arXiv subjects

Weizhong Zhang

Publications and source records attributed to Weizhong Zhang.

52 records · Page 3Linked to original sources

arXiv2022

Robust Federated Learning against both Data Heterogeneity and Poisoning Attack via Aggregation Optimization

Non-IID data distribution across clients and poisoning attacks are two main challenges in real-world federated learning (FL) systems. While both of them have attracted great research interest with specific strategies developed, no known solution manages to address them in a unified framework. To universally overcome both challenges, we propose SmartFL, a generic approach that optimizes the server-side aggregation process with a small amount of proxy data collected by the service provider itself via a subspace training technique. Specifically, the aggregation weight of each participating client at each round is optimized using the server-collected proxy data, which is essentially the optimization of the global model in the convex hull spanned by client models. Since at each round, the number of tunable parameters optimized on the server side equals the number of participating clients (thus independent of the model size), we are able to train a global model with massive parameters using only a small amount of proxy data (e.g., around one hundred samples). With optimized aggregation, SmartFL ensures robustness against both heterogeneous and malicious clients, which is desirable in real-world FL where either or both problems may occur. We provide theoretical analyses of the convergence and generalization capacity for SmartFL. Empirically, SmartFL achieves state-of-the-art performance on both FL with non-IID data distribution and FL with malicious clients. The source code will be released.

cs.LG↗

arXiv2022

DYNAFED: Tackling Client Data Heterogeneity with Global Dynamics

The Federated Learning (FL) paradigm is known to face challenges under heterogeneous client data. Local training on non-iid distributed data results in deflected local optimum, which causes the client models drift further away from each other and degrades the aggregated global model's performance. A natural solution is to gather all client data onto the server, such that the server has a global view of the entire data distribution. Unfortunately, this reduces to regular training, which compromises clients' privacy and conflicts with the purpose of FL. In this paper, we put forth an idea to collect and leverage global knowledge on the server without hindering data privacy. We unearth such knowledge from the dynamics of the global model's trajectory. Specifically, we first reserve a short trajectory of global model snapshots on the server. Then, we synthesize a small pseudo dataset such that the model trained on it mimics the dynamics of the reserved global model trajectory. Afterward, the synthesized data is used to help aggregate the deflected clients into the global model. We name our method Dynafed, which enjoys the following advantages: 1) we do not rely on any external on-server dataset, which requires no additional cost for data collection; 2) the pseudo data can be synthesized in early communication rounds, which enables Dynafed to take effect early for boosting the convergence and stabilizing training; 3) the pseudo data only needs to be synthesized once and can be directly utilized on the server to help aggregation in subsequent rounds. Experiments across extensive benchmarks are conducted to showcase the effectiveness of Dynafed. We also provide insights and understanding of the underlying mechanism of our method.

cs.LG↗

arXiv2022

Approximation algorithms for Steiner Tree Augmentation Problems

In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The goal is to augment $T$ by adding a minimum cost set of links, so that there are 2 edge-disjoint paths between each pair of vertices in $R$. This problem is a special case of the Survivable Network Design Problem, which can be approximated to within a factor of 2 using iterative rounding~\cite{J2001}. We give the first polynomial time algorithm for STAP with approximation ratio better than 2. In particular, we achieve an approximation ratio of $(1.5 + \varepsilon)$. To do this, we employ the Local Search approach of~\cite{TZ2022} for the Tree Augmentation Problem and generalize their main decomposition theorem from links (of size two) to hyper-links. We also consider the Node-Weighted Steiner Tree Augmentation Problem (NW-STAP) in which the non-terminal nodes have non-negative costs. We seek a cheapest subset $S \subseteq V \setminus R$ so that $G[R \cup S]$ is 2-edge-connected. Using a result of Nutov~\cite{N2010}, there exists an $O(\log |R|)$-approximation for this problem. We provide an $O(\log^2 (|R|))$-approximation algorithm for NW-STAP using a greedy algorithm leveraging the spider decomposition of optimal solutions.

