Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
This work offers a mathematically certified framework for neural networks, potentially benefiting researchers in machine learning theory and applications, though it appears incremental in building on existing PDE models.
The paper tackles the problem of understanding neural networks by formulating them as convection-diffusion equations, providing a theoretical foundation, and designs a novel network structure incorporating diffusion mechanisms, validated through experiments on benchmark datasets and real-world applications.
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.