arXiv subjects

Yangyang Xu

Publications and source records attributed to Yangyang Xu.

At least 73 records · Page 4Linked to original sources

arXiv2023

Decentralized gradient descent maximization method for composite nonconvex strongly-concave minimax problems

Minimax problems have recently attracted a lot of research interests. A few efforts have been made to solve decentralized nonconvex strongly-concave (NCSC) minimax-structured optimization; however, all of them focus on smooth problems with at most a constraint on the maximization variable. In this paper, we make the first attempt on solving composite NCSC minimax problems that can have convex nonsmooth terms on both minimization and maximization variables. Our algorithm is designed based on a novel reformulation of the decentralized minimax problem that introduces a multiplier to absorb the dual consensus constraint. The removal of dual consensus constraint enables the most aggressive (i.e., local maximization instead of a gradient ascent step) dual update that leads to the benefit of taking a larger primal stepsize and better complexity results. In addition, the decoupling of the nonsmoothness and consensus on the dual variable eases the analysis of a decentralized algorithm; thus our reformulation creates a new way for interested researchers to design new (and possibly more efficient) decentralized methods on solving NCSC minimax problems. We show a global convergence result of the proposed algorithm and an iteration complexity result to produce a (near) stationary point of the reformulation. Moreover, a relation is established between the (near) stationarities of the reformulation and the original formulation. With this relation, we show that when the dual regularizer is smooth, our algorithm can have lower complexity results (with reduced dependence on a condition number) than existing ones to produce a near-stationary point of the original formulation. Numerical experiments are conducted on a distributionally robust logistic regression to demonstrate the performance of the proposed algorithm.

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arXiv2023

DeMT: Deformable Mixer Transformer for Multi-Task Learning of Dense Prediction

Convolution neural networks (CNNs) and Transformers have their own advantages and both have been widely used for dense prediction in multi-task learning (MTL). Most of the current studies on MTL solely rely on CNN or Transformer. In this work, we present a novel MTL model by combining both merits of deformable CNN and query-based Transformer for multi-task learning of dense prediction. Our method, named DeMT, is based on a simple and effective encoder-decoder architecture (i.e., deformable mixer encoder and task-aware transformer decoder). First, the deformable mixer encoder contains two types of operators: the channel-aware mixing operator leveraged to allow communication among different channels ($i.e.,$ efficient channel location mixing), and the spatial-aware deformable operator with deformable convolution applied to efficiently sample more informative spatial locations (i.e., deformed features). Second, the task-aware transformer decoder consists of the task interaction block and task query block. The former is applied to capture task interaction features via self-attention. The latter leverages the deformed features and task-interacted features to generate the corresponding task-specific feature through a query-based Transformer for corresponding task predictions. Extensive experiments on two dense image prediction datasets, NYUD-v2 and PASCAL-Context, demonstrate that our model uses fewer GFLOPs and significantly outperforms current Transformer- and CNN-based competitive models on a variety of metrics. The code are available at https://github.com/yangyangxu0/DeMT .

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arXiv2023

Compressed Decentralized Proximal Stochastic Gradient Method for Nonconvex Composite Problems with Heterogeneous Data

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save communication cost, we then extend DProxSGT to a compressed method by compressing the communicated information. Both methods need only $\mathcal{O}(1)$ samples per worker for each proximal update, which is important to achieve good generalization performance on training deep neural networks. With a smoothness condition on the expected loss function (but not on each sample function), the proposed methods can achieve an optimal sample complexity result to produce a near-stationary point. Numerical experiments on training neural networks demonstrate the significantly better generalization performance of our methods over large-batch training methods and momentum variance-reduction methods and also, the ability of handling heterogeneous data by the gradient tracking scheme.

