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Dropout and DropConnect are two techniques to facilitate the regularization of neural network models, having achieved the state-of-the-art results in several benchmarks. In this paper, to improve the generalization capability of spiking neural networks (SNNs), the two drop techniques are first applied to the state-of-the-art SpikeProp learning algorithm resulting in two improved learning algorithms called SPDO (SpikeProp with Dropout) and SPDC (SpikeProp with DropConnect). In view that a higher membrane potential of a biological neuron implies a higher probability of neural activation, three adaptive drop algorithms, SpikeProp with Adaptive Dropout (SPADO), SpikeProp with Adaptive DropConnect (SPADC), and SpikeProp with Group Adaptive Drop (SPGAD), are proposed by adaptively adjusting the keep probability for training SNNs. A convergence theorem for SPDC is proven under the assumptions of the bounded norm of connection weights and a finite number of equilibria. In addition, the five proposed algorithms are carried out in a collaborative neurodynamic optimization framework to improve the learning performance of SNNs. The experimental results on the four benchmark data sets demonstrate that the three adaptive algorithms converge faster than SpikeProp, SPDO, and SPDC, and the generalization errors of the five proposed algorithms are significantly smaller than that of SpikeProp. Furthermore, the experimental results also show that the five algorithms based on collaborative neurodynamic optimization can be improved in terms of several measures. [ABSTRACT FROM AUTHOR]

Most modern learning problems are highly overparameterized, i.e., have many more model parameters than the number of training data points. As a result, the training loss may have infinitely many global minima (parameter vectors that perfectly “interpolate” the training data). It is therefore imperative to understand which interpolating solutions we converge to, how they depend on the initialization and learning algorithm, and whether they yield different test errors. In this article, we study these questions for the family of stochastic mirror descent (SMD) algorithms, of which stochastic gradient descent (SGD) is a special case. Recently, it has been shown that for overparameterized linear models, SMD converges to the closest global minimum to the initialization point, where closeness is in terms of the Bregman divergence corresponding to the potential function of the mirror descent. With appropriate initialization, this yields convergence to the minimum-potential interpolating solution, a phenomenon referred to as implicit regularization. On the theory side, we show that for sufficiently-overparameterized nonlinear models, SMD with a (small enough) fixed step size converges to a global minimum that is “very close” (in Bregman divergence) to the minimum-potential interpolating solution, thus attaining approximate implicit regularization. On the empirical side, our experiments on the MNIST and CIFAR-10 datasets consistently confirm that the above phenomenon occurs in practical scenarios. They further indicate a clear difference in the generalization performances of different SMD algorithms: experiments on the CIFAR-10 dataset with different regularizers, $\ell _{1}$ to encourage sparsity, $\ell _{2}$ (SGD) to encourage small Euclidean norm, and $\ell _{\infty }$ to discourage large components, surprisingly show that the $\ell _{\infty }$ norm consistently yields better generalization performance than SGD, which in turn generalizes better than the $\ell _{1}$ norm. [ABSTRACT FROM AUTHOR]

In online learning, the dynamic regret metric chooses the reference oracle that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The dynamic regret metric is particularly interesting for applications, such as online recommendation (since the customers’ preference always evolves over time). While the online gradient (OG) method has been shown to be optimal for the static regret metric, the optimal algorithm for the dynamic regret remains unknown. In this article, we show that proximal OG (a general version of OG) is optimum to the dynamic regret by showing that the proved lower bound matches the upper bound. It is highlighted that we provide a new and general lower bound of dynamic regret. It provides new understanding about the difficulty to follow the dynamics in the online setting. [ABSTRACT FROM AUTHOR]

It is challenging to bridge the performance gap between binary convolutional neural network (BCNN) and floating-point CNN (FCNN). This performance gap is mainly caused by the inferior modeling capability and training strategy of BCNN, which leads to substantial residuals in intermediate feature maps between BCNN and FCNN. To minimize the performance gap, we enforce BCNN to produce similar intermediate feature maps with the ones of FCNN. This intuition leads to a more effective training strategy for BCNN, i.e., optimizing each binary convolutional block with blockwise distillation loss derived from FCNN. The goal of minimizing the residuals in intermediate feature maps also motivates us to update the binary convolutional block architecture to facilitate the optimization of blockwise distillation loss. Specifically, a lightweight shortcut branch is inserted into each binary convolutional block to complement residuals at each block. Benefited from its squeeze-and-interaction (SI) structure, this shortcut branch introduces a fraction of parameters, e.g., less than 10% overheads, but effectively boosts the modeling capability of binary convolution blocks in BCNN. Extensive experiments on ImageNet demonstrate the superior performance of our method in both classification efficiency and accuracy, e.g., BCNN trained with our methods achieves the accuracy of 60.45% on ImageNet, better than many state-of-the-art ones. [ABSTRACT FROM AUTHOR]

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies. [ABSTRACT FROM AUTHOR]

We propose a novel network pruning approach by information preserving of pretrained network weights (filters). Network pruning with the information preserving is formulated as a matrix sketch problem, which is efficiently solved by the off-the-shelf frequent direction method. Our approach, referred to as FilterSketch, encodes the second-order information of pretrained weights, which enables the representation capacity of pruned networks to be recovered with a simple fine-tuning procedure. FilterSketch requires neither training from scratch nor data-driven iterative optimization, leading to a several-orders-of-magnitude reduction of time cost in the optimization of pruning. Experiments on CIFAR-10 show that FilterSketch reduces 63.3% of floating-point operations (FLOPs) and prunes 59.9% of network parameters with negligible accuracy cost for ResNet-110. On ILSVRC-2012, it reduces 45.5% of FLOPs and removes 43.0% of parameters with only 0.69% accuracy drop for ResNet-50. Our code and pruned models can be found at https://github.com/lmbxmu/FilterSketch. [ABSTRACT FROM AUTHOR]

