Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
<|reference_start|>Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks: 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.<|reference_end|>
@article{wang2024convection-diffusion,
    title={Convection-Diffusion Equation: A Theoretically Certified Framework for
  Neural Networks},
    author={Tangjun Wang, Chenglong Bao, Zuoqiang Shi},
    journal={arXiv preprint arXiv:2403.15726},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.15726},
    primaryClass={cs.LG}
}