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arXiv2023

A Decentralized Primal-Dual Framework for Non-convex Smooth Consensus Optimization

In this work, we introduce ADAPD, $\textbf{A}$ $\textbf{D}$ecentr$\textbf{A}$lized $\textbf{P}$rimal-$\textbf{D}$ual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. The proposed framework relies on a novel problem formulation that elicits ADMM-type updates, where each agent first inexactly solves a local strongly convex subproblem with any method of its choice and then performs a neighbor communication to update a set of dual variables. We present two variants that allow for a single gradient step for the primal updates or multiple communications for the dual updates, to exploit the tradeoff between the per-iteration cost and the number of iterations. When multiple communications are performed, ADAPD can achieve theoretically optimal communication complexity results for non-convex and smooth consensus problems. Numerical experiments on several applications, including a deep-learning one, demonstrate the superiority of ADAPD over several popularly used decentralized methods.

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arXiv2022

Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization

Many real-world problems not only have complicated nonconvex functional constraints but also use a large number of data points. This motivates the design of efficient stochastic methods on finite-sum or expectation constrained problems. In this paper, we design and analyze stochastic inexact augmented Lagrangian methods (Stoc-iALM) to solve problems involving a nonconvex composite (i.e. smooth+nonsmooth) objective and nonconvex smooth functional constraints. We adopt the standard iALM framework and design a subroutine by using the momentum-based variance-reduced proximal stochastic gradient method (PStorm) and a postprocessing step. Under certain regularity conditions (assumed also in existing works), to reach an $\varepsilon$-KKT point in expectation, we establish an oracle complexity result of $O(\varepsilon^{-5})$, which is better than the best-known $O(\varepsilon^{-6})$ result. Numerical experiments on the fairness constrained problem and the Neyman-Pearson classification problem with real data demonstrate that our proposed method outperforms an existing method with the previously best-known complexity result.

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arXiv2022

When Neural Networks Fail to Generalize? A Model Sensitivity Perspective

Domain generalization (DG) aims to train a model to perform well in unseen domains under different distributions. This paper considers a more realistic yet more challenging scenario,namely Single Domain Generalization (Single-DG), where only a single source domain is available for training. To tackle this challenge, we first try to understand when neural networks fail to generalize? We empirically ascertain a property of a model that correlates strongly with its generalization that we coin as "model sensitivity". Based on our analysis, we propose a novel strategy of Spectral Adversarial Data Augmentation (SADA) to generate augmented images targeted at the highly sensitive frequencies. Models trained with these hard-to-learn samples can effectively suppress the sensitivity in the frequency space, which leads to improved generalization performance. Extensive experiments on multiple public datasets demonstrate the superiority of our approach, which surpasses the state-of-the-art single-DG methods.

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arXiv2022

Separation conditions for iterated function systems with overlaps on Riemannian manifolds

We formulate the weak separation condition and the finite type condition for conformal iterated function systems on Riemannian manifolds with nonnegative Ricci curvature, and generalize the main theorems by Lau \textit{et al.} in [Monatsch. Math. 156 (2009), 325-355]. We also obtain a formula for the Hausdorff dimension of a self-similar set defined by an iterated function system satisfying the finite type condition, generalizing a corresponding result by Jin-Yau [Comm. Anal. Geom. 13 (2005), 821--843] and Lau-Ngai [Adv. Math. 208 (2007), 647-671] on Euclidean spaces. Moreover, we obtain a formula for the Hausdorff dimension of a graph self-similar set generated by a graph-directed iterated function system satisfying the graph finite type condition, extending a result by Ngai \textit{et al.} in [Nonlinearity 23 (2010), 2333--2350].

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arXiv2022

Hybrid Multimodal Feature Extraction, Mining and Fusion for Sentiment Analysis

In this paper, we present our solutions for the Multimodal Sentiment Analysis Challenge (MuSe) 2022, which includes MuSe-Humor, MuSe-Reaction and MuSe-Stress Sub-challenges. The MuSe 2022 focuses on humor detection, emotional reactions and multimodal emotional stress utilizing different modalities and data sets. In our work, different kinds of multimodal features are extracted, including acoustic, visual, text and biological features. These features are fused by TEMMA and GRU with self-attention mechanism frameworks. In this paper, 1) several new audio features, facial expression features and paragraph-level text embeddings are extracted for accuracy improvement. 2) we substantially improve the accuracy and reliability of multimodal sentiment prediction by mining and blending the multimodal features. 3) effective data augmentation strategies are applied in model training to alleviate the problem of sample imbalance and prevent the model from learning biased subject characters. For the MuSe-Humor sub-challenge, our model obtains the AUC score of 0.8932. For the MuSe-Reaction sub-challenge, the Pearson's Correlations Coefficient of our approach on the test set is 0.3879, which outperforms all other participants. For the MuSe-Stress sub-challenge, our approach outperforms the baseline in both arousal and valence on the test dataset, reaching a final combined result of 0.5151.

