Guojun Zhang

Alex Bie, Gautam Kamath, Guojun Zhang

We show that the canonical approach for training differentially private GANs -- updating the discriminator with differentially private stochastic gradient descent (DPSGD) -- can yield significantly improved results after modifications to training. Specifically, we propose that existing instantiations of this approach neglect to consider how adding noise only to discriminator updates inhibits discriminator training, disrupting the balance between the generator and discriminator necessary for successful GAN training. We show that a simple fix -- taking more discriminator steps between generator steps -- restores parity between the generator and discriminator and improves results. Additionally, with the goal of restoring parity, we experiment with other modifications -- namely, large batch sizes and adaptive discriminator update frequency -- to improve discriminator training and see further improvements in generation quality. Our results demonstrate that on standard image synthesis benchmarks, DPSGD outperforms all alternative GAN privatization schemes. Code: https://github.com/alexbie98/dpgan-revisit.

Sobhan Hemati, Guojun Zhang, Amir Estiri et al.

Out-of-distribution (OOD) generalization is a critical ability for deep learning models in many real-world scenarios including healthcare and autonomous vehicles. Recently, different techniques have been proposed to improve OOD generalization. Among these methods, gradient-based regularizers have shown promising performance compared with other competitors. Despite this success, our understanding of the role of Hessian and gradient alignment in domain generalization is still limited. To address this shortcoming, we analyze the role of the classifier's head Hessian matrix and gradient in domain generalization using recent OOD theory of transferability. Theoretically, we show that spectral norm between the classifier's head Hessian matrices across domains is an upper bound of the transfer measure, a notion of distance between target and source domains. Furthermore, we analyze all the attributes that get aligned when we encourage similarity between Hessians and gradients. Our analysis explains the success of many regularizers like CORAL, IRM, V-REx, Fish, IGA, and Fishr as they regularize part of the classifier's head Hessian and/or gradient. Finally, we propose two simple yet effective methods to match the classifier's head Hessians and gradients in an efficient way, based on the Hessian Gradient Product (HGP) and Hutchinson's method (Hutchinson), and without directly calculating Hessians. We validate the OOD generalization ability of proposed methods in different scenarios, including transferability, severe correlation shift, label shift and diversity shift. Our results show that Hessian alignment methods achieve promising performance on various OOD benchmarks. The code is available at \url{https://github.com/huawei-noah/Federated-Learning/tree/main/HessianAlignment}.

Mohsin Hasan, Zehao Zhang, Kaiyang Guo et al.

Making predictions robust is an important challenge. A separate challenge in federated learning (FL) is to reduce the number of communication rounds, particularly since doing so reduces performance in heterogeneous data settings. To tackle both issues, we take a Bayesian perspective on the problem of learning a global model. We show how the global predictive posterior can be approximated using client predictive posteriors. This is unlike other works which aggregate the local model space posteriors into the global model space posterior, and are susceptible to high approximation errors due to the posterior's high dimensional multimodal nature. In contrast, our method performs the aggregation on the predictive posteriors, which are typically easier to approximate owing to the low-dimensionality of the output space. We present an algorithm based on this idea, which performs MCMC sampling at each client to obtain an estimate of the local posterior, and then aggregates these in one round to obtain a global ensemble model. Through empirical evaluation on several classification and regression tasks, we show that despite using one round of communication, the method is competitive with other FL techniques, and outperforms them on heterogeneous settings. The code is publicly available at https://github.com/hasanmohsin/FedPredSpace_1Round.

Guojun Zhang, Mahdi Beitollahi, Alex Bie et al.

