Title: Nonlocal Neural Networks, Nonlocal Diffusion and Nonlocal Modeling,
Abstract: Nonlocal neural networks have been proposed and shown to be effective in
several computer vision tasks, where the nonlocal operations can directly
capture long-range dependencies in the feature space. In this paper, we study
the nature of diffusion and damping effect of nonlocal networks by doing
spectrum analysis on the weight matrices of the well-trained networks, and then
propose a new formulation of the nonlocal block. The new block not only learns
the nonlocal interactions but also has stable dynamics, thus allowing deeper
nonlocal structures. Moreover, we interpret our formulation from the general
nonlocal modeling perspective, where we make connections between the proposed
nonlocal network and other nonlocal models, such as nonlocal diffusion process
and Markov jump process.