Collaborative Research: CIF: Small: Deep Sparse Models: Analysis and Algorithms

合作研究：CIF：小型：深度稀疏模型：分析和算法

• 批准号: 2008460
• 负责人: Zhihui Zhu
• 金额: $ 20.55万
• 依托单位: University of Denver
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2008460&HistoricalAwards=false
• 关键词: Collaborative; Research; CIF; Small; Deep

Deep convolutional neural networks are a class of mathematical models that provide a variety of machine learning tools with impressive success, often obtaining state-of-the-art results across different fields. Yet, their theoretical understanding and the fundamental ideas behind these algorithms have remained elusive. These questions are essential to recognize and characterize their limitations, to provide guarantees for their performance, and even to develop and engineer improved practical models. A promising approach to obtain this understanding is to make assumptions about the class of samples on which these models are deployed (e.g., so that these are "simple enough") with the intention of providing theoretical insights about them. Further understanding of this 'multi-layered convolutional sparse model' is what this project seeks accomplish, broadening the understanding of its related optimization and learning problems, and shedding light on deep learning methodologies.This project proposes to advance the state of the art in generalized sparse models of different numbers of layers, focusing on both inference and learning problems. Provable and efficient optimization methods will be derived for the inverse problems associated with multilayer sparse models by relying on new results in proximal gradient and subgradient descent methods. This proposal will further extend the formulation of the pursuit to other settings, increasing stability and robustness to the choice of parameters and to outliers. Furthermore, efficient algorithms for the corresponding unsupervised learning problem will be proposed and analyzed. Questions of sample complexity and generalization bounds will in turn be studied in supervised learning settings. Throughout this project, the resulting algorithms will be studied in terms of their relation to specific convolutional network architectures. The project brings together combined expertise in signal processing, dictionary learning, machine learning, and the design, analysis and implementation of optimization methods for large-scale 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.

深度卷积神经网络是一类数学模型，它提供了各种机器学习工具，取得了令人印象深刻的成功，通常在不同领域获得最先进的结果。然而，他们对这些算法背后的理论理解和基本思想仍然难以捉摸。这些问题对于认识和描述其局限性、为其性能提供保证、甚至开发和设计改进的实用模型至关重要。获得这种理解的一个有前途的方法是对部署这些模型的样本类别做出假设（例如，以便这些模型“足够简单”），旨在提供有关它们的理论见解。该项目寻求实现的目标是进一步理解这种“多层卷积稀疏模型”，拓宽对其相关优化和学习问题的理解，并阐明深度学习方法。该项目旨在推进广义领域的最新技术不同层数的稀疏模型，重点关注推理和学习问题。依靠近端梯度和次梯度下降方法的新结果，将针对与多层稀疏模型相关的反问题导出可证明且有效的优化方法。该提案将进一步将追求的制定扩展到其他设置，提高参数选择和异常值的稳定性和鲁棒性。此外，还将提出并分析相应的无监督学习问题的有效算法。样本复杂性和泛化界限的问题将在监督学习环境中依次进行研究。在整个项目中，将根据生成的算法与特定卷积网络架构的关系来研究它们。该项目汇集了信号处理、字典学习、机器学习以及大规模问题优化方法的设计、分析和实施方面的综合专业知识。该奖项反映了 NSF 的法定使命，并通过使用基金会的评估进行评估，认为值得支持。智力价值和更广泛的影响审查标准。

项目成果

Learning Approach For Fast Approximate Matrix Factorizations

• DOI: 10.1109/icassp43922.2022.9747165
• 发表时间: 2022-05
• 期刊: ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
• 作者: Haiyan Yu;Zhen Qin;Zhihui Zhu

Recovery and Generalization in Over-Realized Dictionary Learning

• 发表时间: 2020-06
• 期刊: ArXiv
• 作者: Jeremias Sulam;Chong You;Zhihui Zhu

A Geometric Analysis of Neural Collapse with Unconstrained Features

• 发表时间: 2021-05
• 作者: Zhihui Zhu;Tianyu Ding;Jinxin Zhou;Xiao Li;Chong You;Jeremias Sulam;Qing Qu

Convolutional Normalization: Improving Deep Convolutional Network Robustness and Training

• 发表时间: 2021-03
• 作者: Sheng Liu;Xiao Li;Yuexiang Zhai;Chong You;Zhihui Zhu;C. Fernandez‐Granda;Qing Qu

On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features

• DOI: 10.48550/arxiv.2203.01238
• 发表时间: 2022-03
• 期刊: ArXiv
• 作者: Jinxin Zhou-;Xiao Li;Tian Ding;Chong You;Qing Qu;Zhihui Zhu