cs.DS↗

arXiv2022

Fast Adversarial Training with Adaptive Step Size

While adversarial training and its variants have shown to be the most effective algorithms to defend against adversarial attacks, their extremely slow training process makes it hard to scale to large datasets like ImageNet. The key idea of recent works to accelerate adversarial training is to substitute multi-step attacks (e.g., PGD) with single-step attacks (e.g., FGSM). However, these single-step methods suffer from catastrophic overfitting, where the accuracy against PGD attack suddenly drops to nearly 0% during training, destroying the robustness of the networks. In this work, we study the phenomenon from the perspective of training instances. We show that catastrophic overfitting is instance-dependent and fitting instances with larger gradient norm is more likely to cause catastrophic overfitting. Based on our findings, we propose a simple but effective method, Adversarial Training with Adaptive Step size (ATAS). ATAS learns an instancewise adaptive step size that is inversely proportional to its gradient norm. The theoretical analysis shows that ATAS converges faster than the commonly adopted non-adaptive counterparts. Empirically, ATAS consistently mitigates catastrophic overfitting and achieves higher robust accuracy on CIFAR10, CIFAR100 and ImageNet when evaluated on various adversarial budgets.

cs.LG↗

arXiv2022

Finding Dynamics Preserving Adversarial Winning Tickets

Modern deep neural networks (DNNs) are vulnerable to adversarial attacks and adversarial training has been shown to be a promising method for improving the adversarial robustness of DNNs. Pruning methods have been considered in adversarial context to reduce model capacity and improve adversarial robustness simultaneously in training. Existing adversarial pruning methods generally mimic the classical pruning methods for natural training, which follow the three-stage 'training-pruning-fine-tuning' pipelines. We observe that such pruning methods do not necessarily preserve the dynamics of dense networks, making it potentially hard to be fine-tuned to compensate the accuracy degradation in pruning. Based on recent works of \textit{Neural Tangent Kernel} (NTK), we systematically study the dynamics of adversarial training and prove the existence of trainable sparse sub-network at initialization which can be trained to be adversarial robust from scratch. This theoretically verifies the \textit{lottery ticket hypothesis} in adversarial context and we refer such sub-network structure as \textit{Adversarial Winning Ticket} (AWT). We also show empirical evidences that AWT preserves the dynamics of adversarial training and achieve equal performance as dense adversarial training.

cs.LG↗

arXiv2021

Safe Screening for Sparse Conditional Random Fields

Sparse Conditional Random Field (CRF) is a powerful technique in computer vision and natural language processing for structured prediction. However, solving sparse CRFs in large-scale applications remains challenging. In this paper, we propose a novel safe dynamic screening method that exploits an accurate dual optimum estimation to identify and remove the irrelevant features during the training process. Thus, the problem size can be reduced continuously, leading to great savings in the computational cost without sacrificing any accuracy on the finally learned model. To the best of our knowledge, this is the first screening method which introduces the dual optimum estimation technique -- by carefully exploring and exploiting the strong convexity and the complex structure of the dual problem -- in static screening methods to dynamic screening. In this way, we can absorb the advantages of both the static and dynamic screening methods and avoid their drawbacks. Our estimation would be much more accurate than those developed based on the duality gap, which contributes to a much stronger screening rule. Moreover, our method is also the first screening method in sparse CRFs and even structure prediction models. Experimental results on both synthetic and real-world datasets demonstrate that the speedup gained by our method is significant.

cs.CV↗

arXiv2021

A Structure Feature Algorithm for Multi-modal Forearm Registration

Augmented reality technology based on image registration is becoming increasingly popular for the convenience of pre-surgery preparation and medical education. This paper focuses on the registration of forearm images and digital anatomical models. Due to the difference in texture features of forearm multi-modal images, this paper proposes a forearm feature representation curve (FFRC) based on structure compliant multi-modal image registration framework (FAM) for the forearm.

cs.CV↗

arXiv2021

Efficient Neural Network Training via Forward and Backward Propagation Sparsification

Sparse training is a natural idea to accelerate the training speed of deep neural networks and save the memory usage, especially since large modern neural networks are significantly over-parameterized. However, most of the existing methods cannot achieve this goal in practice because the chain rule based gradient (w.r.t. structure parameters) estimators adopted by previous methods require dense computation at least in the backward propagation step. This paper solves this problem by proposing an efficient sparse training method with completely sparse forward and backward passes. We first formulate the training process as a continuous minimization problem under global sparsity constraint. We then separate the optimization process into two steps, corresponding to weight update and structure parameter update. For the former step, we use the conventional chain rule, which can be sparse via exploiting the sparse structure. For the latter step, instead of using the chain rule based gradient estimators as in existing methods, we propose a variance reduced policy gradient estimator, which only requires two forward passes without backward propagation, thus achieving completely sparse training. We prove that the variance of our gradient estimator is bounded. Extensive experimental results on real-world datasets demonstrate that compared to previous methods, our algorithm is much more effective in accelerating the training process, up to an order of magnitude faster.

