Linjun Zhang

Huaxiu Yao, Yiping Wang, Linjun Zhang et al.

Improving the generalization of deep networks is an important open challenge, particularly in domains without plentiful data. The mixup algorithm improves generalization by linearly interpolating a pair of examples and their corresponding labels. These interpolated examples augment the original training set. Mixup has shown promising results in various classification tasks, but systematic analysis of mixup in regression remains underexplored. Using mixup directly on regression labels can result in arbitrarily incorrect labels. In this paper, we propose a simple yet powerful algorithm, C-Mixup, to improve generalization on regression tasks. In contrast with vanilla mixup, which picks training examples for mixing with uniform probability, C-Mixup adjusts the sampling probability based on the similarity of the labels. Our theoretical analysis confirms that C-Mixup with label similarity obtains a smaller mean square error in supervised regression and meta-regression than vanilla mixup and using feature similarity. Another benefit of C-Mixup is that it can improve out-of-distribution robustness, where the test distribution is different from the training distribution. By selectively interpolating examples with similar labels, it mitigates the effects of domain-associated information and yields domain-invariant representations. We evaluate C-Mixup on eleven datasets, ranging from tabular to video data. Compared to the best prior approach, C-Mixup achieves 6.56%, 4.76%, 5.82% improvements in in-distribution generalization, task generalization, and out-of-distribution robustness, respectively. Code is released at https://github.com/huaxiuyao/C-Mixup.

Yiyang Zhou, Chenhang Cui, Jaehong Yoon et al.

Large vision-language models (LVLMs) have shown remarkable abilities in understanding visual information with human languages. However, LVLMs still suffer from object hallucination, which is the problem of generating descriptions that include objects that do not actually exist in the images. This can negatively impact many vision-language tasks, such as visual summarization and reasoning. To address this issue, we propose a simple yet powerful algorithm, LVLM Hallucination Revisor (LURE), to post-hoc rectify object hallucination in LVLMs by reconstructing less hallucinatory descriptions. LURE is grounded in a rigorous statistical analysis of the key factors underlying object hallucination, including co-occurrence (the frequent appearance of certain objects alongside others in images), uncertainty (objects with higher uncertainty during LVLM decoding), and object position (hallucination often appears in the later part of the generated text). LURE can also be seamlessly integrated with any LVLMs. We evaluate LURE on six open-source LVLMs, achieving a 23% improvement in general object hallucination evaluation metrics over the previous best approach. In both GPT and human evaluations, LURE consistently ranks at the top. Our data and code are available at https://github.com/YiyangZhou/LURE.

Peng Xia, Kangyu Zhu, Haoran Li et al.

The recent emergence of Medical Large Vision Language Models (Med-LVLMs) has enhanced medical diagnosis. However, current Med-LVLMs frequently encounter factual issues, often generating responses that do not align with established medical facts. Retrieval-Augmented Generation (RAG), which utilizes external knowledge, can improve the factual accuracy of these models but introduces two major challenges. First, limited retrieved contexts might not cover all necessary information, while excessive retrieval can introduce irrelevant and inaccurate references, interfering with the model's generation. Second, in cases where the model originally responds correctly, applying RAG can lead to an over-reliance on retrieved contexts, resulting in incorrect answers. To address these issues, we propose RULE, which consists of two components. First, we introduce a provably effective strategy for controlling factuality risk through the calibrated selection of the number of retrieved contexts. Second, based on samples where over-reliance on retrieved contexts led to errors, we curate a preference dataset to fine-tune the model, balancing its dependence on inherent knowledge and retrieved contexts for generation. We demonstrate the effectiveness of RULE on medical VQA and report generation tasks across three datasets, achieving an average improvement of 47.4% in factual accuracy. We publicly release our benchmark and code in https://github.com/richard-peng-xia/RULE.

Ryumei Nakada, Halil Ibrahim Gulluk, Zhun Deng et al.

