Extraction of nonlinearity in neural networks and model compression with Koopman operator

Nonlinearity plays a crucial role in deep neural networks. In this paper, we first investigate the degree to which the nonlinearity of the neural network is essential. For this purpose, we employ the Koopman operator, extended dynamic mode decomposition, and the tensor-train format. The results imply that restricted nonlinearity is enough for the classification of handwritten numbers. Then, we propose a model compression method for deep neural networks, which could be beneficial to handling large networks in resource-constrained environments. Leveraging the Koopman operator, the proposed method enables us to use linear algebra in the internal processing of neural networks. We numerically show that the proposed method performs comparably or better than conventional methods in highly compressed model settings for the handwritten number recognition task.