A single clustering refers to the partitioning of data such that the similar data are assigned into the same group, whereas the dissimilar data are separated into different groups. Recently, multiview clustering has received significant attention in recent years. However, most existing works tackle the single-clustering scenario, which only use single clustering to partition the data. In practice, nevertheless, the real-world data are complex and can be clustered in multiple ways depending on different interpretations of the data. Unlike these methods, in this article, we apply dual clustering to multiview subspace clustering. We propose a multiview dual-clustering method to simultaneously explore consensus representation and dual-clustering structure in a unified framework. First, multiview features are integrated into a latent embedding representation through a multiview learning process. Second, the dual-clustering segmentation is incorporated into the subspace clustering framework. Finally, the learned dual representations are assigned to the corresponding clusterings. The proposed approach is efficiently solved using an alternating optimization scheme. Extensive experiments demonstrate the superiority of our method on real-world multiview dual- and single-clustering datasets. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM algorithm was proposed, which is claimed to achieve exponential speedup for least squares SVM (LS-SVM). Here, inspired by the quantum SVM algorithm, we present a quantum-inspired classical algorithm for LS-SVM. In our approach, an improved fast sampling technique, namely indirect sampling, is proposed for sampling the kernel matrix and classifying. We first consider the LS-SVM with a linear kernel, and then discuss the generalization of our method to nonlinear kernels. Theoretical analysis shows our algorithm can make classification with arbitrary success probability in logarithmic runtime of both the dimension of data space and the number of data points for low rank, low condition number, and high dimensional data matrix, matching the runtime of the quantum SVM. [ABSTRACT FROM AUTHOR]

Image smoothing is a prerequisite for many computer vision and graphics applications. In this article, we raise an intriguing question whether a dataset that semantically describes meaningful structures and unimportant details can facilitate a deep learning model to smooth complex natural images. To answer it, we generate ground-truth labels from easy samples by candidate generation and a screening test and synthesize hard samples in structure-preserving smoothing by blending intricate and multifarious details with the labels. To take full advantage of this dataset, we present a joint edge detection and structure-preserving image smoothing neural network (JESS-Net). Moreover, we propose the distinctive total variation loss as prior knowledge to narrow the gap between synthetic and real data. Experiments on different datasets and real images show clear improvements of our method over the state of the arts in terms of both the image cleanness and structure-preserving ability. Code and dataset are available at https://github.com/YidFeng/Easy2Hard. [ABSTRACT FROM AUTHOR]

This article concerns with terminal recurrent neural network (RNN) models for time-variant computing, featuring finite-valued activation functions (AFs), and finite-time convergence of error variables. Terminal RNNs stand for specific models that admit terminal attractors, and the dynamics of each neuron retains finite-time convergence. The might-existing imperfection in solving time-variant problems, through theoretically examining the asymptotically convergent RNNs, is pointed out for which the finite-time-convergent models are most desirable. The existing AFs are summarized, and it is found that there is a lack of the AFs that take only finite values. A finitely valued terminal RNN, among others, is taken into account, which involves only basic algebraic operations and taking roots. The proposed terminal RNN model is used to solve the time-variant problems undertaken, including the time-variant quadratic programming and motion planning of redundant manipulators. The numerical results are presented to demonstrate effectiveness of the proposed neural network, by which the convergence rate is comparable with that of the existing power-rate RNN. [ABSTRACT FROM AUTHOR]

Twin support vector machine (TWSVM), which constructs two nonparallel classifying hyperplanes, is widely applied to various fields. However, TWSVM solves two quadratic programming problems (QPPs) separately such that the final classifiers lack consistency and enough prediction accuracy. Moreover, by reason of only considering the 1-norm penalty for slack variables, TWSVM is not well defined in the geometrical view. In this article, we propose a novel elastic net nonparallel hyperplane support vector machine (ENNHSVM), which adopts elastic net penalty for slack variables and constructs two nonparallel separating hyperplanes simultaneously. We further discuss the properties of ENNHSVM theoretically and derive the violation tolerance upper bound to better demonstrate the relative violations of training samples in the same class. In particular, we design a safe screening rule for ENNHSVM to speed up the calculations. We finally compare the performance of ENNHSVM on both synthetic datasets and benchmark datasets with the Lagrangian SVM, the twin parametric-margin SVM, the elastic net SVM, the TWSVM, and the nonparallel hyperplane SVM. [ABSTRACT FROM AUTHOR]

Modern convolutional neural network (CNN)-based object detectors focus on feature configuration during training but often ignore feature optimization during inference. In this article, we propose a new feature optimization approach to enhance features and suppress background noise in both the training and inference stages. We introduce a generic inference-aware feature filtering (IFF) module that can be easily combined with existing detectors, resulting in our iffDetector. Unlike conventional open-loop feature calculation approaches without feedback, the proposed IFF module performs the closed-loop feature optimization by leveraging high-level semantics to enhance the convolutional features. By applying the Fourier transform to analyze our detector, we prove that the IFF module acts as a negative feedback that can theoretically guarantee the stability of the feature learning. IFF can be fused with CNN-based object detectors in a plug-and-play manner with little computational cost overhead. Experiments on the PASCAL VOC and MS COCO datasets demonstrate that our iffDetector consistently outperforms state-of-the-art methods with significant margins. [ABSTRACT FROM AUTHOR]

This article develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications, such as distributed machine learning. Different from the existing works based on quantization and sparsification, we introduce a communication-censoring technique to reduce the transmissions of variables, which leads to our communication-censored distributed stochastic gradient descent (CSGD) algorithm. Specifically, in CSGD, the latest minibatch stochastic gradient at a worker will be transmitted to the server if and only if it is sufficiently informative. When the latest gradient is not available, the stale one will be reused at the server. To implement this communication-censoring strategy, the batch size is increasing in order to alleviate the effect of stochastic gradient noise. Theoretically, CSGD enjoys the same order of convergence rate as that of SGD but effectively reduces communication. Numerical experiments demonstrate the sizable communication saving of CSGD. [ABSTRACT FROM AUTHOR]

The staggering innovations and emergence of numerous deep learning (DL) applications have forced researchers to reconsider hardware architecture to accommodate fast and efficient application-specific computations. Applications, such as object detection, image recognition, speech translation, as well as music synthesis and image generation, can be performed with high accuracy at the expense of substantial computational resources using DL. Furthermore, the desire to adopt Industry 4.0 and smart technologies within the Internet of Things infrastructure has initiated several studies to enable on-chip DL capabilities for resource-constrained devices. Specialized DL processors reduce dependence on cloud servers, improve privacy, lessen latency, and mitigate bandwidth congestion. As we reach the limits of shrinking transistors, researchers are exploring various application-specific hardware architectures to meet the performance and efficiency requirements for DL tasks. Over the past few years, several software optimizations and hardware innovations have been proposed to efficiently perform these computations. In this article, we review several DL accelerators, as well as technologies with emerging devices, to highlight their architectural features in application-specific integrated circuit (IC) and field-programmable gate array (FPGA) platforms. Finally, the design considerations for DL hardware in portable applications have been discussed, along with some deductions about the future trends and potential research directions to innovate DL accelerator architectures further. By compiling this review, we expect to help aspiring researchers widen their knowledge in custom hardware architectures for DL. [ABSTRACT FROM AUTHOR]