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arXiv2022

Momentum-based variance-reduced proximal stochastic gradient method for composite nonconvex stochastic optimization

Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and nonconvex cases. Most of them require a large number of samples in some or all iterations of the improved SGMs. In this paper, we propose a new SGM, named PStorm, for solving nonconvex nonsmooth stochastic problems. With a momentum-based variance reduction technique, PStorm can achieve the optimal complexity result $O(\varepsilon^{-3})$ to produce a stochastic $\varepsilon$-stationary solution, if a mean-squared smoothness condition holds. Different from existing optimal methods, PStorm can achieve the ${O}(\varepsilon^{-3})$ result by using only one or $O(1)$ samples in every update. With this property, PStorm can be applied to online learning problems that favor real-time decisions based on one or $O(1)$ new observations. In addition, for large-scale machine learning problems, PStorm can generalize better by small-batch training than other optimal methods that require large-batch training and the vanilla SGM, as we demonstrate on training a sparse fully-connected neural network and a sparse convolutional neural network.

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arXiv2022

Parallel and distributed asynchronous adaptive stochastic gradient methods

Stochastic gradient methods (SGMs) are the predominant approaches to train deep learning models. The adaptive versions (e.g., Adam and AMSGrad) have been extensively used in practice, partly because they achieve faster convergence than the non-adaptive versions while incurring little overhead. On the other hand, asynchronous (async) parallel computing has exhibited significantly higher speed-up over its synchronous (sync) counterpart. Async-parallel non-adaptive SGMs have been well studied in the literature from the perspectives of both theory and practical performance. Adaptive SGMs can also be implemented without much difficulty in an async-parallel way. However, to the best of our knowledge, no theoretical result of async-parallel adaptive SGMs has been established. The difficulty for analyzing adaptive SGMs with async updates originates from the second moment term. In this paper, we propose an async-parallel adaptive SGM based on AMSGrad. We show that the proposed method inherits the convergence guarantee of AMSGrad for both convex and non-convex problems, if the staleness (also called delay) caused by asynchrony is bounded. Our convergence rate results indicate a nearly linear parallelization speed-up if $τ=o(K^{\frac{1}{4}})$, where $τ$ is the staleness and $K$ is the number of iterations. The proposed method is tested on both convex and non-convex machine learning problems, and the numerical results demonstrate its clear advantages over the sync counterpart and the async-parallel nonadaptive SGM.

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arXiv2022

High-resolution Face Swapping via Latent Semantics Disentanglement

We present a novel high-resolution face swapping method using the inherent prior knowledge of a pre-trained GAN model. Although previous research can leverage generative priors to produce high-resolution results, their quality can suffer from the entangled semantics of the latent space. We explicitly disentangle the latent semantics by utilizing the progressive nature of the generator, deriving structure attributes from the shallow layers and appearance attributes from the deeper ones. Identity and pose information within the structure attributes are further separated by introducing a landmark-driven structure transfer latent direction. The disentangled latent code produces rich generative features that incorporate feature blending to produce a plausible swapping result. We further extend our method to video face swapping by enforcing two spatio-temporal constraints on the latent space and the image space. Extensive experiments demonstrate that the proposed method outperforms state-of-the-art image/video face swapping methods in terms of hallucination quality and consistency. Code can be found at: https://github.com/cnnlstm/FSLSD_HiRes.