Layer normalization (LN) is a widely adopted deep learning technique especially in the era of foundation models. Recently, LN has been shown to be surprisingly effective in federated learning (FL) with non-i.i.d. data. However, exactly why and how it works remains mysterious. In this work, we reveal the profound connection between layer normalization and the label shift problem in federated learning. To understand layer normalization better in FL, we identify the key contributing mechanism of normalization methods in FL, called feature normalization (FN), which applies normalization to the latent feature representation before the classifier head. Although LN and FN do not improve expressive power, they control feature collapse and local overfitting to heavily skewed datasets, and thus accelerates global training. Empirically, we show that normalization leads to drastic improvements on standard benchmarks under extreme label shift. Moreover, we conduct extensive ablation studies to understand the critical factors of layer normalization in FL. Our results verify that FN is an essential ingredient inside LN to significantly improve the convergence of FL while remaining robust to learning rate choices, especially under extreme label shift where each client has access to few classes. Our code is available at \url{https://github.com/huawei-noah/Federated-Learning/tree/main/Layer_Normalization}.

Ehsan Imani, Guojun Zhang, Runjia Li et al. · oxford

Recent work has highlighted the label alignment property (LAP) in supervised learning, where the vector of all labels in the dataset is mostly in the span of the top few singular vectors of the data matrix. Drawing inspiration from this observation, we propose a regularization method for unsupervised domain adaptation that encourages alignment between the predictions in the target domain and its top singular vectors. Unlike conventional domain adaptation approaches that focus on regularizing representations, we instead regularize the classifier to align with the unsupervised target data, guided by the LAP in both the source and target domains. Theoretical analysis demonstrates that, under certain assumptions, our solution resides within the span of the top right singular vectors of the target domain data and aligns with the optimal solution. By removing the reliance on the commonly used optimal joint risk assumption found in classic domain adaptation theory, we showcase the effectiveness of our method on addressing problems where traditional domain adaptation methods often fall short due to high joint error. Additionally, we report improved performance over domain adaptation baselines in well-known tasks such as MNIST-USPS domain adaptation and cross-lingual sentiment analysis.

Artur Back de Luca, Guojun Zhang, Xi Chen et al.

Federated Learning (FL) is a prominent framework that enables training a centralized model while securing user privacy by fusing local, decentralized models. In this setting, one major obstacle is data heterogeneity, i.e., each client having non-identically and independently distributed (non-IID) data. This is analogous to the context of Domain Generalization (DG), where each client can be treated as a different domain. However, while many approaches in DG tackle data heterogeneity from the algorithmic perspective, recent evidence suggests that data augmentation can induce equal or greater performance. Motivated by this connection, we present federated versions of popular DG algorithms, and show that by applying appropriate data augmentation, we can mitigate data heterogeneity in the federated setting, and obtain higher accuracy on unseen clients. Equipped with data augmentation, we can achieve state-of-the-art performance using even the most basic Federated Averaging algorithm, with much sparser communication.

Dihong Jiang, Guojun Zhang, Mahdi Karami et al.

Modern machine learning systems achieve great success when trained on large datasets. However, these datasets usually contain sensitive information (e.g. medical records, face images), leading to serious privacy concerns. Differentially private generative models (DPGMs) emerge as a solution to circumvent such privacy concerns by generating privatized sensitive data. Similar to other differentially private (DP) learners, the major challenge for DPGM is also how to achieve a subtle balance between utility and privacy. We propose DP$^2$-VAE, a novel training mechanism for variational autoencoders (VAE) with provable DP guarantees and improved utility via \emph{pre-training on private data}. Under the same DP constraints, DP$^2$-VAE minimizes the perturbation noise during training, and hence improves utility. DP$^2$-VAE is very flexible and easily amenable to many other VAE variants. Theoretically, we study the effect of pretraining on private data. Empirically, we conduct extensive experiments on image datasets to illustrate our superiority over baselines under various privacy budgets and evaluation metrics.

Haolin Yu, Kaiyang Guo, Mahdi Karami et al.

