基于几何和物理性质的深度模型优化研究

Deep learning methods keep setting the new state-of-the-art for many computer vision and machine learning applications, with image classification and understanding as the prominent examples. In spite of these practical successes, however, theoretical analysis of deep learning, in particular optimization challenges and generalization bounds, remains an active research topic. In this project, we study generalization of deep neural networks (DNNs), and measure how generalization error relates to properties of network solutions. Such analysis would provide geometric constraints on weight matrices of DNNs. We then study optimization methods with various types of manifold constraints on weight matrices, and develop the corresponding algorithms which can give exact or approximate solutions. Based on the intuition that features learned at hidden neurons of DNNs can be considered as pattern detectors that characterize the input data from specific views, we also study in this project multi-view learning approaches to regularize trainings of DNNs. We study such regularization techniques and develop the corresponding efficient solving algorithms. Based on the above research, we study and compare the solution properties and generalization capabilities of existing deep architectures. Such comparative studies would provide for practical image classification and understanding problems the principles on selection and design of new deep architectures and optimization methods. Research in this project would also improve robustness of deep learning methods against adversarial examples and their performance in small-sample learning problems.

深度学习技术近年来在以图像理解为代表的视觉和机器学习应用领域取得突破性结果。与此同时，对深度模型工作机理的研究也是一个热点方向。虽取得一定成果，但相关理论研究，尤其是在深度模型优化难点和泛化条件方面仍有待完善。在此背景下，本项目从深度模型泛化理论分析入手，通过量化泛化误差与参数解的性质之间的关系，导出对深度模型中权重矩阵的几何性质约束。本项目进而研究基于不同流形几何约束下的深度模型优化问题，以及相应的严格和近似求解算法。另一方面，本项目基于深度模型中神经元可看作是从不同视角学习到的样本特征检测器这一物理意义，研究基于多视角学习的深度模型正则化方法，并研究相应快速优化算法。在以上研究基础上，本项目对现有主流网络模型在量和质上进行参数解的性质和泛化能力分析，进而为图像理解应用中网络架构和优化方法的选取和设计提供原则性指导。相关研究成果也将提升深度学习方法在对抗样本和小样本等问题上的实际性能。

本项目聚焦深度学习理论与优化研究，主要从解的内在几何性质等角度出发，研究具有更好泛化性能的深度学习优化解，以期提升深度学习方法在对抗样本、迁移学习和小样本学习等问题上的实际性能。项目首先完成“正交深度神经网络”（TPAMI, 2019）等重要基础性工作，并在其基础上沿着项目主方向推进，在域适应学习、对抗样本的产生和工作机理、三维表面生成以及三维语义分析等方向产生重要成果； 以第一或通讯作者共发表期刊论文8篇（包括人工智能顶级期刊TPAMI 5篇），会议论文25篇（包括人工智能顶级会议CVPR 6篇、ICCV 4篇、ICML 2篇以及NeurIPS 2篇），申请发明专利3项；基于单张物体的三维表面重建工作入选CVPR 2019最佳论文候选。通过项目实施，项目负责人与华为、微软亚洲研究院以及奥比中光等建立了紧密合作关系，其中发表于NeurIPS 2020的GPNet等研究成果被应用于奥比中光三维相机系统中。