Language-supervised vision models have recently attracted great attention in computer vision. A common approach to build such models is to use contrastive learning on paired data across the two modalities, as exemplified by Contrastive Language-Image Pre-Training (CLIP). In this paper, under linear representation settings, (i) we initiate the investigation of a general class of nonlinear loss functions for multimodal contrastive learning (MMCL) including CLIP loss and show its connection to singular value decomposition (SVD). Namely, we show that each step of loss minimization by gradient descent can be seen as performing SVD on a contrastive cross-covariance matrix. Based on this insight, (ii) we analyze the performance of MMCL. We quantitatively show that the feature learning ability of MMCL can be better than that of unimodal contrastive learning applied to each modality even under the presence of wrongly matched pairs. This characterizes the robustness of MMCL to noisy data. Furthermore, when we have access to additional unpaired data, (iii) we propose a new MMCL loss that incorporates additional unpaired datasets. We show that the algorithm can detect the ground-truth pairs and improve performance by fully exploiting unpaired datasets. The performance of the proposed algorithm was verified by numerical experiments.

Haotian Ye, James Zou, Linjun Zhang

The existence of spurious correlations such as image backgrounds in the training environment can make empirical risk minimization (ERM) perform badly in the test environment. To address this problem, Kirichenko et al. (2022) empirically found that the core features that are related to the outcome can still be learned well even with the presence of spurious correlations. This opens a promising strategy to first train a feature learner rather than a classifier, and then perform linear probing (last layer retraining) in the test environment. However, a theoretical understanding of when and why this approach works is lacking. In this paper, we find that core features are only learned well when their associated non-realizable noise is smaller than that of spurious features, which is not necessarily true in practice. We provide both theories and experiments to support this finding and to illustrate the importance of non-realizable noise. Moreover, we propose an algorithm called Freeze then Train (FTT), that first freezes certain salient features and then trains the rest of the features using ERM. We theoretically show that FTT preserves features that are more beneficial to test time probing. Across two commonly used spurious correlation datasets, FTT outperforms ERM, IRM, JTT and CVaR-DRO, with substantial improvement in accuracy (by 4.5%) when the feature noise is large. FTT also performs better on general distribution shift benchmarks.

Zhun Deng, Jiayao Zhang, Linjun Zhang et al.

Algorithmic fairness plays an important role in machine learning and imposing fairness constraints during learning is a common approach. However, many datasets are imbalanced in certain label classes (e.g. "healthy") and sensitive subgroups (e.g. "older patients"). Empirically, this imbalance leads to a lack of generalizability not only of classification, but also of fairness properties, especially in over-parameterized models. For example, fairness-aware training may ensure equalized odds (EO) on the training data, but EO is far from being satisfied on new users. In this paper, we propose a theoretically-principled, yet Flexible approach that is Imbalance-Fairness-Aware (FIFA). Specifically, FIFA encourages both classification and fairness generalization and can be flexibly combined with many existing fair learning methods with logits-based losses. While our main focus is on EO, FIFA can be directly applied to achieve equalized opportunity (EqOpt); and under certain conditions, it can also be applied to other fairness notions. We demonstrate the power of FIFA by combining it with a popular fair classification algorithm, and the resulting algorithm achieves significantly better fairness generalization on several real-world datasets.

T. Tony Cai, Yichen Wang, Linjun Zhang

Achieving optimal statistical performance while ensuring the privacy of personal data is a challenging yet crucial objective in modern data analysis. However, characterizing the optimality, particularly the minimax lower bound, under privacy constraints is technically difficult. To address this issue, we propose a novel approach called the score attack, which provides a lower bound on the differential-privacy-constrained minimax risk of parameter estimation. The score attack method is based on the tracing attack concept in differential privacy and can be applied to any statistical model with a well-defined score statistic. It can optimally lower bound the minimax risk of estimating unknown model parameters, up to a logarithmic factor, while ensuring differential privacy for a range of statistical problems. We demonstrate the effectiveness and optimality of this general method in various examples, such as the generalized linear model in both classical and high-dimensional sparse settings, the Bradley-Terry-Luce model for pairwise comparisons, and non-parametric regression over the Sobolev class.

Zhun Deng, He Sun, Zhiwei Steven Wu et al.

