Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence and higher accuracy than the original optimization methods. In this line of research, this paper develops a novel deep recurrent neural network (coined reweighted-RNN) by the unfolding of a reweighted $\ell_1$-$\ell_1$ minimization algorithm and applies it to the task of sequential signal reconstruction. To the best of our knowledge, this is the first deep unfolding method that explores reweighted minimization. Due to the underlying reweighted minimization model, our RNN has a different soft-thresholding function (alias, different activation functions) for each hidden unit in each layer. Furthermore, it has higher network expressivity than existing deep unfolding RNN models due to the over-parameterizing weights. Importantly, we establish theoretical generalization error bounds for the proposed reweighted-RNN model by means of Rademacher complexity. The bounds reveal that the parameterization of the proposed reweighted-RNN ensures good generalization. We apply the proposed reweighted-RNN to the problem of video frame reconstruction from low-dimensional measurements, that is, sequential frame reconstruction. The experimental results on the moving MNIST dataset demonstrate that the proposed deep reweighted-RNN significantly outperforms existing RNN models.
Dual-Stage Reweighted MoE for Long-Tailed Egocentric Mistake Detection
Key Lab. of Intelligent Information Processing, Institute of Computing Technology, CAS（智能信息处理重点实验室，计算技术研究所，中国科学院）；School of Computer Science and Tech., University of Chinese Academy of Sciences（中国科学院大学计算机科学与技术学院）；Institute of Information Engineering, CAS（信息工程研究所，中国科学院）；School of Cyber Security, University of Chinese Academy of Sciences（中国科学院大学网络安全学院）
Ruhr University Bochum（波鸿鲁尔大学）；Technical University Berlin（柏林工业大学）；Technical University of Munich（慕尼黑工业大学）
We address the detection of material defects, which are inside a layered material structure using compressive sensing based multiple-input and multiple-output (MIMO) wireless radar. Here, the strong clutter due to the reflection of the layered structure's surface often makes the detection of the defects challenging. Thus, sophisticated signal separation methods are required for improved defect detection. In many scenarios, the number of defects that we are interested in is limited and the signaling response of the layered structure can be modeled as a low-rank structure. Therefore, we propose …
La Trobe University（拉筹伯大学）；University of Queensland（昆士兰大学）
Support vector machines (SVMs) are an important tool in modern data analysis. Traditionally, support vector machines have been fitted via quadratic programming, either using purpose-built or off-the-shelf algorithms. We present an alternative approach to SVM fitting via the majorization--minimization (MM) paradigm. Algorithms that are derived via MM algorithm constructions can be shown to monotonically decrease their objectives at each iteration, as well as be globally convergent to stationary points. We demonstrate the construction of iteratively-reweighted least-squares (IRLS) algorithms, vi…
In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$ minimization problems. We extend some existing iterative reweighted $l_1$ (IRL1) and $l_2$ (IRL2) minimization methods to solve these problems and proposed new variants for them in which each subproblem has a closed form solution. Also, we provide a unified convergence analysis for these methods. In addition, we propose a novel Lipschitz continuous $ε$-approxi…
National University of Singapore（新加坡国立大学）；Peking University（北京大学）
This work presents a general framework for solving the low rank and/or sparse matrix minimization problems, which may involve multiple non-smooth terms. The Iteratively Reweighted Least Squares (IRLS) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This work generalizes IRLS to solve joint/mixed low rank and sparse minimization problems, which are essential formulations…
We propose a new deep recurrent neural network (RNN) architecture for sequential signal reconstruction. Our network is designed by unfolding the iterations of the proximal gradient method that solves the l1-l1 minimization problem. As such, our network leverages by design that signals have a sparse representation and that the difference between consecutive signal representations is also sparse. We evaluate the proposed model in the task of reconstructing video frames from compressive measurements and show that it outperforms several state-of-the-art RNN models.
