A correlated manifold-capacity formula beats the low-rank approximation

Wakhloo, Sussman & Chung derive a closed-form manifold classification-capacity formula for object manifolds with arbitrary axis and centroid correlation, generalizing base manifold-capacity theory and its low-rank correction [wakhloo-etal-2023-correlated-neural-manifolds] Axis correlations act exactly like shrinking a manifold's radius while centroid correlations act like pulling centers together, a duality between correlation and geometry [wakhloo-etal-2023-correlated-neural-manifolds] On a SimCLR-trained ResNet-50, the new estimator tracks ground-truth simulated capacity more closely than the low-rank correction, which systematically overestimates capacity in later layers [wakhloo-etal-2023-correlated-neural-manifolds]