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Ming Yan

Publications and source records attributed to Ming Yan.

At least 235 records · Page 13Linked to original sources
arXiv2021

On linear convergence of two decentralized algorithms

Decentralized algorithms solve multi-agent problems over a connected network, where the information can only be exchanged with the accessible neighbors. Though there exist several decentralized optimization algorithms, there are still gaps in convergence conditions and rates between decentralized and centralized algorithms. In this paper, we fill some gaps by considering two decentralized algorithms: EXTRA and NIDS. They both converge linearly with strongly convex objective functions. We will answer two questions regarding them. What are the optimal upper bounds for their stepsizes? Do decentralized algorithms require more properties on the functions for linear convergence than centralized ones? More specifically, we relax the required conditions for linear convergence of both algorithms. For EXTRA, we show that the stepsize is comparable to that of centralized algorithms. For NIDS, the upper bound of the stepsize is shown to be exactly the same as the centralized ones. In addition, we relax the requirement for the objective functions and the mixing matrices. We provide the linear convergence results for both algorithms under the weakest conditions.

math.OC↗
arXiv2021

New convergence analysis of a primal-dual algorithm with large stepsizes

We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fréchet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator (PDFP$^2$O) and Proximal Alternating Predictor-Corrector (PAPC). In this paper, we prove its convergence under a weaker condition on the stepsizes than existing ones. With additional assumptions, we show its linear convergence. In addition, we show that this condition (the upper bound of the stepsize) is tight and can not be weakened. This result also recovers a recently proposed positive-indefinite linearized augmented Lagrangian method. In addition, we apply this result to a decentralized consensus algorithm PG-EXTRA and derive the weakest convergence condition.

math.OC↗
arXiv2020

Variational Asymptotic Preserving Scheme for the Vlasov-Poisson-Fokker-Planck System

We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an implicit-explicit framework, wherein the stiff terms coming from the collision and field effects are solved implicitly while the convection terms are solved explicitly. To treat the implicit part, we propose a variational approach by viewing it as a Wasserstein gradient flow of the relative entropy, and solve it via a proximal quasi-Newton method. In so doing we get positivity and asymptotic preservation for free. The method is also massively parallelizable and thus suitable for high dimensional problems. We further show that the convergence of our implicit solver is uniform across different scales. A suite of numerical examples are presented at the end to validate the performance of the proposed scheme.

math.NA↗
arXiv2020

Deep Neural Networks with Short Circuits for Improved Gradient Learning

Deep neural networks have achieved great success both in computer vision and natural language processing tasks. However, mostly state-of-art methods highly rely on external training or computing to improve the performance. To alleviate the external reliance, we proposed a gradient enhancement approach, conducted by the short circuit neural connections, to improve the gradient learning of deep neural networks. The proposed short circuit is a unidirectional connection that single back propagates the sensitive from the deep layer to the shallows. Moreover, the short circuit formulates to be a gradient truncation of its crossing layers which can plug into the backbone deep neural networks without introducing external training parameters. Extensive experiments demonstrate deep neural networks with our short circuit gain a large margin over the baselines on both computer vision and natural language processing tasks.

cs.LG↗
arXiv2020

PALM: Pre-training an Autoencoding&Autoregressive Language Model for Context-conditioned Generation

Self-supervised pre-training, such as BERT, MASS and BART, has emerged as a powerful technique for natural language understanding and generation. Existing pre-training techniques employ autoencoding and/or autoregressive objectives to train Transformer-based models by recovering original word tokens from corrupted text with some masked tokens. The training goals of existing techniques are often inconsistent with the goals of many language generation tasks, such as generative question answering and conversational response generation, for producing new text given context. This work presents PALM with a novel scheme that jointly pre-trains an autoencoding and autoregressive language model on a large unlabeled corpus, specifically designed for generating new text conditioned on context. The new scheme alleviates the mismatch introduced by the existing denoising scheme between pre-training and fine-tuning where generation is more than reconstructing original text. An extensive set of experiments show that PALM achieves new state-of-the-art results on a variety of language generation benchmarks covering generative question answering (Rank 1 on the official MARCO leaderboard), abstractive summarization on CNN/DailyMail as well as Gigaword, question generation on SQuAD, and conversational response generation on Cornell Movie Dialogues.

cs.CL↗
arXiv2020

Fast algorithms for robust principal component analysis with an upper bound on the rank

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular values of a matrix to obtain a low-rank matrix. However, calculating singular values can be very expensive for large matrices. The second type of algorithm replaces the low-rank matrix as the multiplication of two small matrices. They are faster than the first type because no singular value decomposition (SVD) is required. However, the rank of the low-rank matrix is required, and an accurate rank estimation is needed to obtain a reasonable solution. In this paper, we propose algorithms that combine both types. Our proposed algorithms require an upper bound of the rank and SVD on small matrices. First, they are faster than the first type because the cost of SVD on small matrices is negligible. Second, they are more robust than the second type because an upper bound of the rank instead of the exact rank is required. Furthermore, we apply the Gauss-Newton method to increase the speed of our algorithms. Numerical experiments show the better performance of our proposed algorithms.