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arXiv2022

Existence of $L^q$-dimension and entropy dimension of self-conformal measures on Riemannian manifolds

Peres and Solomyak proved that on $\mathbb R^n$, the limits defining the $L^q$-dimension for any $q\in(0,\infty)\setminus\{1\}$, and the entropy dimension of a self-conformal measure exist, without assuming any separation condition. By introducing the notions of heavy maximal packings and partitions, we prove that on a doubling metric space the $L^q$-dimension, $q\in(0,\infty)\setminus\{1\}$, is equivalent to the generalized dimension. We also generalize the result on the existence of the $L^q$-dimension to self-conformal measures on complete Riemannian manifolds with the doubling property. In particular, these results hold for complete Riemannian manifolds with nonnegative Ricci curvature. Moreover, by assuming that the measure is doubling, we extend the result on the existence of the entropy dimension to self-conformal measures on complete Riemannian manifolds.

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arXiv2022

Inexact accelerated proximal gradient method with line search and reduced complexity for affine-constrained and bilinear saddle-point structured convex problems

The goal of this paper is to reduce the total complexity of gradient-based methods for two classes of problems: affine-constrained composite convex optimization and bilinear saddle-point structured non-smooth convex optimization. Our technique is based on a double-loop inexact accelerated proximal gradient (APG) method for minimizing the summation of a non-smooth but proximable convex function and two smooth convex functions with different smoothness constants and computational costs. Compared to the standard APG method, the inexact APG method can reduce the total computation cost if one smooth component has higher computational cost but a smaller smoothness constant than the other. With this property, the inexact APG method can be applied to approximately solve the subproblems of a proximal augmented Lagrangian method for affine-constrained composite convex optimization and the smooth approximation for bilinear saddle-point structured non-smooth convex optimization, where the smooth function with a smaller smoothness constant has significantly higher computational cost. Thus it can reduce total complexity for finding an approximately optimal/stationary solution. This technique is similar to the gradient sliding technique in the literature. The difference is that our inexact APG method can efficiently stop the inner loop by using a computable condition based on a measure of stationarity violation, while the gradient sliding methods need to pre-specify the number of iterations for the inner loop. Numerical experiments demonstrate significantly higher efficiency of our methods over an optimal primal-dual first-order method and the gradient sliding methods.

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arXiv2021

Adaptive Primal-Dual Stochastic Gradient Method for Expectation-constrained Convex Stochastic Programs

Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic optimization problems with expectation constraints. For these problems, it is often extremely expensive to perform projection onto the feasible set. Several SGMs in the literature can be applied to solve the expectation-constrained stochastic problems. We propose a novel primal-dual type SGM based on the Lagrangian function. Different from existing methods, our method incorporates an adaptiveness technique to speed up convergence. At each iteration, our method inquires an unbiased stochastic subgradient of the Lagrangian function, and then it renews the primal variables by an adaptive-SGM update and the dual variables by a vanilla-SGM update. We show that the proposed method has a convergence rate of $O(1/\sqrt{k})$ in terms of the objective error and the constraint violation. Although the convergence rate is the same as those of existing SGMs, we observe its significantly faster convergence than an existing non-adaptive primal-dual SGM and a primal SGM on solving the Neyman-Pearson classification and quadratically constrained quadratic programs. Furthermore, we modify the proposed method to solve convex-concave stochastic minimax problems, for which we perform adaptive-SGM updates to both primal and dual variables. A convergence rate of $O(1/\sqrt{k})$ is also established to the modified method for solving minimax problems in terms of primal-dual gap.

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arXiv2021

Distributed stochastic inertial-accelerated methods with delayed derivatives for nonconvex problems

