Shi Pu

Fan Bao, Shen Nie, Kaiwen Xue et al.

This paper proposes a unified diffusion framework (dubbed UniDiffuser) to fit all distributions relevant to a set of multi-modal data in one model. Our key insight is -- learning diffusion models for marginal, conditional, and joint distributions can be unified as predicting the noise in the perturbed data, where the perturbation levels (i.e. timesteps) can be different for different modalities. Inspired by the unified view, UniDiffuser learns all distributions simultaneously with a minimal modification to the original diffusion model -- perturbs data in all modalities instead of a single modality, inputs individual timesteps in different modalities, and predicts the noise of all modalities instead of a single modality. UniDiffuser is parameterized by a transformer for diffusion models to handle input types of different modalities. Implemented on large-scale paired image-text data, UniDiffuser is able to perform image, text, text-to-image, image-to-text, and image-text pair generation by setting proper timesteps without additional overhead. In particular, UniDiffuser is able to produce perceptually realistic samples in all tasks and its quantitative results (e.g., the FID and CLIP score) are not only superior to existing general-purpose models but also comparable to the bespoken models (e.g., Stable Diffusion and DALL-E 2) in representative tasks (e.g., text-to-image generation).

Shi Pu, Kaili Zhao, Mao Zheng

Most methods tackle zero-shot video classification by aligning visual-semantic representations within seen classes, which limits generalization to unseen classes. To enhance model generalizability, this paper presents an end-to-end framework that preserves alignment and uniformity properties for representations on both seen and unseen classes. Specifically, we formulate a supervised contrastive loss to simultaneously align visual-semantic features (i.e., alignment) and encourage the learned features to distribute uniformly (i.e., uniformity). Unlike existing methods that only consider the alignment, we propose uniformity to preserve maximal-info of existing features, which improves the probability that unobserved features fall around observed data. Further, we synthesize features of unseen classes by proposing a class generator that interpolates and extrapolates the features of seen classes. Besides, we introduce two metrics, closeness and dispersion, to quantify the two properties and serve as new measurements of model generalizability. Experiments show that our method significantly outperforms SoTA by relative improvements of 28.1% on UCF101 and 27.0% on HMDB51. Code is available.

Kun Huang, Linli Zhou, Shi Pu

This paper proposes two distributed random reshuffling methods, namely Gradient Tracking with Random Reshuffling (GT-RR) and Exact Diffusion with Random Reshuffling (ED-RR), to solve the distributed optimization problem over a connected network, where a set of agents aim to minimize the average of their local cost functions. Both algorithms invoke random reshuffling (RR) update for each agent, inherit favorable characteristics of RR for minimizing smooth nonconvex objective functions, and improve the performance of previous distributed random reshuffling methods both theoretically and empirically. Specifically, both GT-RR and ED-RR achieve the convergence rate of $O(1/[(1-λ)^{1/3}m^{1/3}T^{2/3}])$ in driving the (minimum) expected squared norm of the gradient to zero, where $T$ denotes the number of epochs, $m$ is the sample size for each agent, and $1-λ$ represents the spectral gap of the mixing matrix. When the objective functions further satisfy the Polyak-Łojasiewicz (PL) condition, we show GT-RR and ED-RR both achieve $O(1/[(1-λ)mT^2])$ convergence rate in terms of the averaged expected differences between the agents' function values and the global minimum value. Notably, both results are comparable to the convergence rates of centralized RR methods (up to constant factors depending on the network topology) and outperform those of previous distributed random reshuffling algorithms.

Kun Huang, Shi Pu

In this paper, we consider solving the distributed optimization problem over a multi-agent network under the communication restricted setting. We study a compressed decentralized stochastic gradient method, termed ``compressed exact diffusion with adaptive stepsizes (CEDAS)", and show the method asymptotically achieves comparable convergence rate as centralized { stochastic gradient descent (SGD)} for both smooth strongly convex objective functions and smooth nonconvex objective functions under unbiased compression operators. In particular, to our knowledge, CEDAS enjoys so far the shortest transient time (with respect to the graph specifics) for achieving the convergence rate of centralized SGD, which behaves as $\mathcal{O}(n{C^3}/(1-λ_2)^{2})$ under smooth strongly convex objective functions, and $\mathcal{O}(n^3{C^6}/(1-λ_2)^4)$ under smooth nonconvex objective functions, where $(1-λ_2)$ denotes the spectral gap of the mixing matrix, and $C>0$ is the compression-related parameter. In particular, CEDAS exhibits the shortest transient times when $C < \mathcal{O}(1/(1 - λ_2)^2)$, which is common in practice. Numerical experiments further demonstrate the effectiveness of the proposed algorithm.