math.NA↗
arXiv2020

A Novel Regularization Based on the Error Function for Sparse Recovery

Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this paper, we propose a novel regularization framework that uses the error function to approximate the unit step function. It can be considered as a surrogate function for the $L_0$ norm. The asymptotic behavior of the error function with respect to its intrinsic parameter indicates that the proposed regularization can approximate the standard $L_0$, $L_1$ norms as the parameter approaches to $0$ and $\infty,$ respectively. Statistically, it is also less biased than the $L_1$ approach. We then incorporate the error function into either a constrained or an unconstrained model when recovering a sparse signal from an under-determined linear system. Computationally, both problems can be solved via an iterative reweighted $L_1$ (IRL1) algorithm with guaranteed convergence. A large number of experimental results demonstrate that the proposed approach outperforms the state-of-the-art methods in various sparse recovery scenarios.

math.NA↗
arXiv2020

Efficient Hyperparameter Optimization in Deep Learning Using a Variable Length Genetic Algorithm

Convolutional Neural Networks (CNN) have gained great success in many artificial intelligence tasks. However, finding a good set of hyperparameters for a CNN remains a challenging task. It usually takes an expert with deep knowledge, and trials and errors. Genetic algorithms have been used in hyperparameter optimizations. However, traditional genetic algorithms with fixed-length chromosomes may not be a good fit for optimizing deep learning hyperparameters, because deep learning models have variable number of hyperparameters depending on the model depth. As the depth increases, the number of hyperparameters grows exponentially, and searching becomes exponentially harder. It is important to have an efficient algorithm that can find a good model in reasonable time. In this article, we propose to use a variable length genetic algorithm (GA) to systematically and automatically tune the hyperparameters of a CNN to improve its performance. Experimental results show that our algorithm can find good CNN hyperparameters efficiently. It is clear from our experiments that if more time is spent on optimizing the hyperparameters, better results could be achieved. Theoretically, if we had unlimited time and CPU power, we could find the optimized hyperparameters and achieve the best results in the future.

cs.NE↗
arXiv2020

A Multi-Agent Primal-Dual Strategy for Composite Optimization over Distributed Features

This work studies multi-agent sharing optimization problems with the objective function being the sum of smooth local functions plus a convex (possibly non-smooth) function coupling all agents. This scenario arises in many machine learning and engineering applications, such as regression over distributed features and resource allocation. We reformulate this problem into an equivalent saddle-point problem, which is amenable to decentralized solutions. We then propose a proximal primal-dual algorithm and establish its linear convergence to the optimal solution when the local functions are strongly-convex. To our knowledge, this is the first linearly convergent decentralized algorithm for multi-agent sharing problems with a general convex (possibly non-smooth) coupling function.

math.OC↗
arXiv2020

Accelerated Schemes for the $L_1/L_2$ Minimization

In this paper, we consider the $L_1/L_2 $ minimization for sparse recovery and study its relationship with the $L_1$-$ αL_2 $ model. Based on this relationship, we propose three numerical algorithms to minimize this ratio model, two of which work as adaptive schemes and greatly reduce the computation time. Focusing on two adaptive schemes, we discuss their connection to existing approaches and analyze their convergence. The experimental results demonstrate the proposed approaches are comparable to the state-of-the-art methods in sparse recovery and work particularly well when the ground-truth signal has a high dynamic range. Lastly, we reveal some empirical evidence on the exact $L_1$ recovery under various combinations of sparsity, coherence, and dynamic ranges, which calls for theoretical justification in the future.

math.NA↗
arXiv2019

Decentralized Frequency Alignment for Collaborative Beamforming in Distributed Phased Arrays

A new approach to distributed syntonization (frequency alignment) for the coordination of nodes in open loop coherent distributed antenna arrays to enable distributed beamforming is presented. This approach makes use of the concept of consensus optimization among nodes without requiring a centralized control. Decentralized frequency consensus can be achieved through iterative frequency exchange among nodes. We derive a model of the signal received from a coherent distributed array and analyze the effects on beamforming of phase errors induced by oscillator frequency drift. We introduce and discuss the average consensus protocol for frequency transfer in undirected networks where each node transmits and receives frequency information from other nodes. We analyze the following cases: 1) undirected networks with a static topology; 2) undirected networks with dynamic topology, where connections between nodes are made and lost dynamically; and 3) undirected networks with oscillator frequency drift. We show that all the nodes in a given network achieve average consensus and the number of iterations needed to achieve consensus can be minimized for a given cluster of nodes. Numerical simulations demonstrate that the consensus algorithm enables tolerable errors to obtain high coherent gain of greater that 90\% of the ideal gain in an error-free distributed phased array.

eess.SP↗
arXiv2019

Manifold Denoising by Nonlinear Robust Principal Component Analysis

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets.

