arXiv subjects

Hongying Liu

Publications and source records attributed to Hongying Liu.

36 records · Page 2Linked to original sources

arXiv2021

Local Optimality Conditions for a Class of Hidden Convex Optimization

Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden convex optimization. We first introduce a class of hidden convex optimization problems by jointing the classical nonconvex trust-region subproblem (TRS) with convex optimization (CO), and then present a comprehensive study on local optimality conditions. In order to guarantee the existence of a necessary and sufficient condition for local optimality, we need more restrictive assumptions. To our surprise, while (TRS) has at most one local non-global minimizer and (CO) has no local non-global minimizer, their joint problem could have more than one local non-global minimizer.

math.OC↗

arXiv2021

On Local Minimizers of Quadratically Constrained Nonconvex Homogeneous Quadratic Optimization with at Most Two Constraints

We study nonconvex homogeneous quadratically constrained quadratic optimization with one or two constraints, denoted by (QQ1) and (QQ2), respectively. (QQ2) contains (QQ1), trust region subproblem (TRS) and ellipsoid regularized total least squares problem as special cases. It is known that there is a necessary and sufficient optimality condition for the global minimizer of (QQ2). In this paper, we first show that any local minimizer of (QQ1) is globally optimal. Unlike its special case (TRS) with at most one local non-global minimizer, (QQ2) may have infinitely many local non-global minimizers. At any local non-global minimizer of (QQ2), both linearly independent constraint qualification and strict complementary condition hold, and the Hessian of the Lagrangian has exactly one negative eigenvalue. As a main contribution, we prove that the standard second-order sufficient optimality condition for any strict local non-global minimizer of (QQ2) remains necessary. Applications and the impossibility of further extension are discussed.

math.OC↗

arXiv2021

Behavior Mimics Distribution: Combining Individual and Group Behaviors for Federated Learning

Federated Learning (FL) has become an active and promising distributed machine learning paradigm. As a result of statistical heterogeneity, recent studies clearly show that the performance of popular FL methods (e.g., FedAvg) deteriorates dramatically due to the client drift caused by local updates. This paper proposes a novel Federated Learning algorithm (called IGFL), which leverages both Individual and Group behaviors to mimic distribution, thereby improving the ability to deal with heterogeneity. Unlike existing FL methods, our IGFL can be applied to both client and server optimization. As a by-product, we propose a new attention-based federated learning in the server optimization of IGFL. To the best of our knowledge, this is the first time to incorporate attention mechanisms into federated optimization. We conduct extensive experiments and show that IGFL can significantly improve the performance of existing federated learning methods. Especially when the distributions of data among individuals are diverse, IGFL can improve the classification accuracy by about 13% compared with prior baselines.

cs.LG↗

arXiv2021

Learned Interpretable Residual Extragradient ISTA for Sparse Coding

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. In particular, our algorithm can also provide the interpretability for Res-Net to a certain extent. From a theoretical perspective, we prove that our method attains linear convergence. In practice, extensive empirical results verify the advantages of our method.

cs.LG↗

arXiv2021

Quantized Neural Networks via {-1, +1} Encoding Decomposition and Acceleration

The training of deep neural networks (DNNs) always requires intensive resources for both computation and data storage. Thus, DNNs cannot be efficiently applied to mobile phones and embedded devices, which severely limits their applicability in industrial applications. To address this issue, we propose a novel encoding scheme using {-1, +1} to decompose quantized neural networks (QNNs) into multi-branch binary networks, which can be efficiently implemented by bitwise operations (i.e., xnor and bitcount) to achieve model compression, computational acceleration, and resource saving. By using our method, users can achieve different encoding precisions arbitrarily according to their requirements and hardware resources. The proposed mechanism is highly suitable for the use of FPGA and ASIC in terms of data storage and computation, which provides a feasible idea for smart chips. We validate the effectiveness of our method on large-scale image classification (e.g., ImageNet), object detection, and semantic segmentation tasks. In particular, our method with low-bit encoding can still achieve almost the same performance as its high-bit counterparts.

cs.CV↗

arXiv2021

Large Motion Video Super-Resolution with Dual Subnet and Multi-Stage Communicated Upsampling

