Locally Linear Attributes of ReLU Neural Networks

Ben Sattelberg; Renzo Cavalieri; Michael Kirby; Chris Peterson; Ross Beveridge

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arXiv · 2012.01940

Locally Linear Attributes of ReLU Neural Networks

Ben Sattelberg·Renzo Cavalieri·Michael Kirby·Chris Peterson·Ross Beveridge

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Abstract

A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these polytopes the network can be described by a single affine mapping. The structure of the decomposition, together with the affine map attached to each polytope, can be analyzed to investigate the behavior of the associated neural network.

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Ben Sattelberg, Renzo Cavalieri, Michael Kirby, Chris Peterson, Ross Beveridge. 2020-11-30. Locally Linear Attributes of ReLU Neural Networks. https://arxiv.org/abs/2012.01940

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