Controllable Orthogonalization in Training DNNs
This addresses the challenge of balancing optimization benefits and representational capacity in DNNs for researchers and practitioners in machine learning, though it is incremental as it builds on existing orthogonalization techniques.
The paper tackled the problem of training deep neural networks with orthogonal weight matrices by proposing ONI, a computationally efficient method using Newton's iteration to control orthogonality, which improved image classification performance and stabilized GAN training, outperforming spectral normalization.
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.