Multivariate time series data are invasive in different domains, ranging from data center supervision and e-commerce data to financial transactions. This kind of data presents an important challenge for anomaly detection due to the temporal dependency aspect of its observations. In this article, we investigate the problem of unsupervised local anomaly detection in multivariate time series data from temporal modeling and residual analysis perspectives. The residual analysis has been shown to be effective in classical anomaly detection problems. However, it is a nontrivial task in multivariate time series as the temporal dependency between the time series observations complicates the residual modeling process. Methodologically, we propose a unified learning framework to characterize the residuals and their coherence with the temporal aspect of the whole multivariate time series. Experiments on real-world datasets are provided showing the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Deep learning-based methods have achieved notable progress in removing blocking artifacts caused by lossy JPEG compression on images. However, most deep learning-based methods handle this task by designing black-box network architectures to directly learn the relationships between the compressed images and their clean versions. These network architectures are always lack of sufficient interpretability, which limits their further improvements in deblocking performance. To address this issue, in this article, we propose a model-driven deep unfolding method for JPEG artifacts removal, with interpretable network structures. First, we build a maximum posterior (MAP) model for deblocking using convolutional dictionary learning and design an iterative optimization algorithm using proximal operators. Second, we unfold this iterative algorithm into a learnable deep network structure, where each module corresponds to a specific operation of the iterative algorithm. In this way, our network inherits the benefits of both the powerful model ability of data-driven deep learning method and the interpretability of traditional model-driven method. By training the proposed network in an end-to-end manner, all learnable modules can be automatically explored to well characterize the representations of both JPEG artifacts and image content. Experiments on synthetic and real-world datasets show that our method is able to generate competitive or even better deblocking results, compared with state-of-the-art methods both quantitatively and qualitatively. [ABSTRACT FROM AUTHOR]

Recent years have witnessed significant progress of person reidentification (reID) driven by expert-designed deep neural network architectures. Despite the remarkable success, such architectures often suffer from high model complexity and time-consuming pretraining process, as well as the mismatches between the image classification-driven backbones and the reID task. To address these issues, we introduce neural architecture search (NAS) into automatically designing person reID backbones, i.e., reID-NAS, which is achieved via automatically searching attention-based network architectures from scratch. Different from traditional NAS approaches that originated for image classification, we design a reID-based search space as well as a search objective to fit NAS for the reID tasks. In terms of the search space, reID-NAS includes a lightweight attention module to precisely locate arbitrary pedestrian bounding boxes, which is automatically added as attention to the reID architectures. In terms of the search objective, reID-NAS introduces a new retrieval objective to search and train reID architectures from scratch. Finally, we propose a hybrid optimization strategy to improve the search stability in reID-NAS. In our experiments, we validate the effectiveness of different parts in reID-NAS, and show that the architecture searched by reID-NAS achieves a new state of the art, with one order of magnitude fewer parameters on three-person reID datasets. As a concomitant benefit, the reliance on the pretraining process is vastly reduced by reID-NAS, which facilitates one to directly search and train a lightweight reID model from scratch. [ABSTRACT FROM AUTHOR]

The adaptive hinging hyperplane (AHH) model is a popular piecewise linear representation with a generalized tree structure and has been successfully applied in dynamic system identification. In this article, we aim to construct the deep AHH (DAHH) model to extend and generalize the networking of AHH model for high-dimensional problems. The network structure of DAHH is determined through a forward growth, in which the activity ratio is introduced to select effective neurons and no connecting weights are involved between the layers. Then, all neurons in the DAHH network can be flexibly connected to the output in a skip-layer format, and only the corresponding weights are the parameters to optimize. With such a network framework, the backpropagation algorithm can be implemented in DAHH to efficiently tackle large-scale problems and the gradient vanishing problem is not encountered in the training of DAHH. In fact, the optimization problem of DAHH can maintain convexity with convex loss in the output layer, which brings natural advantages in optimization. Different from the existing neural networks, DAHH is easier to interpret, where neurons are connected sparsely and analysis of variance (ANOVA) decomposition can be applied, facilitating to revealing the interactions between variables. A theoretical analysis toward universal approximation ability and explicit domain partitions are also derived. Numerical experiments verify the effectiveness of the proposed DAHH. [ABSTRACT FROM AUTHOR]

Deep learning has become the most powerful machine learning tool in the last decade. However, how to efficiently train deep neural networks remains to be thoroughly solved. The widely used minibatch stochastic gradient descent (SGD) still needs to be accelerated. As a promising tool to better understand the learning dynamic of minibatch SGD, the information bottleneck (IB) theory claims that the optimization process consists of an initial fitting phase and the following compression phase. Based on this principle, we further study typicality sampling, an efficient data selection method, and propose a new explanation of how it helps accelerate the training process of the deep networks. We show that the fitting phase depicted in the IB theory will be boosted with a high signal-to-noise ratio of gradient approximation if the typicality sampling is appropriately adopted. Furthermore, this finding also implies that the prior information of the training set is critical to the optimization process, and the better use of the most important data can help the information flow through the bottleneck faster. Both theoretical analysis and experimental results on synthetic and real-world datasets demonstrate our conclusions. [ABSTRACT FROM AUTHOR]

The neural-network (NN)-based control method is a new emerging promising technique for controller design in a power electronic circuit (PEC). However, the optimization of NN-based controllers (NNCs) has significant challenges in two aspects. The first challenge is that the search space of the NNC optimization problem is such complex that the global optimization ability of the existing algorithms still needs to be improved. The second challenge is that the training process of the NNC parameters is very computationally expensive and requires a long execution time. Thus, in this article, we develop a powerful evolutionary computation-based algorithm to find a high-quality solution and reduce computational time. First, the differential evolution (DE) algorithm is adopted because it is a powerful global optimizer in solving a complex optimization problem. This can help to overcome the premature convergence in local optima to train the NNC parameters well. Second, to reduce the computational time, the DE is extended to distribute DE (DDE) by dispatching all the individuals to different distributed computing resources for parallel computing. Moreover, a resource-aware strategy (RAS) is designed to further efficiently utilize the resources by adaptively dispatching individuals to resources according to the real-time performance of the resources, which can simultaneously concern the computing ability and load state of each resource. Experimental results show that, compared with some other typical evolutionary algorithms, the proposed algorithm can get significantly better solutions within a shorter computational time. [ABSTRACT FROM AUTHOR]

