Approximation theory of structured neural networks

结构化神经网络的逼近理论

• 批准号: DP240101919
• 负责人: Prof Dingxuan Zhou
• 金额: $ 28.01万
• 依托单位: The University of Sydney
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2024
• 资助国家: 澳大利亚
• 起止时间: 2024-08-01 至 2027-07-31
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP240101919
• 关键词: Approximation; theory; structured; neural; networks

Mathematical theory for deep learning has been desired due to the power applications of deep neural networks to deal with big data in various practical domains. The main difficulty lies in the structures and architectures imposed to networks designed for specific learning tasks. Neither the classical approximation theory nor the recent one for depths of ReLU neural networks can be applied due to the structures imposed for processing large dimensional data such as natural images of tens of thousands of dimensions. This project aims at an approximation theory for structured neural networks. We plan to establish mathematical theories for deconvolution with deep convolutional neural networks, operator learning, and spectral graph networks.

由于深度神经网络在处理各种实际领域的大数据方面的强大应用，深度学习的数学理论一直受到人们的欢迎。主要困难在于为特定学习任务设计的网络的结构和架构。由于处理大维数据（例如数万维的自然图像）所强加的结构，无论是经典的近似理论还是最新的 ReLU 神经网络深度近似理论都无法应用。该项目旨在研究结构化神经网络的近似理论。我们计划建立深度卷积神经网络、算子学习和谱图网络的反卷积数学理论。