Zhaoxian Wu

Xingrong Dong, Zhaoxian Wu, Qing Ling et al.

This paper studies distributed online learning under Byzantine attacks. The performance of an online learning algorithm is often characterized by (adversarial) regret, which evaluates the quality of one-step-ahead decision-making when an environment provides adversarial losses, and a sublinear bound is preferred. But we prove that, even with a class of state-of-the-art robust aggregation rules, in an adversarial environment and in the presence of Byzantine participants, distributed online gradient descent can only achieve a linear adversarial regret bound, which is tight. This is the inevitable consequence of Byzantine attacks, even though we can control the constant of the linear adversarial regret to a reasonable level. Interestingly, when the environment is not fully adversarial so that the losses of the honest participants are i.i.d. (independent and identically distributed), we show that sublinear stochastic regret, in contrast to the aforementioned adversarial regret, is possible. We develop a Byzantine-robust distributed online momentum algorithm to attain such a sublinear stochastic regret bound. Extensive numerical experiments corroborate our theoretical analysis.

Quan Xiao, Jindan Li, Zhaoxian Wu et al.

Analog in-memory computing (AIMC) performs computation directly within resistive crossbar arrays, offering an energy-efficient platform to scale large vision and language models. However, non-ideal analog device properties make the training on AIMC devices challenging. In particular, its update asymmetry can induce a systematic drift of weight updates towards a device-specific symmetric point (SP), which typically does not align with the optimum of the training objective. To mitigate this bias, most existing works assume the SP is known and pre-calibrate it to zero before training by setting the reference point as the SP. Nevertheless, calibrating AIMC devices requires costly pulse updates, and residual calibration error can directly degrade training accuracy. In this work, we present the first theoretical characterization of the pulse complexity of SP calibration and the resulting estimation error. We further propose a dynamic SP estimation method that tracks the SP during model training, and establishes its convergence guarantees. In addition, we develop an enhanced variant based on chopping and filtering techniques from digital signal processing. Numerical experiments demonstrate both the efficiency and effectiveness of the proposed method.

Zhaoxian Wu, Quan Xiao, Tayfun Gokmen et al.

As the economic and environmental costs of training and deploying large vision or language models increase dramatically, analog in-memory computing (AIMC) emerges as a promising energy-efficient solution. However, the training perspective, especially its training dynamic, is underexplored. In AIMC hardware, the trainable weights are represented by the conductance of resistive elements and updated using consecutive electrical pulses. While the conductance changes by a constant in response to each pulse, in reality, the change is scaled by asymmetric and non-linear response functions, leading to a non-ideal training dynamic. This paper provides a theoretical foundation for gradient-based training on AIMC hardware with non-ideal response functions. We demonstrate that asymmetric response functions negatively impact Analog SGD by imposing an implicit penalty on the objective. To overcome the issue, we propose Residual Learning algorithm, which provably converges exactly to a critical point by solving a bilevel optimization problem. We demonstrate that the proposed method can be extended to address other hardware imperfections, such as limited response granularity. As we know, it is the first paper to investigate the impact of a class of generic non-ideal response functions. The conclusion is supported by simulations validating our theoretical insights.

Zhaoxian Wu, Quan Xiao, Tayfun Gokmen et al.

Aiming to accelerate the training of large deep neural models (DNN) in an energy-efficient way, an analog in-memory computing (AIMC) accelerator emerges as a solution with immense potential. In AIMC accelerators, trainable weights are kept in memory without the need to move from memory to processors during the training, reducing a bunch of overhead. However, although the in-memory feature enables efficient computation, it also constrains the use of data parallelism since copying weights from one AIMC to another is expensive. To enable parallel training using AIMC, we propose synchronous and asynchronous pipeline parallelism for AIMC accelerators inspired by the pipeline in digital domains. This paper provides a theoretical convergence guarantee for both synchronous and asynchronous pipelines in terms of both sampling and clock cycle complexity, which is non-trivial since the physical characteristic of AIMC accelerators leads to analog updates that suffer from asymmetric bias. The simulations of training DNN on real datasets verify the efficiency of pipeline training.

Yue Huang, Zhaoxian Wu, Shiqian Ma et al.

Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings {of} MSSA are limited: the multi-timescale analysis implies a slow convergence rate, whereas the single-timescale analysis relies on a stringent fixed point smoothness assumption. This paper establishes tighter single-timescale analysis for MSSA, without assuming smoothness of the fixed points. Our theoretical findings reveal that, when all involved operators are strongly monotone, MSSA converges at a rate of $\tilde{\mathcal{O}}(K^{-1})$, where $K$ denotes the total number of iterations. In addition, when all involved operators are strongly monotone except for the main one, MSSA converges at a rate of $\mathcal{O}(K^{-\frac{1}{2}})$. These theoretical findings align with those established for single-sequence SA. Applying these theoretical findings to bilevel optimization and communication-efficient distributed learning offers relaxed assumptions and/or simpler algorithms with performance guarantees, as validated by numerical experiments.

Jindan Li, Zhaoxian Wu, Gaowen Liu et al.