Although deep neural networks have been proved effective in many applications, they are data hungry, and training deep models often requires laboriously labeled data. However, when labeled data contain erroneous labels, they often lead to model performance degradation. A common solution is to assign each sample with a dynamic weight during optimization, and the weight is adjusted in accordance with the loss. However, those weights are usually unreliable since they are measured by the losses of corrupted labels. Thus, this scheme might impede the discriminative ability of neural networks trained on noisy data. To address this issue, we propose a novel reweighting method, dubbed self-reweighting from class centroids (SRCC), by assigning sample weights based on the similarities between the samples and our online learned class centroids. Since we exploit statistical class centers in the image feature space to reweight data samples in learning, our method is robust to noise caused by corrupted labels. In addition, even after reweighting the noisy data, the decision boundaries might still suffer distortions. Thus, we leverage mixed inputs that are generated by linearly interpolating two random images and their labels to further regularize the boundaries. We employ the learned class centroids to evaluate the confidence of our generated mixed data via measuring feature similarities. During the network optimization, the class centroids are updated as more discriminative feature representations of original images are learned. In doing so, SRCC will generate more robust weighting coefficients for noisy and mixed data and facilitates our feature representation learning in return. Extensive experiments on both the synthetic and real image recognition tasks demonstrate that our method SRCC outperforms the state of the art on learning with noisy data. [ABSTRACT FROM AUTHOR]

Domain adaptation is proposed to deal with the challenging problem where the probability distribution of the training source is different from the testing target. Recently, adversarial learning has become the dominating technique for domain adaptation. Usually, adversarial domain adaptation methods simultaneously train a feature learner and a domain discriminator to learn domain-invariant features. Accordingly, how to effectively train the domain-adversarial model to learn domain-invariant features becomes a challenge in the community. To this end, we propose in this article a novel domain adaptation scheme named adversarial entropy optimization (AEO) to address the challenge. Specifically, we minimize the entropy when samples are from the independent distributions of source domain or target domain to improve the discriminability of the model. At the same time, we maximize the entropy when features are from the combined distribution of source domain and target domain so that the domain discriminator can be confused and the transferability of representations can be promoted. This minimax regime is well matched with the core idea of adversarial learning, empowering our model with transferability as well as discriminability for domain adaptation tasks. Also, AEO is flexible and compatible with different deep networks and domain adaptation frameworks. Experiments on five data sets show that our method can achieve state-of-the-art performance across diverse domain adaptation tasks. [ABSTRACT FROM AUTHOR]

Learning with label proportions (LLP) deals with the problem that the training data are provided as bags, where the label proportions of training bags rather than the labels of individual training instances are accessible. Existing LLP studies assume that the label proportions of all training bags are accessible. However, in many applications, it is time-consuming to mark all training bags with label proportions, which leads to the problem of learning with both marked and unmarked bags, namely, semisupervised LLP (SLLP). In this work, we propose semisupervised proportional support vector machine (SS- $\propto $ SVM), which extends the proportional SVM ($\propto $ SVM) model to its semisupervised version. To the best of our knowledge, SS- $\propto $ SVM is the first attempt to cope with the SLLP problem. Two realizations, alter-SS- $\propto $ SVM and conv-SS- $\propto $ SVM, which are based on alternating optimization and convex relaxation, respectively, are developed to solve the proposed SS- $\propto $ SVM model. Moreover, we design a cutting plane (CP) method to optimize conv-SS- $\propto $ SVM with a guaranteed convergence rate and present a fast accelerated proximal gradient method to solve the multiple kernel learning subproblem in conv-SS- $\propto $ SVM efficiently. Empirical experiments not only justify the superiority of SS- $\propto $ SVM over its supervised counterpart in classification accuracy but also demonstrate the high competitive computational efficiency of the CP optimization of conv-SS- $\propto $ SVM. [ABSTRACT FROM AUTHOR]

In this article, we investigate the routing problem of packet networks through multiagent reinforcement learning (RL), which is a very challenging topic in distributed and autonomous networked systems. In specific, the routing problem is modeled as a networked multiagent partially observable Markov decision process (MDP). Since the MDP of a network node is not only affected by its neighboring nodes’ policies but also the network traffic demand, it becomes a multitask learning problem. Inspired by recent success of RL and metalearning, we propose two novel model-free multiagent RL algorithms, named multiagent proximal policy optimization (MAPPO) and multiagent metaproximal policy optimization (meta-MAPPO), to optimize the network performances under fixed and time-varying traffic demand, respectively. A practicable distributed implementation framework is designed based on the separability of exploration and exploitation in training MAPPO. Compared with the existing routing optimization policies, our simulation results demonstrate the excellent performances of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Weakly supervised object detection (WSOD) is a challenging task that requires simultaneously learning object detectors and estimating object locations under the supervision of image category labels. Many WSOD methods that adopt multiple instance learning (MIL) have nonconvex objective functions and, therefore, are prone to get stuck in local minima (falsely localize object parts) while missing full object extent during training. In this article, we introduce classical continuation optimization into MIL, thereby creating continuation MIL (C-MIL) with the aim to alleviate the nonconvexity problem in a systematic way. To fulfill this purpose, we partition instances into class-related and spatially related subsets and approximate MIL’s objective function with a series of smoothed objective functions defined within the subsets. We further propose a parametric strategy to implement continuation smooth functions, which enables C-MIL to be applied to instance selection tasks in a uniform manner. Optimizing smoothed loss functions prevents the training procedure from falling prematurely into local minima and facilities learning full object extent. Extensive experiments demonstrate the superiority of CMIL over conventional MIL methods. As a general instance selection method, C-MIL is also applied to supervised object detection to optimize anchors/features, improving the detection performance with a significant margin. [ABSTRACT FROM AUTHOR]

