Locally Linear Attributes of ReLU Neural Networks
This work provides a mathematical framework for understanding the internal workings of ReLU neural networks, which is important for researchers and practitioners aiming to interpret and debug these models.
This paper analyzes ReLU neural networks as continuous piecewise linear maps, where the network's weights define a decomposition of the input space into convex polytopes. Within each polytope, the network is represented by a single affine mapping, allowing for an investigation into the network's behavior.
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.