Orthogonality is widely used for training deep neural networks (DNNs) due to its ability to maintain all singular values of the Jacobian close to 1 and reduce redundancy in representation. This paper proposes a computationally efficient and numerically stable orthogonalization method using Newton's iteration (ONI), to learn a layer-wise orthogonal weight matrix in DNNs. ONI works by iteratively stretching the singular values of a weight matrix towards 1. This property enables it to control the orthogonality of a weight matrix by its number of iterations. We show that our method improves the performance of image classification networks by effectively controlling the orthogonality to provide an optimal tradeoff between optimization benefits and representational capacity reduction. We also show that ONI stabilizes the training of generative adversarial networks (GANs) by maintaining the Lipschitz continuity of a network, similar to spectral normalization (SN), and further outperforms SN by providing controllable orthogonality.
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