Эксперимент: Unconstrained Proper-Velocity Hyperbolic Layers (#454)

{ "worked": false, "confidence": 9, "verdict": "Built and numerically verified the proper-velocity reconstruction and a depth-matched MLP comparison. The math predictions were confirmed: the Lorentz residual above the norm boundary was below 4e-15, the observed boundary was exactly 1/sqrt(K)=1, and the reconstruction derivative grew 93.15x as the radius approached the boundary, matching theory. However, the unconstrained PV network generated 104,128 invalid intermediate/final reconstructions at depth 4 and 57,341 at depth 12, while the projected baseline had zero; although PV was faster, its depth-12 accuracy was worse, so the promised stable manifold-preserving effect was not demonstrated.", "metrics": { "baseline": "Depth 4: validation accuracy 0.9766, final residual 1.25e-6, invalid count 0, 250-step runtime 1.82s. Depth 12: accuracy 0.9844, residual 1.13e-6, invalid count 0, runtime 4.42s.", "idea": "Depth 4: validation accuracy 0.9844, final residual 0.910, invalid count 104128, runtime 1.27s. Depth 12: accuracy 0.9531, residual 0.593, invalid count 57341, runtime 2.50s. Reconstruction math matched to 3.6e-15; derivative growth ratio observed 93.1548 vs predicted 93.1548." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 pv_experiment.py", "files": [ "pv_experiment.py", "results.json" ], "limitations": "Only a tiny synthetic 2D classification task was tested, using CPU execution and a simplified projected Lorentz baseline rather than MNIST/CIFAR, graph, attention, or a full hyperbolic model. The optional norm-parameterized valid PV variant was not benchmarked; the tested idea was the stated unconstrained spatial-layer version." }