In typical scenarios where the Federated Learning (FL) framework applies, it is common for clients to have insufficient training data to produce an accurate model. Thus, models that provide not only point estimations, but also some notion of confidence are beneficial. Gaussian Process (GP) is a powerful Bayesian model that comes with naturally well-calibrated variance estimations. However, it is challenging to learn a stand-alone global GP since merging local kernels leads to privacy leakage. To preserve privacy, previous works that consider federated GPs avoid learning a global model by focusing on the personalized setting or learning an ensemble of local models. We present Federated Bayesian Neural Regression (FedBNR), an algorithm that learns a scalable stand-alone global federated GP that respects clients' privacy. We incorporate deep kernel learning and random features for scalability by defining a unifying random kernel. We show this random kernel can recover any stationary kernel and many non-stationary kernels. We then derive a principled approach of learning a global predictive model as if all client data is centralized. We also learn global kernels with knowledge distillation methods for non-identically and independently distributed (non-i.i.d.) clients. Experiments are conducted on real-world regression datasets and show statistically significant improvements compared to other federated GP models.

Sijia Cui, Pengyu Cheng, Jiajun Song et al.

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capacity of Large Language Models (LLMs). However, RLVR solely relies on final answers as outcome rewards, neglecting the correctness of intermediate reasoning steps. Training on these process-wrong but outcome-correct rollouts can lead to hallucination and answer-copying, severely undermining the model's generalization and robustness. To address this, we incorporate a Contrastive Learning mechanism into the Policy Optimization (CLIPO) to generalize the RLVR process. By optimizing a contrastive loss over successful rollouts, CLIPO steers the LLM to capture the invariant structure shared across correct reasoning paths. This provides a more robust cross-trajectory regularization than the original single-path supervision in RLVR, effectively mitigating step-level reasoning inconsistencies and suppressing hallucinatory artifacts. In experiments, CLIPO consistently improves multiple RLVR baselines across diverse reasoning benchmarks, demonstrating uniform improvements in generalization and robustness for policy optimization of LLMs. Our code and training recipes are available at https://github.com/Qwen-Applications/CLIPO.

Vahid Partovi Nia, Guojun Zhang, Ivan Kobyzev et al.

Deep models are dominating the artificial intelligence (AI) industry since the ImageNet challenge in 2012. The size of deep models is increasing ever since, which brings new challenges to this field with applications in cell phones, personal computers, autonomous cars, and wireless base stations. Here we list a set of problems, ranging from training, inference, generalization bound, and optimization with some formalism to communicate these challenges with mathematicians, statisticians, and theoretical computer scientists. This is a subjective view of the research questions in deep learning that benefits the tech industry in long run.

Yifei He, Shiji Zhou, Guojun Zhang et al.

Multi-task learning (MTL) considers learning a joint model for multiple tasks by optimizing a convex combination of all task losses. To solve the optimization problem, existing methods use an adaptive weight updating scheme, where task weights are dynamically adjusted based on their respective losses to prioritize difficult tasks. However, these algorithms face a great challenge whenever label noise is present, in which case excessive weights tend to be assigned to noisy tasks that have relatively large Bayes optimal errors, thereby overshadowing other tasks and causing performance to drop across the board. To overcome this limitation, we propose Multi-Task Learning with Excess Risks (ExcessMTL), an excess risk-based task balancing method that updates the task weights by their distances to convergence instead. Intuitively, ExcessMTL assigns higher weights to worse-trained tasks that are further from convergence. To estimate the excess risks, we develop an efficient and accurate method with Taylor approximation. Theoretically, we show that our proposed algorithm achieves convergence guarantees and Pareto stationarity. Empirically, we evaluate our algorithm on various MTL benchmarks and demonstrate its superior performance over existing methods in the presence of label noise. Our code is available at https://github.com/yifei-he/ExcessMTL.

Mohsin Hasan, Guojun Zhang, Kaiyang Guo et al.

