Diffusion Mechanism in Residual Neural Network: Theory and Applications
This work addresses the challenge of enhancing separability and reducing intra-class distances in classification tasks with limited data, representing an incremental improvement by integrating diffusion into existing residual networks.
The authors tackled the problem of improving classification accuracy in tasks with limited training samples by proposing a diffusion residual network (Diff-ResNet) that incorporates diffusion mechanisms into neural network architectures, achieving validated effectiveness across synthetic binary classification, semi-supervised graph node classification, and few-shot image classification in various datasets.
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.