Diffusion Mechanism in Residual Neural Network: Theory and Applications

TL;DR

This paper introduces Diff-ResNet, a neural network architecture inspired by diffusion processes, which enhances class separability and improves performance in semi-supervised and few-shot learning tasks.

Contribution

It proposes a novel diffusion residual network that internally incorporates diffusion mechanisms, backed by theoretical proofs and extensive experimental validation.

Findings

Diff-ResNet increases class separability under structured data assumptions.

The method improves accuracy in semi-supervised and few-shot classification tasks.

The diffusion block enhances intra-class compactness and inter-class separation.

Abstract

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy. Many existing deep learning approaches directly impose the fusion loss when training neural networks. In this work, inspired by the convection-diffusion ordinary differential equations (ODEs), we propose a novel diffusion residual network (Diff-ResNet), internally introduces diffusion into the architectures of neural networks. Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. Moreover, this property can be easily adopted by the residual networks for constructing the separable hyperplanes. Extensive experiments of synthetic binary classification, semi-supervised graph node classification and few-shot image classification in various datasets validate the effectiveness of the proposed method.