Video super-resolution (VSR) aims at restoring a video in low-resolution (LR) and improving it to higher-resolution (HR). Due to the characteristics of video tasks, it is very important that motion information among frames should be well concerned, summarized and utilized for guidance in a VSR algorithm. Especially, when a video contains large motion, conventional methods easily bring incoherent results or artifacts. In this paper, we propose a novel deep neural network with Dual Subnet and Multi-stage Communicated Upsampling (DSMC) for super-resolution of videos with large motion. We design a new module named U-shaped residual dense network with 3D convolution (U3D-RDN) for fine implicit motion estimation and motion compensation (MEMC) as well as coarse spatial feature extraction. And we present a new Multi-Stage Communicated Upsampling (MSCU) module to make full use of the intermediate results of upsampling for guiding the VSR. Moreover, a novel dual subnet is devised to aid the training of our DSMC, whose dual loss helps to reduce the solution space as well as enhance the generalization ability. Our experimental results confirm that our method achieves superior performance on videos with large motion compared to state-of-the-art methods.

cs.CV↗

arXiv2020

Differentially Private ADMM Algorithms for Machine Learning

In this paper, we study efficient differentially private alternating direction methods of multipliers (ADMM) via gradient perturbation for many machine learning problems. For smooth convex loss functions with (non)-smooth regularization, we propose the first differentially private ADMM (DP-ADMM) algorithm with performance guarantee of $(ε,δ)$-differential privacy ($(ε,δ)$-DP). From the viewpoint of theoretical analysis, we use the Gaussian mechanism and the conversion relationship between Rényi Differential Privacy (RDP) and DP to perform a comprehensive privacy analysis for our algorithm. Then we establish a new criterion to prove the convergence of the proposed algorithms including DP-ADMM. We also give the utility analysis of our DP-ADMM. Moreover, we propose an accelerated DP-ADMM (DP-AccADMM) with the Nesterov's acceleration technique. Finally, we conduct numerical experiments on many real-world datasets to show the privacy-utility tradeoff of the two proposed algorithms, and all the comparative analysis shows that DP-AccADMM converges faster and has a better utility than DP-ADMM, when the privacy budget $ε$ is larger than a threshold.

cs.LG↗

arXiv2020

Boosting Gradient for White-Box Adversarial Attacks

Deep neural networks (DNNs) are playing key roles in various artificial intelligence applications such as image classification and object recognition. However, a growing number of studies have shown that there exist adversarial examples in DNNs, which are almost imperceptibly different from original samples, but can greatly change the network output. Existing white-box attack algorithms can generate powerful adversarial examples. Nevertheless, most of the algorithms concentrate on how to iteratively make the best use of gradients to improve adversarial performance. In contrast, in this paper, we focus on the properties of the widely-used ReLU activation function, and discover that there exist two phenomena (i.e., wrong blocking and over transmission) misleading the calculation of gradients in ReLU during the backpropagation. Both issues enlarge the difference between the predicted changes of the loss function from gradient and corresponding actual changes, and mislead the gradients which results in larger perturbations. Therefore, we propose a universal adversarial example generation method, called ADV-ReLU, to enhance the performance of gradient based white-box attack algorithms. During the backpropagation of the network, our approach calculates the gradient of the loss function versus network input, maps the values to scores, and selects a part of them to update the misleading gradients. Comprehensive experimental results on \emph{ImageNet} demonstrate that our ADV-ReLU can be easily integrated into many state-of-the-art gradient-based white-box attack algorithms, as well as transferred to black-box attack attackers, to further decrease perturbations in the ${\ell _2}$-norm.

cs.LG↗

arXiv2020

A Single Frame and Multi-Frame Joint Network for 360-degree Panorama Video Super-Resolution

Spherical videos, also known as \ang{360} (panorama) videos, can be viewed with various virtual reality devices such as computers and head-mounted displays. They attract large amount of interest since awesome immersion can be experienced when watching spherical videos. However, capturing, storing and transmitting high-resolution spherical videos are extremely expensive. In this paper, we propose a novel single frame and multi-frame joint network (SMFN) for recovering high-resolution spherical videos from low-resolution inputs. To take advantage of pixel-level inter-frame consistency, deformable convolutions are used to eliminate the motion difference between feature maps of the target frame and its neighboring frames. A mixed attention mechanism is devised to enhance the feature representation capability. The dual learning strategy is exerted to constrain the space of solution so that a better solution can be found. A novel loss function based on the weighted mean square error is proposed to emphasize on the super-resolution of the equatorial regions. This is the first attempt to settle the super-resolution of spherical videos, and we collect a novel dataset from the Internet, MiG Panorama Video, which includes 204 videos. Experimental results on 4 representative video clips demonstrate the efficacy of the proposed method. The dataset and code are available at https://github.com/lovepiano/SMFN_For_360VSR.

cs.CV↗

arXiv2019

Efficient Relaxed Gradient Support Pursuit for Sparsity Constrained Non-convex Optimization

Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus stochastic optimization methods with hard thresholding (e.g., SVRGHT) become more attractive. Inspired by GraSP, this paper proposes a new general relaxed gradient support pursuit (RGraSP) framework, in which the sub-algorithm only requires to satisfy a slack descent condition. We also design two specific semi-stochastic gradient hard thresholding algorithms. In particular, our algorithms have much less hard thresholding operations than SVRGHT, and their average per-iteration cost is much lower (i.e., O(d) vs. O(d log(d)) for SVRGHT), which leads to faster convergence. Our experimental results on both synthetic and real-world datasets show that our algorithms are superior to the state-of-the-art gradient hard thresholding methods.

cs.LG↗

arXiv2019

A unified approach for projections onto the intersection of $\ell_1$ and $\ell_2$ balls or spheres

This paper focuses on designing a unified approach for computing the projection onto the intersection of an $\ell_1$ ball/sphere and an $\ell_2$ ball/sphere. We show that the major computational efforts of solving these problems all rely on finding the root of the same piecewisely quadratic function, and then propose a unified numerical method to compute the root. In particular, we design breakpoint search methods with/without sorting incorporated with bisection, secant and Newton methods to find the interval containing the root, on which the root has a closed form. It can be shown that our proposed algorithms without sorting possess $O(n log n)$ worst-case complexity and $O(n)$ in practice. The efficiency of our proposed algorithms are demonstrated in numerical experiments.

math.OC↗

arXiv2019

Three-dimensional compacted optical waveguide couplers designed by invariant engineerings

Due to the limitations either on the sizes of devices and signal routing channels, the current planar integrated optical waveguide circuits await for the further developments into the three-dimensional (3D) integrations, although their designs and fabrications are still challenges. In this paper we demonstrate an analytical method, basing on the invariant engineering, to overcome the complication in the usual method by numerically solving the relevant 3D coupled-mode equations for designing various 3D optical waveguide devices such as the typical couplers. Our method is based on the quantum-optical analogy, i.e., the Maxwell equation for the electrcomagnetic wave prorogating along the waveguide structure in the spatial domain is formally similar to the Schrödinger equation for the evolving quantum state in the time domain. We find that the spatial-domain invariants can be effectively constructed to solve the 3D coupled-mode equations, analogously to solve the dynamical evolutions of quantum systems in the time-domain. As a consequence, as long as appropriately set the coupling parameters between the 3D interconnected waveguides, the 3D three-waveguide couplers could be designed for various desirably power divisions. As the invariant method is a natural shortcut to the adiabaticity, the compacted devices designed by the invariant-based engineerings are robust against the coupling coefficient variations and the coupler lengths.

physics.optics↗

arXiv2019

signADAM: Learning Confidences for Deep Neural Networks

In this paper, we propose a new first-order gradient-based algorithm to train deep neural networks. We first introduce the sign operation of stochastic gradients (as in sign-based methods, e.g., SIGN-SGD) into ADAM, which is called as signADAM. Moreover, in order to make the rate of fitting each feature closer, we define a confidence function to distinguish different components of gradients and apply it to our algorithm. It can generate more sparse gradients than existing algorithms do. We call this new algorithm signADAM++. In particular, both our algorithms are easy to implement and can speed up training of various deep neural networks. The motivation of signADAM++ is preferably learning features from the most different samples by updating large and useful gradients regardless of useless information in stochastic gradients. We also establish theoretical convergence guarantees for our algorithms. Empirical results on various datasets and models show that our algorithms yield much better performance than many state-of-the-art algorithms including SIGN-SGD, SIGNUM and ADAM. We also analyze the performance from multiple perspectives including the loss landscape and develop an adaptive method to further improve generalization. The source code is available at https://github.com/DongWanginxdu/signADAM-Learn-by-Confidence.

cs.CV↗

arXiv2019

CU-Net: Cascaded U-Net with Loss Weighted Sampling for Brain Tumor Segmentation

This paper proposes a novel cascaded U-Net for brain tumor segmentation. Inspired by the distinct hierarchical structure of brain tumor, we design a cascaded deep network framework, in which the whole tumor is segmented firstly and then the tumor internal substructures are further segmented. Considering that the increase of the network depth brought by cascade structures leads to a loss of accurate localization information in deeper layers, we construct many skip connections to link features at the same resolution and transmit detailed information from shallow layers to the deeper layers. Then we present a loss weighted sampling (LWS) scheme to eliminate the issue of imbalanced data during training the network. Experimental results on BraTS 2017 data show that our architecture framework outperforms the state-of-the-art segmentation algorithms, especially in terms of segmentation sensitivity.

