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Object manifolds untangle across CNN depth, causally driven by geometry

measured in 1 paper

Cohen et al. apply replica mean-field manifold-capacity theory to ImageNet object manifolds in AlexNet, VGG-16, and ResNet-50 [cohen-etal-2020-separability-geometry-object-manifolds] Classification capacity increases substantially along the trained hierarchy, up to nearly two orders of magnitude over shuffled-label controls for high-variability smooth manifolds [cohen-etal-2020-separability-geometry-object-manifolds] Manifold dimension and radius shrink and inter-manifold center correlations decrease with depth, none of which occur in untrained or label-shuffled controls, isolating training as the cause [cohen-etal-2020-separability-geometry-object-manifolds] Three manifold-perturbation interventions (size scaling, ball approximation, center randomization) confirm dimension reduction drives 55-90% of the capacity gain [cohen-etal-2020-separability-geometry-object-manifolds]

Context

object manifold, manifold capacity (classification capacity), manifold dimension and radius, inter-manifold center correlation, untangling, causal manifold-perturbation validation (scaling, ball approximation, center randomization)

Papers

Separability and Geometry of Object Manifolds in Deep Neural Networks — Cohen, Uri, Chung, SueYeon, Lee, Daniel D., Sompolinsky, Haim2020 · arXiv:1901.09000