Neural networks with trainable matrix activation functions

TL;DR

This paper introduces trainable matrix-valued activation functions for neural networks, enabling the activation functions to be learned during training, which enhances flexibility and robustness.

Contribution

It presents a systematic method for constructing trainable matrix activation functions based on generalized ReLU, integrated into neural networks for improved adaptability.

Findings

Neural networks with trainable matrix activations are simple and efficient.

The approach demonstrates robustness in numerical experiments.

Training these activations alongside weights improves model flexibility.

Abstract

The training process of neural networks usually optimize weights and bias parameters of linear transformations, while nonlinear activation functions are pre-specified and fixed. This work develops a systematic approach to constructing matrix-valued activation functions whose entries are generalized from ReLU. The activation is based on matrix-vector multiplications using only scalar multiplications and comparisons. The proposed activation functions depend on parameters that are trained along with the weights and bias vectors. Neural networks based on this approach are simple and efficient and are shown to be robust in numerical experiments.