Approximation of Lipschitz Functions using Deep Spline Neural Networks. (arXiv:2204.06233v1 [cs.LG])

Lipschitz-constrained neural networks have many applications in machine
learning. Since designing and training expressive Lipschitz-constrained
networks is very challenging, there is a need for improved methods and a better
theoretical understanding. Unfortunately, it turns out that ReLU networks have
provable disadvantages in this setting. Hence, we propose to use learnable
spline activation functions with at least 3 linear regions instead. We prove
that this choice is optimal among all component-wise $1$-Lipschitz activation
functions in the sense that no other weight …

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