Federated Learning (FL) involves training a model over a dataset distributed among clients, with the constraint that each client's dataset is localized and possibly heterogeneous. In FL, small and noisy datasets are common, highlighting the need for well-calibrated models that represent the uncertainty of predictions. The closest FL techniques to achieving such goals are the Bayesian FL methods which collect parameter samples from local posteriors, and aggregate them to approximate the global posterior. To improve scalability for larger models, one common Bayesian approach is to approximate the global predictive posterior by multiplying local predictive posteriors. In this work, we demonstrate that this method gives systematically overconfident predictions, and we remedy this by proposing $β$-Predictive Bayes, a Bayesian FL algorithm that interpolates between a mixture and product of the predictive posteriors, using a tunable parameter $β$. This parameter is tuned to improve the global ensemble's calibration, before it is distilled to a single model. Our method is evaluated on a variety of regression and classification datasets to demonstrate its superiority in calibration to other baselines, even as data heterogeneity increases. Code available at https://github.com/hasanmohsin/betaPredBayesFL

Ahmad Rashid, Serena Hacker, Guojun Zhang et al.

Discriminatively trained, deterministic neural networks are the de facto choice for classification problems. However, even though they achieve state-of-the-art results on in-domain test sets, they tend to be overconfident on out-of-distribution (OOD) data. For instance, ReLU networks - a popular class of neural network architectures - have been shown to almost always yield high confidence predictions when the test data are far away from the training set, even when they are trained with OOD data. We overcome this problem by adding a term to the output of the neural network that corresponds to the logit of an extra class, that we design to dominate the logits of the original classes as we move away from the training data.This technique provably prevents arbitrarily high confidence on far-away test data while maintaining a simple discriminative point-estimate training. Evaluation on various benchmarks demonstrates strong performance against competitive baselines on both far-away and realistic OOD data.

Yihan Wang, Yiwei Lu, Guojun Zhang et al.

Machine unlearning offers effective solutions for revoking the influence of specific training data on pre-trained model parameters. While existing approaches address unlearning for classification and generative models, they overlook an important category of machine learning models: contrastive learning (CL) methods. This paper addresses this gap by introducing the Machine Unlearning for Contrastive Learning (MUC) framework and adapting existing methods. We identify limitations in current approaches, noting that several methods perform inadequately as unlearners and that existing evaluation tools insufficiently validate unlearning effects in contrastive learning. To address these issues, we propose Alignment Calibration (AC), a novel method that explicitly considers contrastive learning properties and optimizes towards new auditing metrics for easy verification of unlearning. Through empirical comparisons with baseline methods on SimCLR, MoCo, and CLIP, we demonstrate that AC: (1) achieves state-of-the-art performance, approximating exact unlearning (retraining); (2) enables data owners to clearly visualize unlearning effects through black-box evaluation. The code is available at https://github.com/EhanW/Alignment-Calibration.

Guojun Zhang, Saber Malekmohammadi, Xi Chen et al.

With the increasingly broad deployment of federated learning (FL) systems in the real world, it is critical but challenging to ensure fairness in FL, i.e. reasonably satisfactory performances for each of the numerous diverse clients. In this work, we introduce and study a new fairness notion in FL, called proportional fairness (PF), which is based on the relative change of each client's performance. From its connection with the bargaining games, we propose PropFair, a novel and easy-to-implement algorithm for finding proportionally fair solutions in FL and study its convergence properties. Through extensive experiments on vision and language datasets, we demonstrate that PropFair can approximately find PF solutions, and it achieves a good balance between the average performances of all clients and of the worst 10% clients. Our code is available at \url{https://github.com/huawei-noah/Federated-Learning/tree/main/FairFL}.

Guojun Zhang, Kaiwen Wu, Pascal Poupart et al.

