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While the last five years have seen considerable progress in understandingthe internal representations of deep learning models, many questions remain.This is especially true when trying to understand the impact of model designchoices, such as model architecture or training algorithm, on hiddenrepresentation geometry and dynamics. In this work we present a new approach tostudying such representations inspired by the idea of a frame on the tangentbundle of a manifold. Our construction, which we call a neural frame, is formedby assembling a set of vectors representing specific types of perturbations ofa data point, for example infinitesimal augmentations, noise perturbations, orperturbations produced by a generative model, and studying how these change asthey pass through a network. Using neural frames, we make observations aboutthe way that models process, layer-by-layer, specific modes of variation withina small neighborhood of a datapoint. Our results provide new perspectives on anumber of phenomena, such as the manner in which training with augmentationproduces model invariance or the proposed trade-off between adversarialtraining and model generalization.

Internal Representations of Vision Models Through the Lens of Frames on Data Manifolds