cs.LG↗

arXiv2021

Effective Sparsification of Neural Networks with Global Sparsity Constraint

Weight pruning is an effective technique to reduce the model size and inference time for deep neural networks in real-world deployments. However, since magnitudes and relative importance of weights are very different for different layers of a neural network, existing methods rely on either manual tuning or handcrafted heuristic rules to find appropriate pruning rates individually for each layer. This approach generally leads to suboptimal performance. In this paper, by directly working on the probability space, we propose an effective network sparsification method called {\it probabilistic masking} (ProbMask), which solves a natural sparsification formulation under global sparsity constraint. The key idea is to use probability as a global criterion for all layers to measure the weight importance. An appealing feature of ProbMask is that the amounts of weight redundancy can be learned automatically via our constraint and thus we avoid the problem of tuning pruning rates individually for different layers in a network. Extensive experimental results on CIFAR-10/100 and ImageNet demonstrate that our method is highly effective, and can outperform previous state-of-the-art methods by a significant margin, especially in the high pruning rate situation. Notably, the gap of Top-1 accuracy between our ProbMask and existing methods can be up to 10\%. As a by-product, we show ProbMask is also highly effective in identifying supermasks, which are subnetworks with high performance in a randomly weighted dense neural network.

cs.LG↗

arXiv2020

Parsimonious Quantile Regression of Financial Asset Tail Dynamics via Sequential Learning

We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time series. It combines the merits of a popular sequential neural network model, i.e., LSTM, with a novel parametric quantile function that we construct to represent the conditional distribution of asset returns. Our model also captures individually the serial dependences of higher moments, rather than just the volatility. Across a wide range of asset classes, the out-of-sample forecasts of conditional quantiles or VaR of our model outperform the GARCH family. Further, the proposed approach does not suffer from the issue of quantile crossing, nor does it expose to the ill-posedness comparing to the parametric probability density function approach.

q-fin.RM↗

arXiv2019

Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations

Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector $\boldsymbol x = (x_1,\dots,x_d)$ such that for each node $v$ in a social network, $v$ could be activated as a seed of diffusion with probability $h_v(\boldsymbol x)$, where $h_v$ is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix $\boldsymbol x$ with constraint $\sum_i x_i \le k$ where $k$ is a budget constraint, such that the total number of activated nodes after the diffusion process, called influence spread and denoted as $g(\boldsymbol x)$, is maximized. In this paper, we extend CIM to consider budget saving, that is, each strategy mix $\boldsymbol x$ has a cost $c(\boldsymbol x)$ where $c$ is a convex cost function, we want to maximize the balanced sum $g(\boldsymbol x) + λ(k - c(\boldsymbol x))$ where $λ$ is a balance parameter, subject to the constraint of $c(\boldsymbol x) \le k$. We denote this problem as CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular or concave, and thus neither the greedy algorithm nor the standard result on gradient method could be directly applied. Our key innovation is the combination of the gradient method with reverse influence sampling to design algorithms that solve CIM-BS: For the general case, we give an algorithm that achieves $\left(\frac{1}{2}-\varepsilon\right)$-approximation, and for the case of independent strategy activations, we present an algorithm that achieves $\left(1-\frac{1}{e}-\varepsilon\right)$ approximation.

math.OC↗

arXiv2019

Convex Formulation of Overparameterized Deep Neural Networks

Analysis of over-parameterized neural networks has drawn significant attention in recentyears. It was shown that such systems behave like convex systems under various restrictedsettings, such as for two-level neural networks, and when learning is only restricted locally inthe so-called neural tangent kernel space around specialized initializations. However, there areno theoretical techniques that can analyze fully trained deep neural networks encountered inpractice. This paper solves this fundamental problem by investigating such overparameterizeddeep neural networks when fully trained. We generalize a new technique called neural feature repopulation, originally introduced in (Fang et al., 2019a) for two-level neural networks, to analyze deep neural networks. It is shown that under suitable representations, overparameterized deep neural networks are inherently convex, and when optimized, the system can learn effective features suitable for the underlying learning task under mild conditions. This new analysis is consistent with empirical observations that deep neural networks are capable of learning efficient feature representations. Therefore, the highly unexpected result of this paper can satisfactorily explain the practical success of deep neural networks. Empirical studies confirm that predictions of our theory are consistent with results observed in practice.

cs.LG↗

arXiv2019

Scaling Up Sparse Support Vector Machines by Simultaneous Feature and Sample Reduction

