SPLASH: Learnable Activation Functions for Improving Accuracy and Adversarial Robustness

TL;DR

SPLASH units are learnable activation functions that enhance both the accuracy and adversarial robustness of deep neural networks across multiple datasets and architectures.

Contribution

Introduction of SPLASH units, a novel learnable activation function that improves accuracy and robustness without complex training procedures.

Findings

SPLASH units outperform nine other activation functions on multiple datasets.

Networks with SPLASH units show up to 31% increased robustness to adversarial attacks.

SPLASH units maintain simplicity while approximating a wide range of non-linear functions.

Abstract

We introduce SPLASH units, a class of learnable activation functions shown to simultaneously improve the accuracy of deep neural networks while also improving their robustness to adversarial attacks. SPLASH units have both a simple parameterization and maintain the ability to approximate a wide range of non-linear functions. SPLASH units are: 1) continuous; 2) grounded (f(0) = 0); 3) use symmetric hinges; and 4) the locations of the hinges are derived directly from the data (i.e. no learning required). Compared to nine other learned and fixed activation functions, including ReLU and its variants, SPLASH units show superior performance across three datasets (MNIST, CIFAR-10, and CIFAR-100) and four architectures (LeNet5, All-CNN, ResNet-20, and Network-in-Network). Furthermore, we show that SPLASH units 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 LeNet5, All-CNN, ResNet-20, and Network-in-Network, can be up to 31% more robust to adversarial attacks by simply using SPLASH units instead of ReLUs.