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各种实际领域中处理大数据的强大应用，深度学习的数学理论已经被需要。主要的困难在于为特定的学习任务而设计的网络的结构和架构。由于处理大维度数据（如数万维的自然图像）所施加的结构，无论是经典的近似理论还是最近的深度ReLU神经网络的近似理论都不能应用。本项目旨在研究结构化神经网络的近似理论。我们计划用深度卷积神经网络、算子学习和谱图网络建立反卷积的数学理论。