Differential games, in particular two-player sequential zero-sum games (a.k.a. minimax optimization), have been an important modeling tool in applied science and received renewed interest in machine learning due to many recent applications, such as adversarial training, generative models and reinforcement learning. However, existing theory mostly focuses on convex-concave functions with few exceptions. In this work, we propose two novel Newton-type algorithms for nonconvex-nonconcave minimax optimization. We prove their local convergence at strict local minimax points, which are surrogates of global solutions. We argue that our Newton-type algorithms nicely complement existing ones in that (a) they converge faster to strict local minimax points; (b) they are much more effective when the problem is ill-conditioned; (c) their computational complexity remains similar. We verify the effectiveness of our Newton-type algorithms through experiments on training GANs which are intrinsically nonconvex and ill-conditioned. Our code is available at https://github.com/watml/min-max-2nd-order.

MiniMax, Aonian Li, Bangwei Gong et al.

We introduce MiniMax-01 series, including MiniMax-Text-01 and MiniMax-VL-01, which are comparable to top-tier models while offering superior capabilities in processing longer contexts. The core lies in lightning attention and its efficient scaling. To maximize computational capacity, we integrate it with Mixture of Experts (MoE), creating a model with 32 experts and 456 billion total parameters, of which 45.9 billion are activated for each token. We develop an optimized parallel strategy and highly efficient computation-communication overlap techniques for MoE and lightning attention. This approach enables us to conduct efficient training and inference on models with hundreds of billions of parameters across contexts spanning millions of tokens. The context window of MiniMax-Text-01 can reach up to 1 million tokens during training and extrapolate to 4 million tokens during inference at an affordable cost. Our vision-language model, MiniMax-VL-01 is built through continued training with 512 billion vision-language tokens. Experiments on both standard and in-house benchmarks show that our models match the performance of state-of-the-art models like GPT-4o and Claude-3.5-Sonnet while offering 20-32 times longer context window. We publicly release MiniMax-01 at https://github.com/MiniMax-AI.

Yiwei Lu, Guojun Zhang, Sun Sun et al.

In self-supervised contrastive learning, a widely-adopted objective function is InfoNCE, which uses the heuristic cosine similarity for the representation comparison, and is closely related to maximizing the Kullback-Leibler (KL)-based mutual information. In this paper, we aim at answering two intriguing questions: (1) Can we go beyond the KL-based objective? (2) Besides the popular cosine similarity, can we design a better similarity function? We provide answers to both questions by generalizing the KL-based mutual information to the $f$-Mutual Information in Contrastive Learning ($f$-MICL) using the $f$-divergences. To answer the first question, we provide a wide range of $f$-MICL objectives which share the nice properties of InfoNCE (e.g., alignment and uniformity), and meanwhile result in similar or even superior performance. For the second question, assuming that the joint feature distribution is proportional to the Gaussian kernel, we derive an $f$-Gaussian similarity with better interpretability and empirical performance. Finally, we identify close relationships between the $f$-MICL objective and several popular InfoNCE-based objectives. Using benchmark tasks from both vision and natural language, we empirically evaluate $f$-MICL with different $f$-divergences on various architectures (SimCLR, MoCo, and MoCo v3) and datasets. We observe that $f$-MICL generally outperforms the benchmarks and the best-performing $f$-divergence is task and dataset dependent.

Mahdi Beitollahi, Alex Bie, Sobhan Hemati et al.

In one-shot federated learning (FL), clients collaboratively train a global model in a single round of communication. Existing approaches for one-shot FL enhance communication efficiency at the expense of diminished accuracy. This paper introduces FedPFT (Federated Learning with Parametric Feature Transfer), a methodology that harnesses the transferability of foundation models to enhance both accuracy and communication efficiency in one-shot FL. The approach involves transferring per-client parametric models (specifically, Gaussian mixtures) of features extracted from foundation models. Subsequently, each parametric model is employed to generate synthetic features for training a classifier head. Experimental results on eight datasets demonstrate that FedPFT enhances the communication-accuracy frontier in both centralized and decentralized FL scenarios, as well as across diverse data-heterogeneity settings such as covariate shift and task shift, with improvements of up to 20.6%. Additionally, FedPFT adheres to the data minimization principle of FL, as clients do not send real features. We demonstrate that sending real features is vulnerable to potent reconstruction attacks. Moreover, we show that FedPFT is amenable to formal privacy guarantees via differential privacy, demonstrating favourable privacy-accuracy tradeoffs.