eess.IV↗

arXiv2018

VR-SGD: A Simple Stochastic Variance Reduction Method for Machine Learning

In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors of VR-SGD are set to the average and last iterate of the previous epoch, respectively. The settings allow us to use much larger learning rates, and also make our convergence analysis more challenging. We also design two different update rules for smooth and non-smooth objective functions, respectively, which means that VR-SGD can tackle non-smooth and/or non-strongly convex problems directly without any reduction techniques. Moreover, we analyze the convergence properties of VR-SGD for strongly convex problems, which show that VR-SGD attains linear convergence. Different from its counterparts that have no convergence guarantees for non-strongly convex problems, we also provide the convergence guarantees of VR-SGD for this case, and empirically verify that VR-SGD with varying learning rates achieves similar performance to its momentum accelerated variant that has the optimal convergence rate $\mathcal{O}(1/T^2)$. Finally, we apply VR-SGD to solve various machine learning problems, such as convex and non-convex empirical risk minimization, and leading eigenvalue computation. Experimental results show that VR-SGD converges significantly faster than SVRG and Prox-SVRG, and usually outperforms state-of-the-art accelerated methods, e.g., Katyusha.

cs.LG↗

arXiv2015

Polarimetric Hierarchical Semantic Model and Scattering Mechanism Based PolSAR Image Classification

For polarimetric SAR (PolSAR) image classification, it is a challenge to classify the aggregated terrain types, such as the urban area, into semantic homogenous regions due to sharp bright-dark variations in intensity. The aggregated terrain type is formulated by the similar ground objects aggregated together. In this paper, a polarimetric hierarchical semantic model (PHSM) is firstly proposed to overcome this disadvantage based on the constructions of a primal-level and a middle-level semantic. The primal-level semantic is a polarimetric sketch map which consists of sketch segments as the sparse representation of a PolSAR image. The middle-level semantic is a region map which can extract semantic homogenous regions from the sketch map by exploiting the topological structure of sketch segments. Mapping the region map to the PolSAR image, a complex PolSAR scene is partitioned into aggregated, structural and homogenous pixel-level subspaces with the characteristics of relatively coherent terrain types in each subspace. Then, according to the characteristics of three subspaces above, three specific methods are adopted, and furthermore polarimetric information is exploited to improve the segmentation result. Experimental results on PolSAR data sets with different bands and sensors demonstrate that the proposed method is superior to the state-of-the-art methods in region homogeneity and edge preservation for terrain classification.

cs.CV↗

arXiv2011

A Large Family of Multi-path Dual Congestion Control Algorithms

The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing scheme fails to react to instantaneous network congestion. Multi-path routing schemes thus have been proposed aiming at improving network efficiency. Unfortunately, the natural optimization problem to consider is concave but not strictly concave. It thus brings a huge challenge to design stable multi-path congestion control algorithms. In this paper, we propose a generalized multi-path utility maximization model to consider the problem of routes selection and flow control, and derive a family of multi-path dual congestion control algorithms. We show that the proposed algorithms are stable in the absence of delays. We also derive decentralized and scalable sufficient conditions for a particular scheme when propagation delays exist in networks. Simulations are implemented using both Matlab and NS2, on which evaluation of the proposed multi-path dual algorithms is exerted. The comparison results, between the proposed algorithms and the other two existing algorithms, show that the proposed multi-path dual algorithms with appropriate parameter settings can achieve a stable aggregated throughput while maintaining fairness among the involved users.

cs.NI↗

arXiv2010

One More Weight is Enough: Toward the Optimal Traffic Engineering with OSPF

Traffic Engineering (TE) leverages information of network traffic to generate a routing scheme optimizing the traffic distribution so as to advance network performance. However, optimize the link weights for OSPF to the offered traffic is an known NP-hard problem. In this paper, motivated by the fairness concept of congestion control, we firstly propose a new generic objective function, where various interests of providers can be extracted with different parameter settings. And then, we model the optimal TE as the utility maximization of multi-commodity flows with the generic objective function and theoretically show that any given set of optimal routes corresponding to a particular objective function can be converted to shortest paths with respect to a set of positive link weights. This can be directly configured on OSPF-based protocols. On these bases, we employ the Network Entropy Maximization(NEM) framework and develop a new OSPF-based routing protocol, SPEF, to realize a flexible way to split traffic over shortest paths in a distributed fashion. Actually, comparing to OSPF, SPEF only needs one more weight for each link and provably achieves optimal TE. Numerical experiments have been done to compare SPEF with the current version of OSPF, showing the effectiveness of SPEF in terms of link utilization and network load distribution.

cs.NI↗