In this article, distributed algorithms are proposed for training a group of neural networks with private data sets. Stochastic gradients are utilized in order to eliminate the requirement for true gradients. To obtain a universal model of the distributed neural networks trained using local data sets only, consensus tools are introduced to derive the model toward the optimum. Most of the existing works employ diminishing learning rates, which are often slow and impracticable for online learning, while constant learning rates are studied in some recent works, but the principle for choosing the rates is not well established. In this article, constant learning rates are adopted to empower the proposed algorithms with tracking ability. Under mild conditions, the convergence of the proposed algorithms is established by exploring the error dynamics of the connected agents, which provides an upper bound for selecting the constant learning rates. Performances of the proposed algorithms are analyzed with and without gradient noises, in the sense of mean square error (MSE). It is proved that the MSE converges with bounded errors determined by the gradient noises, and the MSE converges to zero if the gradient noises are absent. Simulation results are provided to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Network controllability robustness (CR) reflects how well a networked system can maintain its controllability against destructive attacks. Its measure is quantified by a sequence of values that record the remaining controllability of the network after a sequence of node-removal or edge-removal attacks. Traditionally, the CR is determined by attack simulations, which is computationally time-consuming or even infeasible. In this article, an improved method for predicting the network CR is developed based on machine learning using a group of convolutional neural networks (CNNs). In this scheme, a number of training data generated by simulations are used to train the group of CNNs for classification and prediction, respectively. Extensive experimental studies are carried out, which demonstrate that 1) the proposed method predicts more precisely than the classical single-CNN predictor; 2) the proposed CNN-based predictor provides a better predictive measure than the traditional spectral measures and network heterogeneity. [ABSTRACT FROM AUTHOR]

Hash bit selection (HBS) aims to find the most discriminative and informative hash bits from a hash pool generated by using different hashing algorithms. It is usually formulated as a binary quadratic programming problem with an information-theoretic objective function and a string-length constraint. In this article, it is equivalently reformulated in the form of a quadratic unconstrained binary optimization problem by augmenting the objective function with a penalty function. The reformulated problem is solved via collaborative neurodynamic optimization (CNO) with a population of classic discrete Hopfield networks. The two most important hyperparameters of the CNO approach are determined based on Monte Carlo test results. Experimental results on three benchmark data sets are elaborated to substantiate the superiority of the collaborative neurodynamic approach to several existing methods for HBS. [ABSTRACT FROM AUTHOR]

Due to the corruptions or noises that existed in real-world data sets, the affinity graphs constructed by the classical spectral clustering-based subspace clustering algorithms may not be able to reveal the intrinsic subspace structures of data sets faithfully. In this article, we reconsidered the data reconstruction problem in spectral clustering-based algorithms and proposed the idea of “relation reconstruction.” We pointed out that a data sample could be represented by the neighborhood relation computed between its neighbors and itself. The neighborhood relation could indicate the true membership of its corresponding original data sample to the subspaces of a data set. We also claimed that a data sample’s neighborhood relation could be reconstructed by the neighborhood relations of other data samples; then, we suggested a much different way to define affinity graphs consequently. Based on these propositions, a sparse relation representation (SRR) method was proposed for solving subspace clustering problems. Moreover, by introducing the local structure information of original data sets into SRR, an extension of SRR, namely structured sparse relation representation (SSRR) was presented. We gave an optimization algorithm for solving SRR and SSRR problems and analyzed its computation burden and convergence. Finally, plentiful experiments conducted on different types of databases showed the superiorities of SRR and SSRR. [ABSTRACT FROM AUTHOR]

Neural networks have been demonstrated to be trainable even with hundreds of layers, which exhibit remarkable improvement on expressive power and provide significant performance gains in a variety of tasks. However, the prohibitive computational cost has become a severe challenge for deploying them on resource-constrained platforms. Meanwhile, widely adopted deep neural network architectures, for example, ResNets or DenseNets, are manually crafted on benchmark datasets, which hamper their generalization ability to other domains. To cope with these issues, we propose an evolutionary algorithm-based method for shallowing deep neural networks (DNNs) at block levels, which is termed as ESNB. Different from existing studies, ESNB utilizes the ensemble view of block-wise DNNs and employs the multiobjective optimization paradigm to reduce the number of blocks while avoiding performance degradation. It automatically discovers shallower network architectures by pruning less informative blocks, and employs knowledge distillation to recover the performance. Moreover, a novel prior knowledge incorporation strategy is proposed to improve the exploration ability of the evolutionary search process, and a correctness-aware knowledge distillation strategy is designed for better knowledge transferring. Experimental results show that the proposed method can effectively accelerate the inference of DNNs while achieving superior performance when compared with the state-of-the-art competing methods. [ABSTRACT FROM AUTHOR]

Low-rank minimization aims to recover a matrix of minimum rank subject to linear system constraint. It can be found in various data analysis and machine learning areas, such as recommender systems, video denoising, and signal processing. Nuclear norm minimization is a dominating approach to handle it. However, such a method ignores the difference among singular values of target matrix. To address this issue, nonconvex low-rank regularizers have been widely used. Unfortunately, existing methods suffer from different drawbacks, such as inefficiency and inaccuracy. To alleviate such problems, this article proposes a flexible model with a novel nonconvex regularizer. Such a model not only promotes low rankness but also can be solved much faster and more accurate. With it, the original low-rank problem can be equivalently transformed into the resulting optimization problem under the rank restricted isometry property (rank-RIP) condition. Subsequently, Nesterov’s rule and inexact proximal strategies are adopted to achieve a novel algorithm highly efficient in solving this problem at a convergence rate of $O(1/K)$ , with $K$ being the iterate count. Besides, the asymptotic convergence rate is also analyzed rigorously by adopting the Kurdyka- ojasiewicz (KL) inequality. Furthermore, we apply the proposed optimization model to typical low-rank problems, including matrix completion, robust principal component analysis (RPCA), and tensor completion. Exhaustively empirical studies regarding data analysis tasks, i.e., synthetic data analysis, image recovery, personalized recommendation, and background subtraction, indicate that the proposed model outperforms state-of-the-art models in both accuracy and efficiency. [ABSTRACT FROM AUTHOR]

The convergence of generative adversarial networks (GANs) has been studied substantially in various aspects to achieve successful generative tasks. Ever since it is first proposed, the idea has achieved many theoretical improvements by injecting an instance noise, choosing different divergences, penalizing the discriminator, and so on. In essence, these efforts are to approximate a real-world measure with an idle measure through a learning procedure. In this article, we provide an analysis of GANs in the most general setting to reveal what, in essence, should be satisfied to achieve successful convergence. This work is not trivial since handling a converging sequence of an abstract measure requires a lot more sophisticated concepts. In doing so, we find an interesting fact that the discriminator can be penalized in a more general setting than what has been implemented. Furthermore, our experiment results substantiate our theoretical argument on various generative tasks. [ABSTRACT FROM AUTHOR]