Analog in-memory computing (AIMC) accelerators enable efficient deep neural network computation directly within memory using resistive crossbar arrays, where model parameters are represented by the conductance states of memristive devices. However, effective in-memory training typically requires at least 8-bit conductance states to match digital baselines. Realizing such fine-grained states is costly and often requires complex noise mitigation techniques that increase circuit complexity and energy consumption. In practice, many promising memristive devices such as ReRAM offer only about 4-bit resolution due to fabrication constraints, and this limited update precision substantially degrades training accuracy. To enable on-chip training with these limited-state devices, this paper proposes a \emph{residual learning} framework that sequentially learns on multiple crossbar tiles to compensate the residual errors from low-precision weight updates. Our theoretical analysis shows that the optimality gap shrinks with the number of tiles and achieves a linear convergence rate. Experiments on standard image classification benchmarks demonstrate that our method consistently outperforms state-of-the-art in-memory analog training strategies under limited-state settings, while incurring only moderate hardware overhead as confirmed by our cost analysis.

Ying Cao, Zhaoxian Wu, Kun Yuan et al.

This paper proposes a theoretical framework to evaluate and compare the performance of stochastic gradient algorithms for distributed learning in relation to their behavior around local minima in nonconvex environments. Previous works have noticed that convergence toward flat local minima tend to enhance the generalization ability of learning algorithms. This work discovers three interesting results. First, it shows that decentralized learning strategies are able to escape faster away from local minima and favor convergence toward flatter minima relative to the centralized solution. Second, in decentralized methods, the consensus strategy has a worse excess-risk performance than diffusion, giving it a better chance of escaping from local minima and favoring flatter minima. Third, and importantly, the ultimate classification accuracy is not solely dependent on the flatness of the local minimum but also on how well a learning algorithm can approach that minimum. In other words, the classification accuracy is a function of both flatness and optimization performance. In this regard, since diffusion has a lower excess-risk than consensus, when both algorithms are trained starting from random initial points, diffusion enhances the classification accuracy. The paper examines the interplay between the two measures of flatness and optimization error closely. One important conclusion is that decentralized strategies deliver in general enhanced classification accuracy because they strike a more favorable balance between flatness and optimization performance compared to the centralized solution.

Zhaoxian Wu, Tayfun Gokmen, Malte J. Rasch et al.

Given the high economic and environmental costs of using large vision or language models, analog in-memory accelerators present a promising solution for energy-efficient AI. While inference on analog accelerators has been studied recently, the training perspective is underexplored. Recent studies have shown that the "workhorse" of digital AI training - stochastic gradient descent (SGD) algorithm converges inexactly when applied to model training on non-ideal devices. This paper puts forth a theoretical foundation for gradient-based training on analog devices. We begin by characterizing the non-convergent issue of SGD, which is caused by the asymmetric updates on the analog devices. We then provide a lower bound of the asymptotic error to show that there is a fundamental performance limit of SGD-based analog training rather than an artifact of our analysis. To address this issue, we study a heuristic analog algorithm called Tiki-Taka that has recently exhibited superior empirical performance compared to SGD and rigorously show its ability to exactly converge to a critical point and hence eliminates the asymptotic error. The simulations verify the correctness of the analyses.

Jie Peng, Zhaoxian Wu, Qing Ling et al.

We consider the federated learning problem where data on workers are not independent and identically distributed (i.i.d.). During the learning process, an unknown number of Byzantine workers may send malicious messages to the central node, leading to remarkable learning error. Most of the Byzantine-robust methods address this issue by using robust aggregation rules to aggregate the received messages, but rely on the assumption that all the regular workers have i.i.d. data, which is not the case in many federated learning applications. In light of the significance of reducing stochastic gradient noise for mitigating the effect of Byzantine attacks, we use a resampling strategy to reduce the impact of both inner variation (that describes the sample heterogeneity on every regular worker) and outer variation (that describes the sample heterogeneity among the regular workers), along with a stochastic average gradient algorithm to gradually eliminate the inner variation. The variance-reduced messages are then aggregated with a robust geometric median operator. We prove that the proposed method reaches a neighborhood of the optimal solution at a linear convergence rate and the learning error is determined by the number of Byzantine workers. Numerical experiments corroborate the theoretical results and show that the proposed method outperforms the state-of-the-arts in the non-i.i.d. setting.

Zhaoxian Wu, Qing Ling, Tianyi Chen et al.

This paper deals with distributed finite-sum optimization for learning over networks in the presence of malicious Byzantine attacks. To cope with such attacks, most resilient approaches so far combine stochastic gradient descent (SGD) with different robust aggregation rules. However, the sizeable SGD-induced stochastic gradient noise makes it challenging to distinguish malicious messages sent by the Byzantine attackers from noisy stochastic gradients sent by the 'honest' workers. This motivates us to reduce the variance of stochastic gradients as a means of robustifying SGD in the presence of Byzantine attacks. To this end, the present work puts forth a Byzantine attack resilient distributed (Byrd-) SAGA approach for learning tasks involving finite-sum optimization over networks. Rather than the mean employed by distributed SAGA, the novel Byrd- SAGA relies on the geometric median to aggregate the corrected stochastic gradients sent by the workers. When less than half of the workers are Byzantine attackers, the robustness of geometric median to outliers enables Byrd-SAGA to attain provably linear convergence to a neighborhood of the optimal solution, with the asymptotic learning error determined by the number of Byzantine workers. Numerical tests corroborate the robustness to various Byzantine attacks, as well as the merits of Byrd- SAGA over Byzantine attack resilient distributed SGD.

Weiyu Li, Tianyi Chen, Liping Li et al.

This paper 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 mini-batch 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.