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methods / Theoretical / Analytical / Decision-boundary volume estimation (Weyl tube formula + Monte Carlo)

Decision-boundary volume estimation (Weyl tube formula + Monte Carlo)

Techniqueadvanced

Estimates the local surface volume of a classifier's decision boundary by Monte Carlo sampling of an epsilon-tubular neighborhood, using an adversarial-example-finding method (e.g. FGSM) as a cheap distance-to-boundary oracle, justified by Weyl's classical tube formula relating small-epsilon neighborhood volume to the hypersurface's own volume.

Used in (1 observation)

structure: Decision boundary (as a codimension-1 hypersurface) · models: Custom small CNN classifier (MNIST/Fashion-MNIST/CIFAR-10), Custom fully-connected classifier (MNIST/Fashion-MNIST/CIFAR-10) · paper: Understanding the Geometry of Deep Learning with Decision Boundary Volume