Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs
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Proceedings of the 34th International Conference on Machine Learning, PMLR 70:17331741, 2017.
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 longterm 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 pixelpermuted MNIST digit recognition benchmark as well as the Speech Prediction Test (TIMIT). We find that our architecture significantly outperforms both other stateoftheart unitary RNNs and the LSTM architecture, in terms of the final performance and/or the wallclock training speed. EUNNs are thus promising alternatives to RNNs and LSTMs for a wide variety of applications.
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