Nader Asadi, Mahdi Beitollahi, Yasser Khalil et al.

Parameter-efficient fine-tuning stands as the standard for efficiently fine-tuning large language and vision models on downstream tasks. Specifically, the efficiency of low-rank adaptation has facilitated the creation and sharing of hundreds of custom LoRA modules, each trained on distinct data from various downstream tasks. In this paper, we explore the composability of LoRA modules, examining if combining these pre-trained modules enhances generalization to unseen downstream tasks. Our investigation involves evaluating two approaches: (a) uniform composition, involving averaging upstream LoRA modules with equal weights, and (b) learned composition, where we learn the weights for each upstream module and perform weighted averaging. Our experimental results on both vision and language models reveal that in few-shot settings, where only a limited number of samples are available for the downstream task, both uniform and learned composition methods result in better transfer accuracy; outperforming full fine-tuning and training a LoRA from scratch. Moreover, in full-shot settings, learned composition performs comparably to regular LoRA training with significantly fewer number of trainable parameters. Our research unveils the potential of uniform composition for enhancing transferability in low-shot settings, without introducing additional learnable parameters.

Sobhan Hemati, Mahdi Beitollahi, Amir Hossein Estiri et al.

Despite the huge effort in developing novel regularizers for Domain Generalization (DG), adding simple data augmentation to the vanilla ERM which is a practical implementation of the Vicinal Risk Minimization principle (VRM) \citep{chapelle2000vicinal} outperforms or stays competitive with many of the proposed regularizers. The VRM reduces the estimation error in ERM by replacing the point-wise kernel estimates with a more precise estimation of true data distribution that reduces the gap between data points \textbf{within each domain}. However, in the DG setting, the estimation error of true data distribution by ERM is mainly caused by the distribution shift \textbf{between domains} which cannot be fully addressed by simple data augmentation techniques within each domain. Inspired by this limitation of VRM, we propose a novel data augmentation named Cross Domain Generative Augmentation (CDGA) that replaces the pointwise kernel estimates in ERM with new density estimates in the \textbf{vicinity of domain pairs} so that the gap between domains is further reduced. To this end, CDGA, which is built upon latent diffusion models (LDM), generates synthetic images to fill the gap between all domains and as a result, reduces the non-iidness. We show that CDGA outperforms SOTA DG methods under the Domainbed benchmark. To explain the effectiveness of CDGA, we generate more than 5 Million synthetic images and perform extensive ablation studies including data scaling laws, distribution visualization, domain shift quantification, adversarial robustness, and loss landscape analysis.

Haolin Yu, Guojun Zhang, Pascal Poupart

Federated representation learning (FRL) aims to learn personalized federated models with effective feature extraction from local data. FRL algorithms that share the majority of the model parameters face significant challenges with huge communication overhead. This overhead stems from the millions of neural network parameters and slow aggregation progress of the averaging heuristic. To reduce the overhead, we propose to share sufficient data summaries instead of raw model parameters. The data summaries encode minimal sufficient statistics of an exponential family, and Bayesian inference is utilized for global aggregation. It helps to reduce message sizes and communication frequency. To further ensure formal privacy guarantee, we extend it with differential privacy framework. Empirical results demonstrate high learning accuracy with low communication overhead of our method.

Yasser H. Khalil, Amir H. Estiri, Mahdi Beitollahi et al.

