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This work presents a novel algorithm for transforming a neural network into aspline representation. Unlike previous work that required convex andpiecewise-affine network operators to create a max-affine spline alternateform, this work relaxes this constraint. The only constraint is that thefunction be bounded and possess a well-define second derivative, although thiswas shown experimentally to not be strictly necessary. It can also be performedover the whole network rather than on each layer independently. As in previouswork, this bridges the gap between neural networks and approximation theory butalso enables the visualisation of network feature maps. Mathematical proof andexperimental investigation of the technique is performed with approximationerror and feature maps being extracted from a range of architectures, includingconvolutional neural networks.

A max-affine spline approximation of neural networks using the Legendre transform of a convex-concave representation