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Mar, 2024
对流扩散方程:神经网络的理论认证框架
Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks
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Tangjun Wang, Chenglong Bao, Zuoqiang Shi
TL;DR
本文研究神经网络的偏微分方程模型，通过对其进行分析，证明了这些模型可以由对流-扩散方程表达，从而为神经网络提供了数学基础和更深入的理解。基于这个模型，我们设计了一种新的网络结构，将扩散机制融入网络体系结构，并通过广泛实验验证了该模型的性能。
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
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