In the realm of real-world devices, centralized servers in Federated Learning (FL) present challenges including communication bottlenecks and susceptibility to a single point of failure. Additionally, contemporary devices inherently exhibit model and data heterogeneity. Existing work lacks a Decentralized FL (DFL) framework capable of accommodating such heterogeneity without imposing architectural restrictions or assuming the availability of public data. To address these issues, we propose a Decentralized Federated Mutual Learning (DFML) framework that is serverless, supports nonrestrictive heterogeneous models, and avoids reliance on public data. DFML effectively handles model and data heterogeneity through mutual learning, which distills knowledge between clients, and cyclically varying the amount of supervision and distillation signals. Extensive experimental results demonstrate consistent effectiveness of DFML in both convergence speed and global accuracy, outperforming prevalent baselines under various conditions. For example, with the CIFAR-100 dataset and 50 clients, DFML achieves a substantial increase of +17.20% and +19.95% in global accuracy under Independent and Identically Distributed (IID) and non-IID data shifts, respectively.

Yuen Chen, Haozhe Si, Guojun Zhang et al.

Domain generalization (DG) seeks to develop models that generalize well to unseen target domains, addressing the prevalent issue of distribution shifts in real-world applications. One line of research in DG focuses on aligning domain-level gradients and Hessians to enhance generalization. However, existing methods are computationally inefficient and the underlying principles of these approaches are not well understood. In this paper, we develop the theory of moment alignment for DG. Grounded in \textit{transfer measure}, a principled framework for quantifying generalizability between two domains, we first extend the definition of transfer measure to domain generalization that includes multiple source domains and establish a target error bound. Then, we prove that aligning derivatives across domains improves transfer measure both when the feature extractor induces an invariant optimal predictor across domains and when it does not. Notably, moment alignment provides a unifying understanding of Invariant Risk Minimization, gradient matching, and Hessian matching, three previously disconnected approaches to DG. We further connect feature moments and derivatives of the classifier head, and establish the duality between feature learning and classifier fitting. Building upon our theory, we introduce \textbf{C}losed-Form \textbf{M}oment \textbf{A}lignment (CMA), a novel DG algorithm that aligns domain-level gradients and Hessians in closed-form. Our method overcomes the computational inefficiencies of existing gradient and Hessian-based techniques by eliminating the need for repeated backpropagation or sampling-based Hessian estimation. We validate the efficacy of our approach through two sets of experiments: linear probing and full fine-tuning. CMA demonstrates superior performance in both settings compared to Empirical Risk Minimization and state-of-the-art algorithms.

David Acuna, Marc T Law, Guojun Zhang et al.

The dominant line of work in domain adaptation has focused on learning invariant representations using domain-adversarial training. In this paper, we interpret this approach from a game theoretical perspective. Defining optimal solutions in domain-adversarial training as a local Nash equilibrium, we show that gradient descent in domain-adversarial training can violate the asymptotic convergence guarantees of the optimizer, oftentimes hindering the transfer performance. Our analysis leads us to replace gradient descent with high-order ODE solvers (i.e., Runge-Kutta), for which we derive asymptotic convergence guarantees. This family of optimizers is significantly more stable and allows more aggressive learning rates, leading to high performance gains when used as a drop-in replacement over standard optimizers. Our experiments show that in conjunction with state-of-the-art domain-adversarial methods, we achieve up to 3.5% improvement with less than of half training iterations. Our optimizers are easy to implement, free of additional parameters, and can be plugged into any domain-adversarial framework.

David Acuna, Guojun Zhang, Marc T. Law et al.

Unsupervised domain adaptation is used in many machine learning applications where, during training, a model has access to unlabeled data in the target domain, and a related labeled dataset. In this paper, we introduce a novel and general domain-adversarial framework. Specifically, we derive a novel generalization bound for domain adaptation that exploits a new measure of discrepancy between distributions based on a variational characterization of f-divergences. It recovers the theoretical results from Ben-David et al. (2010a) as a special case and supports divergences used in practice. Based on this bound, we derive a new algorithmic framework that introduces a key correction in the original adversarial training method of Ganin et al. (2016). We show that many regularizers and ad-hoc objectives introduced over the last years in this framework are then not required to achieve performance comparable to (if not better than) state-of-the-art domain-adversarial methods. Experimental analysis conducted on real-world natural language and computer vision datasets show that our framework outperforms existing baselines, and obtains the best results for f-divergences that were not considered previously in domain-adversarial learning.

