Interpreting deep neural networks from the ordinary differential equations (ODEs) perspective has inspired many efficient and robust network architectures. However, existing ODE based approaches ignore the relationship among data points, which is a critical component in many problems including few-shot learning and semi-supervised learning. In this paper, inspired by the diffusive ODEs, we propose a novel diffusion residual network (Diff-ResNet) to strengthen the interactions among data points. Under the structured data assumption, it is proved that the diffusion mechanism can decrease the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. This property can be easily adopted by the residual networks for constructing the separable hyperplanes. The synthetic binary classification experiments demonstrate the effectiveness of the proposed diffusion mechanism. Moreover, extensive experiments of few-shot image classification and semi-supervised graph node classification in various datasets validate the advantages of the proposed Diff-ResNet over existing few-shot learning methods.
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