A Significantly Better Class of Activation Functions Than ReLU Like Activation Functions

TL;DR

This paper proposes new cone and parabolic-cone activation functions that outperform ReLU-like functions on benchmarks by enabling neurons to divide input space more precisely, leading to higher accuracy and faster training.

Contribution

Introduction of cone and parabolic-cone activation functions that significantly outperform ReLU-like functions on standard benchmarks and enable simpler neural network architectures.

Findings

Outperform ReLU on CIFAR-10 and Imagenette benchmarks.

Allow neurons to learn XOR with a single neuron.

Speed up training due to larger derivatives.

Abstract

This paper introduces a significantly better class of activation functions than the almost universally used ReLU like and Sigmoidal class of activation functions. Two new activation functions referred to as the Cone and Parabolic-Cone that differ drastically from popular activation functions and significantly outperform these on the CIFAR-10 and Imagenette benchmmarks are proposed. The cone activation functions are positive only on a finite interval and are strictly negative except at the end-points of the interval, where they become zero. Thus the set of inputs that produce a positive output for a neuron with cone activation functions is a hyperstrip and not a half-space as is the usual case. Since a hyper strip is the region between two parallel hyper-planes, it allows neurons to more finely divide the input feature space into positive and negative classes than with infinitely wide half-spaces. In particular the XOR function can be learn by a single neuron with cone-like activation functions. Both the cone and parabolic-cone activation functions are shown to achieve higher accuracies with significantly fewer neurons on benchmarks. The results presented in this paper indicate that many nonlinear real-world datasets may be separated with fewer hyperstrips than half-spaces. The Cone and Parabolic-Cone activation functions have larger derivatives than ReLU and are shown to significantly speedup training.