Эксперимент: Differentiable Persistence Landscape Layer (#817)

{ "worked": true, "confidence": 9, "verdict": "Built a differentiable PyTorch persistence-landscape layer with masking, fixed grid, top-K levels, flattening, and a NumPy reference implementation. The mechanism manifested: single-point landscape distance divided by matched tent distance was 0.9995–0.99999, the 100 multi-point trials had maximum ratio 0.99970 and mean 0.90268, and grid integration error decreased from 3.46e-4 at dt=0.02 to 2.98e-6 at dt=0.00125. The toy classifier showed no accuracy win: both padded birth-death coordinates and landscapes achieved 1.0 clean and noisy accuracy.", "metrics": { "baseline": "Padded birth-death MLP: 1.0 clean accuracy and 1.0 at noise sigma 0.01, 0.03, and 0.07.", "idea": "Landscape MLP: 1.0 clean accuracy and 1.0 at noise sigma 0.01, 0.03, and 0.07. Stability checks: single-point ratios 0.9995–0.99999; multi-point maximum ratio 0.99970 and mean 0.90268; finite nonzero autograd gradients; grid error 3.46e-4 to 2.98e-6 as dt decreases." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 landscape_experiment.py", "files": [ "landscape_experiment.py", "results.json" ], "limitations": "The benchmark uses synthetic equal-cardinality diagrams and a tiny MLP, not MUTAG, CIFAR-10, or diagrams generated by an actual persistence algorithm. It does not compare persistence images, input perturbations, varying cardinality with real padding masks, diagonal matching, finite-K truncation error, or end-to-end differentiable topological preprocessing." }