In most of the existing representation learning frameworks, the noise contaminating the data points is often assumed to be independent and identically distributed (i.i.d.), where the Gaussian distribution is often imposed. This assumption, though greatly simplifies the resulting representation problems, may not hold in many practical scenarios. For example, the noise in face representation is usually attributable to local variation, random occlusion, and unconstrained illumination, which is essentially structural, and hence, does not satisfy the i.i.d. property or the Gaussianity. In this article, we devise a generic noise model, referred to as independent and piecewise identically distributed (i.p.i.d.) model for robust presentation learning, where the statistical behavior of the underlying noise is characterized using a union of distributions. We demonstrate that our proposed i.p.i.d. model can better describe the complex noise encountered in practical scenarios and accommodate the traditional i.i.d. one as a special case. Assisted by the proposed noise model, we then develop a new information-theoretic learning framework for robust subspace representation through a novel minimum weighted error entropy criterion. Thanks to the superior modeling capability of the i.p.i.d. model, our proposed learning method achieves superior robustness against various types of noise. When applying our scheme to the subspace clustering and image recognition problems, we observe significant performance gains over the existing approaches. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel model-parallel learning method, called local critic training, which trains neural networks using additional modules called local critic networks. The main network is divided into several layer groups, and each layer group is updated through error gradients estimated by the corresponding local critic network. We show that the proposed approach successfully decouples the update process of the layer groups for both convolutional neural networks (CNNs) and recurrent neural networks (RNNs). In addition, we demonstrate that the proposed method is guaranteed to converge to a critical point. We also show that trained networks by the proposed method can be used for structural optimization. Experimental results show that our method achieves satisfactory performance, reduces training time greatly, and decreases memory consumption per machine. Code is available at https://github.com/hjdw2/Local-critic-training. [ABSTRACT FROM AUTHOR]

Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e., the classifier) is placed at the end of such models returning a value for each class used for classification. This transformation plays an important role in determining how the generated features change during the learning process. In this work, we argue that this transformation not only can be fixed (i.e., set as nontrainable) with no loss of accuracy and with a reduction in memory usage, but it can also be used to learn stationary and maximally separated embeddings. We show that the stationarity of the embedding and its maximal separated representation can be theoretically justified by setting the weights of the fixed classifier to values taken from the coordinate vertices of the three regular polytopes available in $\mathbb {R}^{d}$ , namely, the $d$ -Simplex, the $d$ -Cube, and the $d$ -Orthoplex. These regular polytopes have the maximal amount of symmetry that can be exploited to generate stationary features angularly centered around their corresponding fixed weights. Our approach improves and broadens the concept of a fixed classifier, recently proposed by Hoffer et al., to a larger class of fixed classifier models. Experimental results confirm the theoretical analysis, the generalization capability, the faster convergence, and the improved performance of the proposed method. Code will be publicly available. [ABSTRACT FROM AUTHOR]

Hyperspectral images (HSIs) are crucial for many research works. Spectral super-resolution (SSR) is a method used to obtain high-spatial-resolution (HR) HSIs from HR multispectral images. Traditional SSR methods include model-driven algorithms and deep learning. By unfolding a variational method, this article proposes an optimization-driven convolutional neural network (CNN) with a deep spatial–spectral prior, resulting in physically interpretable networks. Unlike the fully data-driven CNN, auxiliary spectral response function (SRF) is utilized to guide CNNs to group the bands with spectral relevance. In addition, the channel attention module (CAM) and the reformulated spectral angle mapper loss function are applied to achieve an effective reconstruction model. Finally, experiments on two types of data sets, including natural and remote sensing images, demonstrate the spectral enhancement effect of the proposed method, and also, the classification results on the remote sensing data set verified the validity of the information enhanced by the proposed method. [ABSTRACT FROM AUTHOR]

The performance of a biologically plausible spiking neural network (SNN) largely depends on the model parameters and neural dynamics. This article proposes a parameter optimization scheme for improving the performance of a biologically plausible SNN and a parallel on-field-programmable gate array (FPGA) online learning neuromorphic platform for the digital implementation based on two numerical methods, namely, the Euler and third-order Runge–Kutta (RK3) methods. The optimization scheme explores the impact of biological time constants on information transmission in the SNN and improves the convergence rate of the SNN on digit recognition with a suitable choice of the time constants. The parallel digital implementation leads to a significant speedup over software simulation on a general-purpose CPU. The parallel implementation with the Euler method enables around $180\times $ ($20\times $) training (inference) speedup over a Pytorch-based SNN simulation on CPU. Moreover, compared with previous work, our parallel implementation shows more than $300\times $ ($240\times $) improvement on speed and $180\times $ ($250\times $) reduction in energy consumption for training (inference). In addition, due to the high-order accuracy, the RK3 method is demonstrated to gain $2\times $ training speedup over the Euler method, which makes it suitable for online training in real-time applications. [ABSTRACT FROM AUTHOR]

Attention has been shown highly effective for modeling sequences, capturing the more informative parts in learning a deep representation. However, recent studies show that the attention values do not always coincide with intuition in tasks, such as machine translation and sentiment classification. In this study, we consider using deep reinforcement learning to automatically optimize attention distribution during the minimization of end task training losses. With more sufficient environment states, iterative actions are taken to adjust attention weights so that more informative words receive more attention automatically. Results on different tasks and different attention networks demonstrate that our model is of great effectiveness in improving the end task performances, yielding more reasonable attention distribution. The more in-depth analysis further reveals that our retrofitting method can help to bring explainability for baseline attention. [ABSTRACT FROM AUTHOR]

Accurate electroencephalogram (EEG) pattern decoding for specific mental tasks is one of the key steps for the development of brain–computer interface (BCI), which is quite challenging due to the considerably low signal-to-noise ratio of EEG collected at the brain scalp. Machine learning provides a promising technique to optimize EEG patterns toward better decoding accuracy. However, existing algorithms do not effectively explore the underlying data structure capturing the true EEG sample distribution and, hence, can only yield a suboptimal decoding accuracy. To uncover the intrinsic distribution structure of EEG data, we propose a clustering-based multitask feature learning algorithm for improved EEG pattern decoding. Specifically, we perform affinity propagation-based clustering to explore the subclasses (i.e., clusters) in each of the original classes and then assign each subclass a unique label based on a one-versus-all encoding strategy. With the encoded label matrix, we devise a novel multitask learning algorithm by exploiting the subclass relationship to jointly optimize the EEG pattern features from the uncovered subclasses. We then train a linear support vector machine with the optimized features for EEG pattern decoding. Extensive experimental studies are conducted on three EEG data sets to validate the effectiveness of our algorithm in comparison with other state-of-the-art approaches. The improved experimental results demonstrate the outstanding superiority of our algorithm, suggesting its prominent performance for EEG pattern decoding in BCI applications. [ABSTRACT FROM AUTHOR]