Kun Huang, Xiao Li, Shi Pu

Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical problems, their theoretical guarantees mainly rely on certain boundedness conditions on the stochastic gradients, varying from uniform boundedness to the relaxed growth condition. In addition, how to characterize the data heterogeneity among the agents and its impacts on the algorithmic performance remains challenging. In light of such motivations, we revisit the classical Federated Averaging (FedAvg) algorithm (McMahan et al., 2017) as well as the more recent SCAFFOLD method (Karimireddy et al., 2020) for solving the distributed stochastic optimization problem and establish the convergence results under only a mild variance condition on the stochastic gradients for smooth nonconvex objective functions. Almost sure convergence to a stationary point is also established under the condition. Moreover, we discuss a more informative measurement for data heterogeneity as well as its implications.

Yijie Zhou, Shi Pu

Decentralized optimization has become vital for leveraging distributed data without central control, enhancing scalability and privacy. However, practical deployments face fundamental challenges due to heterogeneous computation speeds and unpredictable communication delays. This paper introduces a refined model of Asynchronous Decentralized Stochastic Gradient Descent (ADSGD) under practical assumptions of bounded computation and communication times. To understand the convergence of ADSGD, we first analyze Asynchronous Stochastic Block Coordinate Descent (ASBCD) as a tool, and then show that ADSGD converges under computation-delay-independent step sizes. The convergence result is established without assuming bounded data heterogeneity. Empirical experiments reveal that ADSGD outperforms existing methods in wall-clock convergence time across various scenarios. With its simplicity, efficiency in memory and communication, and resilience to communication and computation delays, ADSGD is well-suited for real-world decentralized learning tasks.

Shengfang Zhai, Yinpeng Dong, Qingni Shen et al.

With the help of conditioning mechanisms, the state-of-the-art diffusion models have achieved tremendous success in guided image generation, particularly in text-to-image synthesis. To gain a better understanding of the training process and potential risks of text-to-image synthesis, we perform a systematic investigation of backdoor attack on text-to-image diffusion models and propose BadT2I, a general multimodal backdoor attack framework that tampers with image synthesis in diverse semantic levels. Specifically, we perform backdoor attacks on three levels of the vision semantics: Pixel-Backdoor, Object-Backdoor and Style-Backdoor. By utilizing a regularization loss, our methods efficiently inject backdoors into a large-scale text-to-image diffusion model while preserving its utility with benign inputs. We conduct empirical experiments on Stable Diffusion, the widely-used text-to-image diffusion model, demonstrating that the large-scale diffusion model can be easily backdoored within a few fine-tuning steps. We conduct additional experiments to explore the impact of different types of textual triggers, as well as the backdoor persistence during further training, providing insights for the development of backdoor defense methods. Besides, our investigation may contribute to the copyright protection of text-to-image models in the future.

Kun Huang, Xiao Li, Andre Milzarek et al.

In this paper, we consider distributed optimization problems where $n$ agents, each possessing a local cost function, collaboratively minimize the average of the local cost functions over a connected network. To solve the problem, we propose a distributed random reshuffling (D-RR) algorithm that invokes the random reshuffling (RR) update in each agent. We show that D-RR inherits favorable characteristics of RR for both smooth strongly convex and smooth nonconvex objective functions. In particular, for smooth strongly convex objective functions, D-RR achieves $\mathcal{O}(1/T^2)$ rate of convergence (where $T$ counts epoch number) in terms of the squared distance between the iterate and the global minimizer. When the objective function is assumed to be smooth nonconvex, we show that D-RR drives the squared norm of gradient to $0$ at a rate of $\mathcal{O}(1/T^{2/3})$. These convergence results match those of centralized RR (up to constant factors) and outperform the distributed stochastic gradient descent (DSGD) algorithm if we run a relatively large number of epochs. Finally, we conduct a set of numerical experiments to illustrate the efficiency of the proposed D-RR method on both strongly convex and nonconvex distributed optimization problems.

Zhuoqing Song, Lei Shi, Shi Pu et al.

We consider the decentralized optimization problem, where a network of $n$ agents aims to collaboratively minimize the average of their individual smooth and convex objective functions through peer-to-peer communication in a directed graph. To tackle this problem, we propose two accelerated gradient tracking methods, namely APD and APD-SC, for non-strongly convex and strongly convex objective functions, respectively. We show that APD and APD-SC converge at the rates $O\left(\frac{1}{k^2}\right)$ and $O\left(\left(1 - C\sqrt{\fracμ{L}}\right)^k\right)$, respectively, up to constant factors depending only on the mixing matrix. APD and APD-SC are the first decentralized methods over unbalanced directed graphs that achieve the same provable acceleration as centralized methods. Numerical experiments demonstrate the effectiveness of both methods.

