Periodic Activation Functions Induce Stationarity

• URL: http://arxiv.org/abs/2110.13572v1
• Date: Tue, 26 Oct 2021 11:10:37 GMT
• Title: Periodic Activation Functions Induce Stationarity
• Authors: Lassi Meronen, Martin Trapp, Arno Solin
• Abstract summary: We show that periodic activation functions in Bayesian neural networks establish a connection between the prior on the network weights and translation-invariant, stationary Gaussian process priors. In a series of experiments, we show that periodic activation functions obtain comparable performance for in-domain data and capture sensitivity to perturbed inputs in deep neural networks for out-of-domain detection.
• Score: 19.689175123261613
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural network models are known to reinforce hidden data biases, making them unreliable and difficult to interpret. We seek to build models that `know what they do not know' by introducing inductive biases in the function space. We show that periodic activation functions in Bayesian neural networks establish a connection between the prior on the network weights and translation-invariant, stationary Gaussian process priors. Furthermore, we show that this link goes beyond sinusoidal (Fourier) activations by also covering triangular wave and periodic ReLU activation functions. In a series of experiments, we show that periodic activation functions obtain comparable performance for in-domain data and capture sensitivity to perturbed inputs in deep neural networks for out-of-domain detection.

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