Deep Neural Networks motivated by Partial Differential Equations. (arXiv:1804.04272v1 [cs.LG])

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of multivariate functions and the output of image processing algorithms as solutions to certain PDEs. Posing image processing problems in the infinite dimensional setting provides powerful tools for their analysis and solution. Over the last three decades, the reinterpretation of classical image processing tasks through the PDE lens has been creating multiple celebrated approaches that benefit a vast area of tasks including image segmentation, denoising, registration, and reconstruction. In this paper, we establish a new PDE-interpretation of deep convolution neural networks (CNN) that are commonly used for learning tasks involving speech, image, and video data. Our interpretation includes convolution residual neural networks (ResNet), which are among the m 查看全文>>