Эксперимент: Binary Very-Weak PDE Network (#380)

{ "worked": false, "confidence": 9, "verdict": "Built a boundary-preserving binary/step very-weak PDE network with sigmoid training surrogate, straight-through signed weights, quantization penalty, hard deployment evaluation, and analytic test-function Laplacians. The math checks confirmed midpoint-quadrature refinement ratios of 4.49, 4.12, and 4.03 versus the predicted ratio 4, and the bubble factor gave exactly zero hard output on sampled boundary points; lowering temperature also reduced the soft-to-hard output gap from 0.00614 to 0.00095. However, the binary model had relative L2 error 0.946 versus 0.530 for float, weak residual RMS 0.0118 versus 0.000435, and was 6.3x slower in PyTorch inference, despite a 20.4x estimated parameter-storage reduction, so this is not a demonstrated deployment win.", "metrics": { "baseline": "Float MLP: relative_L2=0.5299, weak_residual_rms=0.0004349, inference=1.009 ms/batch of 5000, storage=1348 bytes", "idea": "Binary step network: relative_L2=0.9464 (1.79x baseline), hard weak_residual_rms=0.01178, inference=6.363 ms/batch of 5000 (0.16x baseline speed), estimated storage=66.1 bytes (20.4x reduction), hardening output gap at tau=0.005=0.000952" }, "how_to_run": "/home/maxwelhelp/main/bin/python3 binary_vwf_experiment.py", "files": [ "binary_vwf_experiment.py", "results.json" ], "limitations": "Only a small 2D unit-square smooth Poisson problem was tested, with one hidden width and one seed. Binary operations were simulated by ordinary PyTorch kernels rather than a packed-bit accelerator, so hardware latency and energy benefits were not measured. The benchmark did not test stronger baselines, larger networks, nonzero boundary data, singular forcing, or temperature annealing during training." }