Physical symmetry enhanced neural networks

Abstract

Artificial Intelligence (AI), widely considered "the fourth industrial revolution", has shown its potential to fundamentally change our world. Today's AI technique relies on neural networks. In this thesis, we propose several physical symmetry enhanced neural network models. We first developed unitary recurrent neural networks (RNNs) that solve gradient vanishing and gradient explosion problems. We propose an efficient parametrization method that requires [sigma] (1) complexity per parameter. Our unitary RNN model has shown optimal long-term memory ability. Next, we combine the above model with a gated mechanism. This model outperform popular recurrent neural networks like long short-term memory (LSTMs) and gated recurrent units (GRUs) in many sequential tasks. In the third part, we develop a convolutional neural network architecture that achieves logarithmic scale complexity using symmetry breaking concepts. We demonstrate that our model has superior performance on small image classification tasks. In the last part, we propose a general method to extend convolutional neural networks' inductive bias and embed other types of symmetries. We show that this method improves prediction performance on lens-distorted image