Symmetric-APL Activations: Training Insights and Robustness to Adversarial Attacks

Mohammadamin Tavakoli, Forest Agostinelli, Pierre Baldi

TL;DR: Symmetric Adaptive Piecewise Linear activations are proposed as new activation function with deep explanation on training behavior and robustness to adversarial attacks.

Abstract: Deep neural networks with learnable activation functions have shown superior performance over deep neural networks with fixed activation functions for many different problems. The adaptability of learnable activation functions adds expressive power to the model which results in better performance. Here, we propose a new learnable activation function based on Adaptive Piecewise Linear units (APL), which 1) gives equal expressive power to both the positive and negative halves on the input space and 2) is able to approximate any zero-centered continuous non-linearity in a closed interval. We investigate how the shape of the Symmetric-APL function changes during training and perform ablation studies to gain insight into the reason behind these changes. We hypothesize that these activation functions go through two distinct stages: 1) adding gradient information and 2) adding expressive power. Finally, we show that the use of Symmetric-APL activations can significantly increase the robustness of deep neural networks to adversarial attacks. Our experiments on both black-box and open-box adversarial attacks show that commonly-used architectures, namely Lenet, Network-in-Network, and ResNet-18 can be up to 51% more resistant to adversarial fooling by only using the proposed activation functions instead of ReLUs.

Keywords: Activation function, Adaptive, Training, Robustness, Adversarial attack