PolyNeuron: Automatic Neuron Discovery via Learned Polyharmonic Spline Activations

Abstract: Automated deep neural network architecture design has received a significant amount of recent attention. However, this attention has not been equally shared by one of the fundamental building blocks of a deep neural network, the neurons. In this study, we propose PolyNeuron, a novel automatic neuron discovery approach based on learned polyharmonic spline activations. More specifically, PolyNeuron revolves around learning polyharmonic splines, characterized by a set of control points, that represent the activation functions of the neurons in a deep neural network. A relaxed variant of PolyNeuron, which we term PolyNeuron-R, loosens the constraints imposed by PolyNeuron to reduce the computational complexity for discovering the neuron activation functions in an automated manner. Experiments show both PolyNeuron and PolyNeuron-R lead to networks that have improved or comparable performance on multiple network architectures (LeNet-5 and ResNet-20) using different datasets (MNIST and CIFAR10). As such, automatic neuron discovery approaches such as PolyNeuron is a worthy direction to explore.