ProbAct: A Probabilistic Activation Function for Deep Neural Networks

TL;DR

This paper introduces ProbAct, a novel stochastic activation function for deep neural networks that improves classification accuracy, models uncertainty, and enhances robustness by sampling from a learned distribution during training.

Contribution

The paper proposes ProbAct, a probabilistic activation function that incorporates trainable mean and variance, acting as a form of feature augmentation and model ensemble within neural networks.

Findings

ProbAct improves classification accuracy by 2-3% over ReLU on multiple datasets.

ProbAct enables uncertainty estimation and robustness to noisy inputs.

ProbAct functions as an implicit ensemble of models through its stochastic nature.

Abstract

Activation functions play an important role in training artificial neural networks. The majority of currently used activation functions are deterministic in nature, with their fixed input-output relationship. In this work, we propose a novel probabilistic activation function, called ProbAct. ProbAct is decomposed into a mean and variance and the output value is sampled from the formed distribution, making ProbAct a stochastic activation function. The values of mean and variances can be fixed using known functions or trained for each element. In the trainable ProbAct, the mean and the variance of the activation distribution is trained within the back-propagation framework alongside other parameters. We show that the stochastic perturbation induced through ProbAct acts as a viable generalization technique for feature augmentation. In our experiments, we compare ProbAct with well-known activation functions on classification tasks on different modalities: Images(CIFAR-10, CIFAR-100, and STL-10) and Text (Large Movie Review). We show that ProbAct increases the classification accuracy by +2-3% compared to ReLU or other conventional activation functions on both original datasets and when datasets are reduced to 50% and 25% of the original size. Finally, we show that ProbAct learns an ensemble of models by itself that can be used to estimate the uncertainties associated with the prediction and provides robustness to noisy inputs.