Zhuoqing Song, Lei Shi, Shi Pu et al.

In this paper, we propose two communication efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of CPP (B-CPP), and it also achieves linear convergence rate under the same conditions on the objective functions. B-CPP can be applied in an asynchronous broadcast setting and further reduce communication costs compared to CPP. Numerical experiments complement the theoretical analysis and confirm the effectiveness of the proposed methods.

Kun Huang, Shi Pu

We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is available, we study a distributed stochastic gradient algorithm, called exact diffusion with adaptive stepsizes (EDAS) adapted from the Exact Diffusion method and NIDS and perform a non-asymptotic convergence analysis. We not only show that EDAS asymptotically achieves the same network independent convergence rate as centralized stochastic gradient descent (SGD) for minimizing strongly convex and smooth objective functions, but also characterize the transient time needed for the algorithm to approach the asymptotic convergence rate, which behaves as $K_T=\mathcal{O}\left(\frac{n}{1-λ_2}\right)$, where $1-λ_2$ stands for the spectral gap of the mixing matrix. To the best of our knowledge, EDAS achieves the shortest transient time when the average of the $n$ cost functions is strongly convex and each cost function is smooth. Numerical simulations further corroborate and strengthen the obtained theoretical results.

Ran Xin, Shi Pu, Angelia Nedić et al.

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation problems. More recently, the emergence of sophisticated computing and large-scale data science needs have led to a resurgence of activity in this area. In this article, we discuss decentralized first-order gradient methods, which have found tremendous success in control, signal processing, and machine learning problems, where such methods, due to their simplicity, serve as the first method of choice for many complex inference and training tasks. In particular, we provide a general framework of decentralized first-order methods that is applicable to undirected and directed communication networks alike, and show that much of the existing work on optimization and consensus can be related explicitly to this framework. We further extend the discussion to decentralized stochastic first-order methods that rely on stochastic gradients at each node and describe how local variance reduction schemes, previously shown to have promise in the centralized settings, are able to improve the performance of decentralized methods when combined with what is known as gradient tracking. We motivate and demonstrate the effectiveness of the corresponding methods in the context of machine learning and signal processing problems that arise in decentralized environments.

Shi Pu, Alex Olshevsky, Ioannis Ch. Paschalidis

We provide a discussion of several recent results which, in certain scenarios, are able to overcome a barrier in distributed stochastic optimization for machine learning. Our focus is the so-called asymptotic network independence property, which is achieved whenever a distributed method executed over a network of n nodes asymptotically converges to the optimal solution at a comparable rate to a centralized method with the same computational power as the entire network. We explain this property through an example involving the training of ML models and sketch a short mathematical analysis for comparing the performance of distributed stochastic gradient descent (DSGD) with centralized stochastic gradient decent (SGD).

Shi Pu, Alex Olshevsky, Ioannis Ch. Paschalidis

This paper is concerned with minimizing the average of $n$ cost functions over a network in which agents may communicate and exchange information with each other. We consider the setting where only noisy gradient information is available. To solve the problem, we study the distributed stochastic gradient descent (DSGD) method and perform a non-asymptotic convergence analysis. For strongly convex and smooth objective functions, DSGD asymptotically achieves the optimal network independent convergence rate compared to centralized stochastic gradient descent (SGD). Our main contribution is to characterize the transient time needed for DSGD to approach the asymptotic convergence rate, which we show behaves as $K_T=\mathcal{O}\left(\frac{n}{(1-ρ_w)^2}\right)$, where $1-ρ_w$ denotes the spectral gap of the mixing matrix. Moreover, we construct a "hard" optimization problem for which we show the transient time needed for DSGD to approach the asymptotic convergence rate is lower bounded by $Ω\left(\frac{n}{(1-ρ_w)^2} \right)$, implying the sharpness of the obtained result. Numerical experiments demonstrate the tightness of the theoretical results.

Shi Pu, Alfredo Garcia

We study a distributed framework for stochastic optimization which is inspired by models of collective motion found in nature (e.g., swarming) with mild communication requirements. Specifically, we analyze a scheme in which each one of $N > 1$ independent threads, implements in a distributed and unsynchronized fashion, a stochastic gradient-descent algorithm which is perturbed by a swarming potential. Assuming the overhead caused by synchronization is not negligible, we show the swarming-based approach exhibits better performance than a centralized algorithm (based upon the average of $N$ observations) in terms of (real-time) convergence speed. We also derive an error bound that is monotone decreasing in network size and connectivity. We characterize the scheme's finite-time performances for both convex and non-convex objective functions.

Shi Pu, Angelia Nedić

In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size $n$, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.