CIF: Medium: Collaborative Research: Theory of Optimization Geometry and Algorithms for Neural Networks

CIF：媒介：协作研究：神经网络优化几何理论和算法

• 批准号: 2002272
• 负责人: Jason Lee
• 金额: $ 40万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-10-15 至 2024-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2002272&HistoricalAwards=false
• 关键词: CIF; Medium; Collaborative; Research; Theory

Deep learning has attracted a significant amount of interest in recent years due to its widespread applicability in computer vision, artificial intelligence and natural language processing, alongside recent strides in autonomous driving. The theoretical underpinnings behind such success, however, remain elusive to a large extent, hindering its further adoption in other applications. This project aims to advance the theoretical foundations of training neural networks in terms of optimization landscape and algorithmic efficacy, which in turn should have a measurable impact on the practice of deep learning by providing guiding principles for network design, algorithm selection, hyperparameter tuning, and adversarial training. This project adopts an interdisciplinary approach fusing ideas from machine learning, optimization, statistical signal processing, high-dimensional statistics, nonparametric statistics, and information theory. This project will likewise develop courses and tutorials on theoretical foundations of large-scale machine learning and provide extensive training opportunities for students at all levels.This project aims to develop a comprehensive theory to characterize the optimization landscape and geometry of loss functions and algorithmic regularizations of major neural network training problems, and explore how the network architecture---including depth, width, and activation functions---affect these properties, thus providing guidelines for the design of algorithms to train these networks more efficiently with theoretical performance guarantees. The project will explore the geometric properties and their impact on the optimization performance in training multi-layer neural networks, auto-encoders, generative adversarial networks, and adversarial training involving non-convex and saddle-point problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

近年来，由于其在计算机视觉，人工智能和自然语言处理中的广泛适用性以及最近在自主驾驶方面的进步，深度学习引起了极大的兴趣。但是，这种成功背后的理论基础在很大程度上仍然难以捉摸，阻碍了其在其他应用中的进一步采用。该项目旨在从优化景观和算法效力方面推进训练神经网络的理论基础，这反过来又应通过为网络设计，算法选择，超级参数调整和对抗性培训提供指导性的指导原理来对深度学习实践产生可衡量的影响。该项目采用了一种跨学科的方法，从机器学习，优化，统计信号处理，高维统计，非参数统计和信息理论融合了思想。 This project will likewise develop courses and tutorials on theoretical foundations of large-scale machine learning and provide extensive training opportunities for students at all levels.This project aims to develop a comprehensive theory to characterize the optimization landscape and geometry of loss functions and algorithmic regularizations of major neural network training problems, and explore how the network architecture---including depth, width, and activation functions---affect these properties, thus providing设计算法设计指南，可以通过理论性能保证更有效地培训这些网络。该项目将探索几何特性及其对培训多层神经网络，自动编码器，生成对抗网络以及涉及非convex和鞍点问题的对抗性培训的影响的影响。该奖项反映了NSF的法定任务，并通过评估基金会的范围，反映了NSF的法定任务，并已被评估了基金会的范围。

项目成果

Neural Networks can Learn Representations with Gradient Descent

• DOI: 10.48550/arxiv.2206.15144
• 发表时间: 2022-06
• 期刊: ArXiv
• 作者: Alexandru Damian;Jason D. Lee;M. Soltanolkotabi