In distributed learning and optimization, a network of multiple computing units coordinates to solve a large-scale problem. This article focuses on dynamic optimization over a decentralized network. We develop a communication-efficient algorithm based on the alternating direction method of multipliers (ADMM) with quantized and censored communications, termed DQC-ADMM. At each time of the algorithm, the nodes collaborate to minimize the summation of their time-varying, local objective functions. Through local iterative computation and communication, DQC-ADMM is able to track the time-varying optimal solution. Different from traditional approaches requiring transmissions of the exact local iterates among the neighbors at every time, we propose to quantize the transmitted information, as well as adopt a communication-censoring strategy for the sake of reducing the communication cost in the optimization process. To be specific, a node transmits the quantized version of the local information to its neighbors, if and only if the value sufficiently deviates from the one previously transmitted. We theoretically justify that the proposed DQC-ADMM is capable of tracking the time-varying optimal solution, subject to a bounded error caused by the quantized and censored communications, as well as the system dynamics. Through numerical experiments, we evaluate the tracking performance and communication savings of the proposed DQC-ADMM. [ABSTRACT FROM AUTHOR]

Data in many practical problems are acquired according to decisions or actions made by users or experts to achieve specific goals. For instance, policies in the mind of biologists during the intervention process in genomics and metagenomics are often reflected in available data in these domains, or data in cyber–physical systems are often acquired according to actions/decisions made by experts/engineers for purposes, such as control or stabilization. Quantification of experts’ policies through available data, which is also known as reward function learning, has been discussed extensively in the literature in the context of inverse reinforcement learning (IRL). However, most of the available techniques come short to deal with practical problems due to the following main reasons: 1) lack of scalability: arising from incapability or poor performance of existing techniques in dealing with large systems and 2) lack of reliability: coming from the incapability of the existing techniques to properly learn the optimal reward function during the learning process. Toward this, in this brief, we propose a multifidelity Bayesian optimization (MFBO) framework that significantly scales the learning process of a wide range of existing IRL techniques. The proposed framework enables the incorporation of multiple approximators and efficiently takes their uncertainty and computational costs into account to balance exploration and exploitation during the learning process. The proposed framework’s high performance is demonstrated through genomics, metagenomics, and sets of random simulated problems. [ABSTRACT FROM AUTHOR]

MixUp is an effective data augmentation method to regularize deep neural networks via random linear interpolations between pairs of samples and their labels. It plays an important role in model regularization, semisupervised learning (SSL), and domain adaption. However, despite its empirical success, its deficiency of randomly mixing samples has poorly been studied. Since deep networks are capable of memorizing the entire data set, the corrupted samples generated by vanilla MixUp with a badly chosen interpolation policy will degrade the performance of networks. To overcome overfitting to corrupted samples, inspired by metalearning (learning to learn), we propose a novel technique of learning to a mixup in this work, namely, MetaMixUp. Unlike the vanilla MixUp that samples interpolation policy from a predefined distribution, this article introduces a metalearning-based online optimization approach to dynamically learn the interpolation policy in a data-adaptive way (learning to learn better). The validation set performance via metalearning captures the noisy degree, which provides optimal directions for interpolation policy learning. Furthermore, we adapt our method for pseudolabel-based SSL along with a refined pseudolabeling strategy. In our experiments, our method achieves better performance than vanilla MixUp and its variants under SL configuration. In particular, extensive experiments show that our MetaMixUp adapted SSL greatly outperforms MixUp and many state-of-the-art methods on CIFAR-10 and SVHN benchmarks under the SSL configuration. [ABSTRACT FROM AUTHOR]

Deep generative models are challenging the classical methods in the field of anomaly detection nowadays. Every newly published method provides evidence of outperforming its predecessors, sometimes with contradictory results. The objective of this article is twofold: to compare anomaly detection methods of various paradigms with a focus on deep generative models and identification of sources of variability that can yield different results. The methods were compared on popular tabular and image datasets. We identified that the main sources of variability are the experimental conditions: 1) the type of dataset (tabular or image) and the nature of anomalies (statistical or semantic) and 2) strategy of selection of hyperparameters, especially the number of available anomalies in the validation set. Methods perform differently in different contexts, i.e., under a different combination of experimental conditions together with computational time. This explains the variability of the previous results and highlights the importance of careful specification of the context in the publication of a new method. All our code and results are available for download. [ABSTRACT FROM AUTHOR]

Weight pruning methods of deep neural networks (DNNs) have been demonstrated to achieve a good model pruning rate without loss of accuracy, thereby alleviating the significant computation/storage requirements of large-scale DNNs. Structured weight pruning methods have been proposed to overcome the limitation of irregular network structure and demonstrated actual GPU acceleration. However, in prior work, the pruning rate (degree of sparsity) and GPU acceleration are limited (to less than 50%) when accuracy needs to be maintained. In this work, we overcome these limitations by proposing a unified, systematic framework of structured weight pruning for DNNs. It is a framework that can be used to induce different types of structured sparsity, such as filterwise, channelwise, and shapewise sparsity, as well as nonstructured sparsity. The proposed framework incorporates stochastic gradient descent (SGD; or ADAM) with alternating direction method of multipliers (ADMM) and can be understood as a dynamic regularization method in which the regularization target is analytically updated in each iteration. Leveraging special characteristics of ADMM, we further propose a progressive, multistep weight pruning framework and a network purification and unused path removal procedure, in order to achieve higher pruning rate without accuracy loss. Without loss of accuracy on the AlexNet model, we achieve $2.58\times $ and $3.65\times $ average measured speedup on two GPUs, clearly outperforming the prior work. The average speedups reach $3.15\times $ and $8.52\times $ when allowing a moderate accuracy loss of 2%. In this case, the model compression for convolutional layers is $15.0\times $ , corresponding to $11.93\times $ measured CPU speedup. As another example, for the ResNet-18 model on the CIFAR-10 data set, we achieve an unprecedented $54.2\times $ structured pruning rate on CONV layers. This is $32\times $ higher pruning rate compared with recent work and can further translate into $7.6\times $ inference time speedup on the Adreno 640 mobile GPU compared with the original, unpruned DNN model. We share our codes and models at the link http://bit.ly/2M0V7DO. [ABSTRACT FROM AUTHOR]

