Revise Saturated Activation Functions

TL;DR

This paper revises saturated activation functions, specifically the logistic sigmoid and tanh, demonstrating improved training performance and challenging previous beliefs about saturation hindering deep network training.

Contribution

It introduces rescaled sigmoid and penalized tanh functions, showing they outperform or match state-of-the-art non-saturated functions in deep neural networks.

Findings

Rescaled sigmoid achieves comparable results to tanh.

Penalized tanh outperforms ReLU and leaky ReLU.

Saturation may not hinder training as previously thought.

Abstract

In this paper, we revise two commonly used saturated functions, the logistic sigmoid and the hyperbolic tangent (tanh). We point out that, besides the well-known non-zero centered property, slope of the activation function near the origin is another possible reason making training deep networks with the logistic function difficult to train. We demonstrate that, with proper rescaling, the logistic sigmoid achieves comparable results with tanh. Then following the same argument, we improve tahn by penalizing in the negative part. We show that "penalized tanh" is comparable and even outperforms the state-of-the-art non-saturated functions including ReLU and leaky ReLU on deep convolution neural networks. Our results contradict to the conclusion of previous works that the saturation property causes the slow convergence. It suggests further investigation is necessary to better understand activation functions in deep architectures.