A Unified Framework to Analyze and Design the Nonlocal Blocks for Neural Networks

The nonlocal-based blocks are designed for capturing long-range spatial-temporal dependencies in computer vision tasks. Although having shown excellent performances, they lack the mechanism to encode the rich, structured information among elements in an image. In this paper, to theoretically analyze the property of these nonlocal-based blocks, we provide a unified framework to interpret them, where we view them as a graph filter generated on a fully-connected graph. When choosing Chebyshev graph filter, a generalized formulation can be derived for explaining the existing nonlocal-based blocks (e.g. nonlocal block, nonlocal stage, double attention block) and uses to analyze their irrationality. Furthermore, by removing the irrationality, we propose an efficient and robust Chebyshev spectral nonlocal block, which can be more flexibly inserted into deep neural networks than the existing nonlocal blocks. Experimental results demonstrate the clear-cut improvements and practical applicabilities of the proposed spectral nonlocal blocks on image classification (Cifar-10/100, ImageNet), fine-grained image classification (CUB-200), action recognition (UCF-101) tasks.