Guojun Zhang, Han Zhao, Yaoliang Yu et al.

Out-of-distribution generalization is one of the key challenges when transferring a model from the lab to the real world. Existing efforts mostly focus on building invariant features among source and target domains. Based on invariant features, a high-performing classifier on source domains could hopefully behave equally well on a target domain. In other words, the invariant features are \emph{transferable}. However, in practice, there are no perfectly transferable features, and some algorithms seem to learn "more transferable" features than others. How can we understand and quantify such \emph{transferability}? In this paper, we formally define transferability that one can quantify and compute in domain generalization. We point out the difference and connection with common discrepancy measures between domains, such as total variation and Wasserstein distance. We then prove that our transferability can be estimated with enough samples and give a new upper bound for the target error based on our transferability. Empirically, we evaluate the transferability of the feature embeddings learned by existing algorithms for domain generalization. Surprisingly, we find that many algorithms are not quite learning transferable features, although few could still survive. In light of this, we propose a new algorithm for learning transferable features and test it over various benchmark datasets, including RotatedMNIST, PACS, Office-Home and WILDS-FMoW. Experimental results show that the proposed algorithm achieves consistent improvement over many state-of-the-art algorithms, corroborating our theoretical findings.

Zeou Hu, Kiarash Shaloudegi, Guojun Zhang et al.

Federated learning has emerged as a promising, massively distributed way to train a joint deep model over large amounts of edge devices while keeping private user data strictly on device. In this work, motivated from ensuring fairness among users and robustness against malicious adversaries, we formulate federated learning as multi-objective optimization and propose a new algorithm FedMGDA+ that is guaranteed to converge to Pareto stationary solutions. FedMGDA+ is simple to implement, has fewer hyperparameters to tune, and refrains from sacrificing the performance of any participating user. We establish the convergence properties of FedMGDA+ and point out its connections to existing approaches. Extensive experiments on a variety of datasets confirm that FedMGDA+ compares favorably against state-of-the-art.

Guojun Zhang, Pascal Poupart, Yaoliang Yu

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an intriguing research challenge how local optimal points are defined and which algorithm can converge to such points. An interesting concept is known as the local minimax point, which strongly correlates with the widely-known gradient descent ascent algorithm. This paper aims to provide a comprehensive analysis of local minimax points, such as their relation with other solution concepts and their optimality conditions. We find that local saddle points can be regarded as a special type of local minimax points, called uniformly local minimax points, under mild continuity assumptions. In (non-convex) quadratic games, we show that local minimax points are (in some sense) equivalent to global minimax points. Finally, we study the stability of gradient algorithms near local minimax points. Although gradient algorithms can converge to local/global minimax points in the non-degenerate case, they would often fail in general cases. This implies the necessity of either novel algorithms or concepts beyond saddle points and minimax points in non-convex smooth games.

Guojun Zhang, Yaoliang Yu

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.

Guojun Zhang, Pascal Poupart, George Trimponias

The expectation-maximization (EM) algorithm has been widely used in minimizing the negative log likelihood (also known as cross entropy) of mixture models. However, little is understood about the goodness of the fixed points it converges to. In this paper, we study the regions where one component is missing in two-component mixture models, which we call one-cluster regions. We analyze the propensity of such regions to trap EM and gradient descent (GD) for mixtures of two Gaussians and mixtures of two Bernoullis. In the case of Gaussian mixtures, EM escapes one-cluster regions exponentially fast, while GD escapes them linearly fast. In the case of mixtures of Bernoullis, we find that there exist one-cluster regions that are stable for GD and therefore trap GD, but those regions are unstable for EM, allowing EM to escape. Those regions are local minima that appear universally in experiments and can be arbitrarily bad. This work implies that EM is less likely than GD to converge to certain bad local optima in mixture models.