Эксперимент: Gram-Whitened Directional Pooling (#878)

{ "worked": true, "confidence": 8, "verdict": "Built a NumPy MVP for softmax directional atoms, finite-quadrature Gram matrices, Gram whitening, projected energy, and ridge stabilization. The checks confirmed partition-of-unity error 3.3e-16, projection energy 0.2967 <= signal energy 0.845, projection reconstruction identity error 9.4e-16, monotone energy reduction across lambda, and asymptotic lambdaE=0.0342766 versus predicted c^T c=0.0342827. The dense atom sweep approached full signal energy (0.8450), validating the totality-style trend, but the toy classification accuracy was identical for raw pooling and whitening (0.5854), so no downstream performance win was observed.", "metrics": { "baseline": "Raw soft pooling nearest-centroid accuracy: 0.5854; signal energy: 0.8450; Gram condition number: 37.87.", "idea": "Gram-whitened nearest-centroid accuracy: 0.5854; projection energy: 0.2967; projection energy fraction: 0.3512; lambda=1000 asymptotic lambdaE: 0.0342766 vs predicted 0.0342827." }, "how_to_run": "/home/maxwelhelp/main/bin/python3 gram_directional_pooling.py", "files": [ "gram_directional_pooling.py", "results.json" ], "limitations": "Only a small synthetic 2D directional signal experiment was tested; no CNN, CIFAR-100/ModelNet40, learned atoms, rotation-robustness benchmark, GPU execution, FLOP measurement, or training-loss variance study was performed. The atom-count energy trend was sampled and approached full energy but was not strictly monotone at every intermediate count." }