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Tunable Efficient Unitary Neural Networks (EUNN) and their application to RNNs
Li Jing · Yichen Shen · Tena Dubcek · John E Peurifoy · Scott Skirlo · Yann LeCun · Max Tegmark · Marin Soljačić

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #47
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.

Author Information

Li Jing (Massachusetts Institute of Technology)
Yichen Shen (MIT)
Tena Dubcek (MIT)
John E Peurifoy (MIT)
Scott Skirlo (MIT)
Yann LeCun (New York University)
Max Tegmark (MIT)
Marin Soljačić (MIT)

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