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

arXiv:2403.15726v1 Announce Type: new
Abstract: 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 …

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