Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs

TL;DR

This paper introduces a tunable, computationally efficient unitary neural network architecture (EUNN) that enhances RNN performance on tasks requiring long-term memory, outperforming existing models in accuracy and training speed.

Contribution

The paper presents a novel EUNN architecture with fully tunable unitary space and low computational complexity, improving RNN capabilities for long-term data correlations.

Findings

EUNNs outperform state-of-the-art unitary RNNs and LSTMs in benchmarks.

EUNNs achieve faster training speeds while maintaining high accuracy.

The architecture effectively solves gradient issues in RNNs.

Abstract

Using unitary (instead of general) matrices in artificial neural networks (ANNs) is a promising way to solve the gradient explosion/vanishing problem, as well as to enable ANNs to learn long-term correlations in the data. This approach appears particularly promising for Recurrent Neural Networks (RNNs). In this work, we present a new architecture for implementing an Efficient Unitary Neural Network (EUNNs); its main advantages can be summarized as follows. Firstly, the representation capacity of the unitary space in an EUNN is fully tunable, ranging from a subspace of SU(N) to the entire unitary space. Secondly, the computational complexity for training an EUNN is merely $\mathcal{O}(1)$ per parameter. Finally, we test the performance of EUNNs on the standard copying task, the pixel-permuted MNIST digit recognition benchmark as well as the Speech Prediction Test (TIMIT). We find that our architecture significantly outperforms both other state-of-the-art unitary RNNs and the LSTM architecture, in terms of the final performance and/or the wall-clock training speed. EUNNs are thus promising alternatives to RNNs and LSTMs for a wide variety of applications.