Currently, numerical optimization methods are used to solve distributed optimal power allocation (OPA) problems for islanded microgrid (MG) systems. Most of them are developed based on rigorous mathematical derivation. However, the complexity of such optimization algorithms inevitably creates a gap between theoretical analysis and real-time implementation. In order to bridge such a gap, in this article we provide a new distributed learning-based framework to solve the real-time OPA problem. Specifically, inspired by the human-thinking scheme, distributed deep neural networks (DNNs) together with a dynamic average consensus algorithm are first employed to obtain an approximate OPA solution in a distributed manner. Then a distributed balance generation and demand algorithm is designed to fine-tune it to obtain the final optimal feasible solution. In addition, it is theoretically proved that the proposed DNN can well approximate one existing OPA algorithm (Guo et al. 2018), where quantitative numbers of at most how many hidden layers and neurons are provided. Several experimental case studies show that our proposed distributed learning framework can achieve similar optimal results to those obtained by using typical existing distributed numerical optimization methods while it is superior in terms of simplicity and real-time capability. [ABSTRACT FROM AUTHOR]

Adaptive computing (AC) is a technique to dynamically select the layers to pass in a prespecified deep neural network (DNN) according to the input samples. In previous literature, AC was deemed as a standalone complexity-reduction skill. This brief studies AC through a different lens: we investigate how this strategy interacts with mainstream compression techniques in a unified complexity-reduction framework and whether its “input sample related” feature helps with the improvement of model robustness. Following this direction, we first propose a defensive accelerating branch (DAB) based on the AC strategy that can reduce the average computational cost and inference time of DNNs with higher accuracy compared with its counterparts. Then, the proposed DAB is jointly applied with the mainstream parameterwise compression skills, pruning and quantization, to build a unified complexity-reduction framework. Extensive experiments are conducted, and the results reveal quasi-orthogonality between the input-related and parameterwise complexity-reduction skills, which means that the proposed AC can be integrated into an off-the-shelf compressed model without hurting its accuracy. Besides, the robustness of the proposed compression framework is explored, and the experimental results demonstrate that DAB can be used as both the detector and the defensive tool when the model is under adversarial attacks. All these findings shed light on the great potential of DAB in building a unified complexity-reduction framework with both a high compression ratio and great adversarial robustness. [ABSTRACT FROM AUTHOR]

Most of the deep quantization methods adopt unsupervised approaches, and the quantization process usually occurs in the Euclidean space on top of the deep feature and its approximate value. When this approach is applied to the retrieval tasks, since the internal product space of the retrieval process is different from the Euclidean space of quantization, minimizing the quantization error (QE) does not necessarily lead to a good performance on the maximum inner product search (MIPS). To solve these problems, we treat Softmax classification as vector quantization (VQ) with angular decision boundaries and propose angular deep supervised VQ (ADSVQ) for image retrieval. Our approach can simultaneously learn the discriminative feature representation and the updatable codebook, both lying on a hypersphere. To reduce the QE between centroids and deep features, two regularization terms are proposed as supervision signals to encourage the intra-class compactness and inter-class balance, respectively. ADSVQ explicitly reformulates the asymmetric distance computation in MIPS to transform the image retrieval process into a two-stage classification process. Moreover, we discuss the extension of multiple-label cases from the perspective of quantization with binary classification. Extensive experiments demonstrate that the proposed ADSVQ has excellent performance on four well-known image data sets when compared with the state-of-the-art hashing methods. [ABSTRACT FROM AUTHOR]

Momentum technique has recently emerged as an effective strategy in accelerating convergence of gradient descent (GD) methods and exhibits improved performance in deep learning as well as regularized learning. Typical momentum examples include Nesterov’s accelerated gradient (NAG) and heavy-ball (HB) methods. However, so far, almost all the acceleration analyses are only limited to NAG, and a few investigations about the acceleration of HB are reported. In this article, we address the convergence about the last iterate of HB in nonsmooth optimizations with constraints, which we name individual convergence. This question is significant in machine learning, where the constraints are required to impose on the learning structure and the individual output is needed to effectively guarantee this structure while keeping an optimal rate of convergence. Specifically, we prove that HB achieves an individual convergence rate of $O({1}/{\sqrt {t}})$ , where $t$ is the number of iterations. This indicates that both of the two momentum methods can accelerate the individual convergence of basic GD to be optimal. Even for the convergence of averaged iterates, our result avoids the disadvantages of the previous work in restricting the optimization problem to be unconstrained as well as limiting the performed number of iterations to be predefined. The novelty of convergence analysis presented in this article provides a clear understanding of how the HB momentum can accelerate the individual convergence and reveals more insights about the similarities and differences in getting the averaging and individual convergence rates. The derived optimal individual convergence is extended to regularized and stochastic settings, in which an individual solution can be produced by the projection-based operation. In contrast to the averaged output, the sparsity can be reduced remarkably without sacrificing the theoretical optimal rates. Several real experiments demonstrate the performance of HB momentum strategy. [ABSTRACT FROM AUTHOR]

Optimization in a deep neural network is always challenging due to the vanishing gradient problem and intensive fine-tuning of network hyperparameters. Inspired by multistage decision control systems, the stochastic diagonal approximate greatest descent (SDAGD) algorithm is proposed in this article to seek for optimal learning weights using a two-phase switching optimization strategy. The proposed optimizer controls the relative step length derived based on the long-term optimal trajectory and adopts the diagonal approximated Hessian for efficient weight update. In Phase-I, it computes the greatest step length at the boundary of each local spherical search region and, subsequently, descends rapidly toward the direction of an optimal solution. In Phase-II, it switches to an approximate Newton method automatically once it is closer to the optimal solution to achieve fast convergence. The experiments show that SDAGD produces steeper learning curves and achieves lower misclassification rates compared with other optimization techniques. Implementation of the proposed optimizer to deeper networks is also investigated in this article to study the vanishing gradient problem. [ABSTRACT FROM AUTHOR]

We propose a general and scalable global optimization framework directly operating on annotated graph data by introducing a Bayesian graph neural network to approximate the expensive-to-evaluate objectives. It prevents the cubical complexity of Gaussian processes and can scale linearly with the number of observations. Its parallelized variant makes it scalable. We provide strict theoretical support on its convergence. Intensive experiments conducted on both artificial and real-world problems, including molecular discovery and urban road network design, demonstrate the effectiveness of the proposed methods compared with the current state of the art. [ABSTRACT FROM AUTHOR]