cs.LG↗
arXiv2019

A Double Residual Compression Algorithm for Efficient Distributed Learning

Large-scale machine learning models are often trained by parallel stochastic gradient descent algorithms. However, the communication cost of gradient aggregation and model synchronization between the master and worker nodes becomes the major obstacle for efficient learning as the number of workers and the dimension of the model increase. In this paper, we propose DORE, a DOuble REsidual compression stochastic gradient descent algorithm, to reduce over $95\%$ of the overall communication such that the obstacle can be immensely mitigated. Our theoretical analyses demonstrate that the proposed strategy has superior convergence properties for both strongly convex and nonconvex objective functions. The experimental results validate that DORE achieves the best communication efficiency while maintaining similar model accuracy and convergence speed in comparison with start-of-the-art baselines.

cs.LG↗
arXiv2019

StructBERT: Incorporating Language Structures into Pre-training for Deep Language Understanding

Recently, the pre-trained language model, BERT (and its robustly optimized version RoBERTa), has attracted a lot of attention in natural language understanding (NLU), and achieved state-of-the-art accuracy in various NLU tasks, such as sentiment classification, natural language inference, semantic textual similarity and question answering. Inspired by the linearization exploration work of Elman [8], we extend BERT to a new model, StructBERT, by incorporating language structures into pre-training. Specifically, we pre-train StructBERT with two auxiliary tasks to make the most of the sequential order of words and sentences, which leverage language structures at the word and sentence levels, respectively. As a result, the new model is adapted to different levels of language understanding required by downstream tasks. The StructBERT with structural pre-training gives surprisingly good empirical results on a variety of downstream tasks, including pushing the state-of-the-art on the GLUE benchmark to 89.0 (outperforming all published models), the F1 score on SQuAD v1.1 question answering to 93.0, the accuracy on SNLI to 91.7.

cs.CL↗
arXiv2019

Incorporating External Knowledge into Machine Reading for Generative Question Answering

Commonsense and background knowledge is required for a QA model to answer many nontrivial questions. Different from existing work on knowledge-aware QA, we focus on a more challenging task of leveraging external knowledge to generate answers in natural language for a given question with context. In this paper, we propose a new neural model, Knowledge-Enriched Answer Generator (KEAG), which is able to compose a natural answer by exploiting and aggregating evidence from all four information sources available: question, passage, vocabulary and knowledge. During the process of answer generation, KEAG adaptively determines when to utilize symbolic knowledge and which fact from the knowledge is useful. This allows the model to exploit external knowledge that is not explicitly stated in the given text, but that is relevant for generating an answer. The empirical study on public benchmark of answer generation demonstrates that KEAG improves answer quality over models without knowledge and existing knowledge-aware models, confirming its effectiveness in leveraging knowledge.

cs.CL↗
arXiv2019

Incorporating Relation Knowledge into Commonsense Reading Comprehension with Multi-task Learning

This paper focuses on how to take advantage of external relational knowledge to improve machine reading comprehension (MRC) with multi-task learning. Most of the traditional methods in MRC assume that the knowledge used to get the correct answer generally exists in the given documents. However, in real-world task, part of knowledge may not be mentioned and machines should be equipped with the ability to leverage external knowledge. In this paper, we integrate relational knowledge into MRC model for commonsense reasoning. Specifically, based on a pre-trained language model (LM). We design two auxiliary relation-aware tasks to predict if there exists any commonsense relation and what is the relation type between two words, in order to better model the interactions between document and candidate answer option. We conduct experiments on two multi-choice benchmark datasets: the SemEval-2018 Task 11 and the Cloze Story Test. The experimental results demonstrate the effectiveness of the proposed method, which achieves superior performance compared with the comparable baselines on both datasets.

cs.CL↗
arXiv2019

Heat transfer and flow regimes in quasi-static magnetoconvection with a vertical magnetic field

Numerical simulations of quasi-static magnetoconvection with a vertical magnetic field are carried out up to a Chandrasekhar number of $Q=10^8$ over a broad range of Rayleigh numbers $Ra$. Three magnetoconvection regimes are identified: two of the regimes are magnetically-constrained in the sense that a leading-order balance exists between the Lorentz and buoyancy forces, whereas the third regime is characterized by unbalanced dynamics that is similar to non-magnetic convection. Each regime is distinguished by flow morphology, momentum and heat equation balances, and heat transport behavior. One of the magnetically-constrained regimes appears to represent an `ultimate' magnetoconvection regime in the dual limit of asymptotically-large buoyancy forcing and magnetic field strength; this regime is characterized by an interconnected network of anisotropic, spatially-localized fluid columns aligned with the direction of the imposed magnetic field that remain quasi-laminar despite having large flow speeds. As for non-magnetic convection, heat transport is controlled primarily by the thermal boundary layer. Empirically, the scaling of the heat transport and flow speeds with $Ra$ appear to be independent of the thermal Prandtl number within the magnetically-constrained, high-$Q$ regimes.

physics.flu-dyn↗