": "Built a nonnormal accretive resolvent fractional-power layer using positive log-grid quadrature and shifted linear solves, with a principal-matrix-power and stability verification. The resolvent approximation stayed finite as skew increased, but the truncated quadrature produced 19.3% scalar error and 4.6–6.0% matrix error. On one tiny classification task it achieved 1.000 versus 0.989 validation accuracy and lower loss at step 60, but was 2.8x slower, had higher gradient-norm variance, and was not parameter- or FLOP-matched, so no demonstrated win was established.", "metrics": { "baseline": "final train loss 0.000683; step-60 loss 0.00553; validation accuracy 0.9889; gradient-norm variance 0.01619; runtime 1.91 s; no NaN/Inf", "idea": "final train loss 0.001224; step-60 loss 0.00454; validation accuracy 1.0000; gradient-norm variance 0.02102; runtime 5.35 s; no NaN/Inf; scalar max relative approximation error 0.1926; matrix relative error 0.0472 at skew 1.8" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 run_experiment.py", "files": [ "run_experiment.py", "results.json" ], "limitations": "Only one small synthetic dataset and one seed were tested; the comparison was not parameter- or FLOP-matched, no CIFAR-10 or Transformer experiment was run, quadrature nodes were not optimized, and no large-width scalability or GMRES study was performed." }