Differential Equation Networks

MohamadAli Torkamani, Phillip Wallis

Sep 27, 2018 ICLR 2019 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: Most deep neural networks use simple, fixed activation functions, such as sigmoids or rectified linear units, regardless of domain or network structure. We introduce differential equation networks, an improvement to modern neural networks in which each neuron learns the particular nonlinear activation function that it requires. We show that enabling each neuron with the ability to learn its own activation function results in a more compact network capable of achieving comperable, if not superior performance when compared to much larger networks. We also showcase the capability of a differential equation neuron to learn behaviors, such as oscillation, currently only obtainable by a large group of neurons. The ability of differential equation networks to essentially compress a large neural network, without loss of overall performance makes them suitable for on-device applications, where predictions must be computed locally. Our experimental evaluation of real-world and toy datasets show that differential equation networks outperform fixed activatoin networks in several areas.
  • Keywords: deep learning, activation function, differential equations
  • TL;DR: We introduce a method to learn the nonlinear activation function for each neuron in the network.
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