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arXiv 2302.05587cs.LG
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分层优化衍生学习

Hierarchical Optimization-Derived Learning

Dalian University of Technology(大连理工大学);University of Victoria(维多利亚大学);Southern University of Science and Technology(南方科技大学);National Center for Applied Mathematics Shenzhen(深圳国家应用数学中心);Peng Cheng Laboratory(鹏城实验室);The Hong Kong Polytechnic University(香港理工大学)

Risheng Liu, Xuan Liu, Shangzhi Zeng, Jin Zhang, Yixuan Zhang

AI总结:

针对现有优化衍生学习将模型构建与学习割裂的问题,提出分层优化衍生学习(HODL)框架,同时研究两者的内在耦合行为,并首次严格证明了优化与学习的联合收敛性,在合成与真实数据上验证了其优越性能。

摘要:

近年来,通过利用优化技术来构建深度模型的传播过程,提出了多种所谓的优化衍生学习(Optimization-Derived Learning, ODL)方法来解决各种学习与视觉任务。尽管已取得相对令人满意的实际性能,但现有ODL方法仍存在一些基本问题。具体而言,当前的ODL方法倾向于将模型构建和学习视为两个独立的阶段,从而未能构建它们潜在的耦合与依赖关系。在本研究中,我们首先建立了一个名为分层ODL(HODL)的新框架,以同时研究优化衍生模型构建及其相应学习过程的内在行为。随后,我们从逼近质量和稳定性分析的角度,严格证明了这两个子任务的联合收敛性。据我们所知,这是针对优化与学习这两个耦合ODL组件的首次理论保证。我们通过将HODL应用于现有ODL方法未能妥善解决的挑战性学习任务,进一步证明了该框架的灵活性。最后,我们在合成数据以及视觉和其他学习任务的实际应用上进行了广泛实验,验证了HODL在各种应用场景中的理论性质和实际性能。

英文摘要:

In recent years, by utilizing optimization techniques to formulate the propagation of deep model, a variety of so-called Optimization-Derived Learning (ODL) approaches have been proposed to address diverse learning and vision tasks. Although having achieved relatively satisfying practical performance, there still exist fundamental issues in existing ODL methods. In particular, current ODL methods tend to consider model construction and learning as two separate phases, and thus fail to formulate their underlying coupling and depending relationship. In this work, we first establish a new framework, named Hierarchical ODL (HODL), to simultaneously investigate the intrinsic behaviors of optimization-derived model construction and its corresponding learning process. Then we rigorously prove the joint convergence of these two sub-tasks, from the perspectives of both approximation quality and stationary analysis. To our best knowledge, this is the first theoretical guarantee for these two coupled ODL components: optimization and learning. We further demonstrate the flexibility of our framework by applying HODL to challenging learning tasks, which have not been properly addressed by existing ODL methods. Finally, we conduct extensive experiments on both synthetic data and real applications in vision and other learning tasks to verify the theoretical properties and practical performance of HODL in various application scenarios.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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