Nowadays, the availability of large-scale data in disparate application domains urges the deployment of sophisticated tools for extracting valuable knowledge out of this huge bulk of information. In that vein, low-rank representations (LRRs) which seek low-dimensional embeddings of data have naturally appeared. In an effort to reduce computational complexity and improve estimation performance, LRR has been viewed via a matrix factorization (MF) perspective. Recently, low-rank MF (LRMF) approaches have been proposed for tackling the inherent weakness of MF i.e., the unawareness of the dimension…
Efficient Low-rank Identification via Accelerated Iteratively Reweighted Nuclear Norm Minimization
School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）；Center for Applied Mathematics of Henan Province, Henan University（河南大学河南省应用数学中心）
University of Michigan（密歇根大学）；Fudan University（复旦大学）；Amazon Web Services（亚马逊云科技）
Deep learning models such as the Transformer are often constructed by heuristics and experience. To provide a complementary foundation, in this work we study the following problem: Is it possible to find an energy function underlying the Transformer model, such that descent steps along this energy correspond with the Transformer forward pass? By finding such a function, we can view Transformers as the unfolding of an interpretable optimization process across iterations. This unfolding perspective has been frequently adopted in the past to elucidate more straightforward deep models such as MLPs…
Precise asymptotics of reweighted least-squares algorithms for linear diagonal networks
School of Electrical and Computer Engineering, Georgia Institute of Technology（佐治亚理工学院电气与计算机工程学院）；School of Industrial & Systems Engineering, Georgia Institute of Technology（佐治亚理工学院工业与系统工程学院）
Vrije Universiteit Brussel（布鲁塞尔自由大学）；imec（欧洲微电子研究中心）；Weizmann Institute of Science（魏茨曼科学研究所）
Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new deep-unfolding-based network design for the problem of Robust Principal Component Analysis (RPCA) with application to video foreground-background separation. Unlike existing designs, our approach focuses on modeling the temporal correlation between the sparse representations of consecutive video frames. To this end, we perform the unfolding of an iterative algorithm …
Recently, the paradigm of unfolding iterative algorithms into finite-length feed-forward neural networks has achieved a great success in the area of sparse recovery. Benefit from available training data, the learned networks have achieved state-of-the-art performance in respect of both speed and accuracy. However, the structure behind sparsity, imposing constraint on the support of sparse signals, is often an essential prior knowledge but seldom considered in the existing networks. In this paper, we aim at bridging this gap. Specifically, exploiting the iterative reweighted $\ell_1$ minimizati…
RWTH Aachen University（亚琛工业大学）；Institute for Theoretical Information Technology（理论信息技术研究所）；Chair for Mathematics of Information Processing（信息处理数学讲座教授席位）
Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on generalization properties of neural networks have been made, great challenges remain. In this chapter, we discuss and combine these topics to present a generalization error analysis for a class of neural networks suitable for sparse reconstruction from few linear measurements. The hypothesis class considered is inspired by the classical iterative soft-thresholding al…
University of Southern California（南加州大学）；University of Cambridge（剑桥大学）；Carnegie Mellon University（卡内基梅隆大学）
Deep neural networks are often overparameterized and may not easily achieve model generalization. Adversarial training has shown effectiveness in improving generalization by regularizing the change of loss on top of adversarially chosen perturbations. The recently proposed sharpness-aware minimization (SAM) algorithm conducts adversarial weight perturbation, encouraging the model to converge to a flat minima. SAM finds a common adversarial weight perturbation per-batch. Although per-instance adversarial weight perturbations are stronger adversaries and can potentially lead to better generaliza…
Iterative Reweighted Framework Based Algorithms for Sparse Linear Regression with Generalized Elastic Net Penalty
Institute of Applied Mathematics, Shenzhen Polytechnic University（深圳职业技术学院应用数学研究所）；School of Mathematics and Statistics, Henan University（河南大学数学与统计学院）；Center for Applied Mathematics of Henan Province, Henan University（河南大学河南省应用数学中心）
Institute of Information Science, Academia Sinica（中央研究院信息科学研究所）
In this paper, we reformulate the non-convex $\ell_q$-norm minimization problem with $q\in(0,1)$ into a 2-step problem, which consists of one convex and one non-convex subproblems, and propose a novel iterative algorithm called QISTA ($\ell_q$-ISTA) to solve the $\left(\ell_q\right)$-problem. By taking advantage of deep learning in accelerating optimization algorithms, together with the speedup strategy that using the momentum from all previous layers in the network, we propose a learning-based method, called QISTA-Net-s, to solve the sparse signal reconstruction problem. Extensive experimenta…
