1-Lipschitz Neural Networks are more expressive with N-Activations

• URL: http://arxiv.org/abs/2311.06103v2
• Date: Mon, 3 Jun 2024 15:20:13 GMT
• Title: 1-Lipschitz Neural Networks are more expressive with N-Activations
• Authors: Bernd Prach, Christoph H. Lampert,
• Abstract summary: Small changes to a system's inputs should not result in large changes to its outputs. We show that commonly used activation functions, such as MaxMin, unnecessarily restrict the class of representable functions. We introduce the new N-activation function that is provably more expressive than currently popular activation functions.
• Score: 19.858602457988194
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives for networks with a small Lipschitz constant. Several recent works have focused on how to construct such Lipschitz networks, typically by imposing constraints on the weight matrices. In this work, we study an orthogonal aspect, namely the role of the activation function. We show that commonly used activation functions, such as MaxMin, as well as all piece-wise linear ones with two segments unnecessarily restrict the class of representable functions, even in the simplest one-dimensional setting. We furthermore introduce the new N-activation function that is provably more expressive than currently popular activation functions. We provide code at https://github.com/berndprach/NActivation.

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