Sparse support vector machine (SVM) is a popular classification technique that can simultaneously learn a small set of the most interpretable features and identify the support vectors. It has achieved great successes in many real-world applications. However, for large-scale problems involving a huge number of samples and ultra-high dimensional features, solving sparse SVMs remains challenging. By noting that sparse SVMs induce sparsities in both feature and sample spaces, we propose a novel approach, which is based on accurate estimations of the primal and dual optima of sparse SVMs, to simultaneously identify the inactive features and samples that are guaranteed to be irrelevant to the outputs. Thus, we can remove the identified inactive samples and features from the training phase, leading to substantial savings in the computational cost without sacrificing the accuracy. Moreover, we show that our method can be extended to multi-class sparse support vector machines. To the best of our knowledge, the proposed method is the \emph{first} \emph{static} feature and sample reduction method for sparse SVMs and multi-class sparse SVMs. Experiments on both synthetic and real data sets demonstrate that our approach significantly outperforms state-of-the-art methods and the speedup gained by our approach can be orders of magnitude.

stat.ML↗

arXiv2019

A Sufficient Condition for Convergences of Adam and RMSProp

Adam and RMSProp are two of the most influential adaptive stochastic algorithms for training deep neural networks, which have been pointed out to be divergent even in the convex setting via a few simple counterexamples. Many attempts, such as decreasing an adaptive learning rate, adopting a big batch size, incorporating a temporal decorrelation technique, seeking an analogous surrogate, etc., have been tried to promote Adam/RMSProp-type algorithms to converge. In contrast with existing approaches, we introduce an alternative easy-to-check sufficient condition, which merely depends on the parameters of the base learning rate and combinations of historical second-order moments, to guarantee the global convergence of generic Adam/RMSProp for solving large-scale non-convex stochastic optimization. Moreover, we show that the convergences of several variants of Adam, such as AdamNC, AdaEMA, etc., can be directly implied via the proposed sufficient condition in the non-convex setting. In addition, we illustrate that Adam is essentially a specifically weighted AdaGrad with exponential moving average momentum, which provides a novel perspective for understanding Adam and RMSProp. This observation coupled with this sufficient condition gives much deeper interpretations on their divergences. At last, we validate the sufficient condition by applying Adam and RMSProp to tackle a certain counterexample and train deep neural networks. Numerical results are exactly in accord with our theoretical analysis.

cs.LG↗

arXiv2018

Safe Element Screening for Submodular Function Minimization

Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. However, in large-scale applications, solving Submodular Function Minimization (SFM) problems remains challenging. In this paper, we make the first attempt to extend the emerging technique named screening in large-scale sparse learning to SFM for accelerating its optimization process. We first conduct a careful studying of the relationships between SFM and the corresponding convex proximal problems, as well as the accurate primal optimum estimation of the proximal problems. Relying on this study, we subsequently propose a novel safe screening method to quickly identify the elements guaranteed to be included (we refer to them as active) or excluded (inactive) in the final optimal solution of SFM during the optimization process. By removing the inactive elements and fixing the active ones, the problem size can be dramatically reduced, leading to great savings in the computational cost without sacrificing any accuracy. To the best of our knowledge, the proposed method is the first screening method in the fields of SFM and even combinatorial optimization, thus pointing out a new direction for accelerating SFM algorithms. Experiment results on both synthetic and real datasets demonstrate the significant speedups gained by our approach.

stat.ML↗

arXiv2018

Hierarchical Attention-Based Recurrent Highway Networks for Time Series Prediction

Time series prediction has been studied in a variety of domains. However, it is still challenging to predict future series given historical observations and past exogenous data. Existing methods either fail to consider the interactions among different components of exogenous variables which may affect the prediction accuracy, or cannot model the correlations between exogenous data and target data. Besides, the inherent temporal dynamics of exogenous data are also related to the target series prediction, and thus should be considered as well. To address these issues, we propose an end-to-end deep learning model, i.e., Hierarchical attention-based Recurrent Highway Network (HRHN), which incorporates spatio-temporal feature extraction of exogenous variables and temporal dynamics modeling of target variables into a single framework. Moreover, by introducing the hierarchical attention mechanism, HRHN can adaptively select the relevant exogenous features in different semantic levels. We carry out comprehensive empirical evaluations with various methods over several datasets, and show that HRHN outperforms the state of the arts in time series prediction, especially in capturing sudden changes and sudden oscillations of time series.

cs.LG↗