Deep Learning using Rectified Linear Units (ReLU)

TL;DR

This paper clarifies the historical origin of ReLU, compares its performance with Tanh and Sigmoid across various tasks, and confirms the superiority of non-saturating functions like ReLU in deep learning.

Contribution

It corrects the historical record of ReLU's origin and provides a comprehensive empirical comparison of activation functions in deep learning tasks.

Findings

ReLU outperforms Sigmoid and Tanh in deep vision and text tasks.

Sigmoid fails to converge due to vanishing gradients.

Tanh performs best in image reconstruction.

Abstract

The Rectified Linear Unit (ReLU) is a foundational activation function in artficial neural networks. Recent literature frequently misattributes its origin to the 2018 (initial) version of this paper, which exclusively investigated ReLU at the classification layer. This paper formally corrects the citation record by tracing the mathematical lineage of piecewise linear functions from early biological models to their definitive integration into deep learning by Nair & Hinton (2010). Alongside this historical rectification, we present a comprehensive empirical comparison of the ReLU, Hyperbolic Tangent (Tanh), and Logistic (Sigmoid) activation functions across image classification, text classification, and image reconstruction tasks. To ensure statistical robustness, we evaluated these functions using 10 independent randomized trials and assessed significance using the non-parametric Kruskal-Wallis $H$ test. The empirical data validates the theoretical limitations of saturating functions. Sigmoid failed to converge in deep convolutional vision tasks due to the vanishing gradient problem, thus yielding accuracies equivalent to random probability. Conversely, ReLU and Tanh exhibited stable convergence. ReLU achieved the highest mean accuracy and F1-score on image classification and text classification tasks, while Tanh yielded the highest peak signal to noise ratio in image reconstruction. Ultimately, this study confirms a statistically significant performance variance among activations, thus reaffirming the necessity of non-saturating functions in deep architectures, and restores proper historical attribution to prior literature.