Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks

2024-03-23 · Tangjun Wang, Chenglong Bao, Zuoqiang Shi

In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated by a convection-diffusion equation. This theoretically certified framework gives mathematical foundation and more understanding of neural networks. Moreover, based on the convection-diffusion equation model, we design a novel network structure, which incorporates diffusion mechanism into network architecture. Extensive experiments on both benchmark datasets and real-world applications validate the performance of the proposed model.

📄 PDF Abstract BibTeX arXiv:2403.15726

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