Stochastic gradient methods (SGMs) are predominant approaches for solving stochastic optimization. On smooth nonconvex problems, a few acceleration techniques have been applied to improve the convergence rate of SGMs. However, little exploration has been made on applying a certain acceleration technique to a stochastic subgradient method (SsGM) for nonsmooth nonconvex problems. In addition, few efforts have been made to analyze an (accelerated) SsGM with delayed derivatives. The information delay naturally happens in a distributed system, where computing workers do not coordinate with each other. In this paper, we propose an inertial proximal SsGM for solving nonsmooth nonconvex stochastic optimization problems. The proposed method can have guaranteed convergence even with delayed derivative information in a distributed environment. Convergence rate results are established to three classes of nonconvex problems: weakly-convex nonsmooth problems with a convex regularizer, composite nonconvex problems with a nonsmooth convex regularizer, and smooth nonconvex problems. For each problem class, the convergence rate is $O(1/K^{\frac{1}{2}})$ in the expected value of the gradient norm square, for $K$ iterations. In a distributed environment, the convergence rate of the proposed method will be slowed down by the information delay. Nevertheless, the slow-down effect will decay with the number of iterations for the latter two problem classes. We test the proposed method on three applications. The numerical results clearly demonstrate the advantages of using the inertial-based acceleration. Furthermore, we observe higher parallelization speed-up in asynchronous updates over the synchronous counterpart, though the former uses delayed derivatives. Our source code is released at https://github.com/RPI-OPT/Inertial-SsGM

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arXiv2021

Zeroth-order Optimization for Composite Problems with Functional Constraints

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods or sometimes the only options. In this paper, we propose a novel zeroth-order inexact augmented Lagrangian method (ZO-iALM) to solve black-box optimization problems, which involve a composite (i.e., smooth+nonsmooth) objective and functional constraints. Under a certain regularity condition (also assumed by several existing works on FO methods), the query complexity of our ZO-iALM is $\tilde{O}(d\varepsilon^{-3})$ to find an $\varepsilon$-KKT point for problems with a nonconvex objective and nonconvex constraints, and $\tilde{O}(d\varepsilon^{-2.5})$ for nonconvex problems with convex constraints, where $d$ is the variable dimension. This appears to be the first work that develops an iALM-based ZO method for functional constrained optimization and meanwhile achieves query complexity results matching the best-known FO complexity results up to a factor of $d$. With an extensive experimental study, we show the effectiveness of our method. The applications of our method span from classical optimization problems to practical machine learning examples such as resource allocation in sensor networks and adversarial example generation.

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arXiv2021

From Continuity to Editability: Inverting GANs with Consecutive Images

Existing GAN inversion methods are stuck in a paradox that the inverted codes can either achieve high-fidelity reconstruction, or retain the editing capability. Having only one of them clearly cannot realize real image editing. In this paper, we resolve this paradox by introducing consecutive images (\eg, video frames or the same person with different poses) into the inversion process. The rationale behind our solution is that the continuity of consecutive images leads to inherent editable directions. This inborn property is used for two unique purposes: 1) regularizing the joint inversion process, such that each of the inverted code is semantically accessible from one of the other and fastened in a editable domain; 2) enforcing inter-image coherence, such that the fidelity of each inverted code can be maximized with the complement of other images. Extensive experiments demonstrate that our alternative significantly outperforms state-of-the-art methods in terms of reconstruction fidelity and editability on both the real image dataset and synthesis dataset. Furthermore, our method provides the first support of video-based GAN inversion, and an interesting application of unsupervised semantic transfer from consecutive images. Source code can be found at: \url{https://github.com/cnnlstm/InvertingGANs_with_ConsecutiveImgs}.

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arXiv2021

First-order methods for problems with O(1) functional constraints can have almost the same convergence rate as for unconstrained problems

First-order methods (FOMs) have recently been applied and analyzed for solving problems with complicated functional constraints. Existing works show that FOMs for functional constrained problems have lower-order convergence rates than those for unconstrained problems. In particular, an FOM for a smooth strongly-convex problem can have linear convergence, while it can only converge sublinearly for a constrained problem if the projection onto the constraint set is prohibited. In this paper, we point out that the slower convergence is caused by the large number of functional constraints but not the constraints themselves. When there are only $m=O(1)$ functional constraints, we show that an FOM can have almost the same convergence rate as that for solving an unconstrained problem, even without the projection onto the feasible set. In addition, given an $\varepsilon>0$, we show that a complexity result that is better than a lower bound can be obtained, if there are only $m=o(\varepsilon^{-\frac{1}{2}})$ functional constraints. Our result is surprising but does not contradict to the existing lower complexity bound, because we focus on a specific subclass of problems. Experimental results on quadratically-constrained quadratic programs demonstrate our theory.

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