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Lin Kong

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2 papers

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AAAI Conference 2022 Conference Paper

HNO: High-Order Numerical Architecture for ODE-Inspired Deep Unfolding Networks

Lin Kong
Wei Sun
Fanhua Shang
Yuanyuan Liu
Hongying Liu

Recently, deep unfolding networks (DUNs) based on optimization algorithms have received increasing attention, and their high efficiency has been confirmed by many experimental and theoretical results. Since this type of networks combines model-based traditional optimization algorithms, they have high interpretability. In addition, ordinary differential equations (ODEs) are often used to explain deep neural networks, and provide some inspiration for designing innovative network models. In this paper, we transform DUNs into first-order ODE forms, and propose a high-order numerical architecture for ODE-inspired deep unfolding networks. To the best of our knowledge, this is the first work to establish the relationship between DUNs and ODEs. Moreover, we take two representative DUNs as examples, apply our architecture to them and design novel DUNs. In theory, we prove the existence, uniqueness of the solution and convergence of the proposed network, and also prove that our network obtains a fast linear convergence rate. Extensive experiments verify the effectiveness and advantages of our architecture.

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AAAI Conference 2021 Conference Paper

Learned Extragradient ISTA with Interpretable Residual Structures for Sparse Coding

Yangyang Li
Lin Kong
Fanhua Shang
Yuanyuan Liu
Hongying Liu
Zhouchen Lin

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding problems. However, existing LISTA methods are all serial connection. To address this issue, we propose a novel extragradient based LISTA (ELISTA), which has a residual structure and theoretical guarantees. Moreover, most LISTA methods use the soft thresholding function, which has been found to cause a large estimation bias. Therefore, we propose a thresholding function for ELISTA instead of soft thresholding. From a theoretical perspective, we prove that our method attains linear convergence. Through ablation experiments, the improvements of our method on the network structure and the thresholding function are verified in practice. Extensive empirical results verify the advantages of our method.

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