On Generalization Bounds of a Family of Recurrent Neural Networks

TL;DR

This paper develops theoretical generalization bounds for various RNN architectures, including vanilla, MGU, LSTM, and Conv RNNs, under the PAC-Learning framework, highlighting their differences and advantages.

Contribution

It provides the first known generalization bounds for MGU, LSTM, and Conv RNNs, and offers tighter bounds for vanilla RNNs compared to previous results.

Findings

Tighter generalization bounds for vanilla RNNs.

First bounds established for MGU, LSTM, and Conv RNNs.

Variants like LSTM and Conv RNNs show improved generalization.

Abstract

Recurrent Neural Networks (RNNs) have been widely applied to sequential data analysis. Due to their complicated modeling structures, however, the theory behind is still largely missing. To connect theory and practice, we study the generalization properties of vanilla RNNs as well as their variants, including Minimal Gated Unit (MGU), Long Short Term Memory (LSTM), and Convolutional (Conv) RNNs. Specifically, our theory is established under the PAC-Learning framework. The generalization bound is presented in terms of the spectral norms of the weight matrices and the total number of parameters. We also establish refined generalization bounds with additional norm assumptions, and draw a comparison among these bounds. We remark: (1) Our generalization bound for vanilla RNNs is significantly tighter than the best of existing results; (2) We are not aware of any other generalization bounds for MGU, LSTM, and Conv RNNs in the exiting literature; (3) We demonstrate the advantages of these variants in generalization.