Sigsoftmax: Reanalysis of the Softmax Bottleneck

TL;DR

This paper introduces sigsoftmax, a new output activation function designed to overcome the softmax bottleneck in neural networks, improving language modeling performance without adding extra parameters.

Contribution

The paper proposes sigsoftmax, a novel activation function that breaks the softmax bottleneck by re-analyzing its limitations and providing a parameter-free solution.

Findings

Sigsoftmax outperforms softmax in language modeling tasks.

Mixture of sigsoftmax surpasses mixture of softmax.

Re-analysis clarifies the cause of the softmax bottleneck.

Abstract

Softmax is an output activation function for modeling categorical probability distributions in many applications of deep learning. However, a recent study revealed that softmax can be a bottleneck of representational capacity of neural networks in language modeling (the softmax bottleneck). In this paper, we propose an output activation function for breaking the softmax bottleneck without additional parameters. We re-analyze the softmax bottleneck from the perspective of the output set of log-softmax and identify the cause of the softmax bottleneck. On the basis of this analysis, we propose sigsoftmax, which is composed of a multiplication of an exponential function and sigmoid function. Sigsoftmax can break the softmax bottleneck. The experiments on language modeling demonstrate that sigsoftmax and mixture of sigsoftmax outperform softmax and mixture of softmax, respectively.