AI methods are used in societally important settings, ranging from credit to employment to housing, and it is crucial to provide fairness in regard to algorithmic decision making. Moreover, many settings are dynamic, with populations responding to sequential decision policies. We introduce the study of reinforcement learning (RL) with stepwise fairness constraints, requiring group fairness at each time step. Our focus is on tabular episodic RL, and we provide learning algorithms with strong theoretical guarantees in regard to policy optimality and fairness violation. Our framework provides useful tools to study the impact of fairness constraints in sequential settings and brings up new challenges in RL.

Alyssa Huang, Peihan Liu, Ryumei Nakada et al.

The surge in multimodal AI's success has sparked concerns over data privacy in vision-and-language tasks. While CLIP has revolutionized multimodal learning through joint training on images and text, its potential to unintentionally disclose sensitive information necessitates the integration of privacy-preserving mechanisms. We introduce a differentially private adaptation of the Contrastive Language-Image Pretraining (CLIP) model that effectively addresses privacy concerns while retaining accuracy. Our proposed method, Dp-CLIP, is rigorously evaluated on benchmark datasets encompassing diverse vision-and-language tasks such as image classification and visual question answering. We demonstrate that our approach retains performance on par with the standard non-private CLIP model. Furthermore, we analyze our proposed algorithm under linear representation settings. We derive the convergence rate of our algorithm and show a trade-off between utility and privacy when gradients are clipped per-batch and the loss function does not satisfy smoothness conditions assumed in the literature for the analysis of DP-SGD.

Siwei Han, Jiaqi Liu, Yaofeng Su et al.

As Large Language Model (LLM) agents increasingly gain self-evolutionary capabilities to adapt and refine their strategies through real-world interaction, their long-term reliability becomes a critical concern. We identify the Alignment Tipping Process (ATP), a critical post-deployment risk unique to self-evolving LLM agents. Unlike training-time failures, ATP arises when continual interaction drives agents to abandon alignment constraints established during training in favor of reinforced, self-interested strategies. We formalize and analyze ATP through two complementary paradigms: Self-Interested Exploration, where repeated high-reward deviations induce individual behavioral drift, and Imitative Strategy Diffusion, where deviant behaviors spread across multi-agent systems. Building on these paradigms, we construct controllable testbeds and benchmark Qwen3-8B and Llama-3.1-8B-Instruct. Our experiments show that alignment benefits erode rapidly under self-evolution, with initially aligned models converging toward unaligned states. In multi-agent settings, successful violations diffuse quickly, leading to collective misalignment. Moreover, current reinforcement learning-based alignment methods provide only fragile defenses against alignment tipping. Together, these findings demonstrate that alignment of LLM agents is not a static property but a fragile and dynamic one, vulnerable to feedback-driven decay during deployment. Our data and code are available at https://github.com/aiming-lab/ATP.

Shirley Wu, Mert Yuksekgonul, Linjun Zhang et al.

Deep neural networks often rely on spurious correlations to make predictions, which hinders generalization beyond training environments. For instance, models that associate cats with bed backgrounds can fail to predict the existence of cats in other environments without beds. Mitigating spurious correlations is crucial in building trustworthy models. However, the existing works lack transparency to offer insights into the mitigation process. In this work, we propose an interpretable framework, Discover and Cure (DISC), to tackle the issue. With human-interpretable concepts, DISC iteratively 1) discovers unstable concepts across different environments as spurious attributes, then 2) intervenes on the training data using the discovered concepts to reduce spurious correlation. Across systematic experiments, DISC provides superior generalization ability and interpretability than the existing approaches. Specifically, it outperforms the state-of-the-art methods on an object recognition task and a skin-lesion classification task by 7.5% and 9.6%, respectively. Additionally, we offer theoretical analysis and guarantees to understand the benefits of models trained by DISC. Code and data are available at https://github.com/Wuyxin/DISC.

Huiying Zhong, Zhun Deng, Weijie J. Su et al.

Reinforcement learning with human feedback (RLHF) is an emerging paradigm to align models with human preferences. Typically, RLHF aggregates preferences from multiple individuals who have diverse viewpoints that may conflict with each other. Our work \textit{initiates} the theoretical study of multi-party RLHF that explicitly models the diverse preferences of multiple individuals. We show how traditional RLHF approaches can fail since learning a single reward function cannot capture and balance the preferences of multiple individuals. To overcome such limitations, we incorporate meta-learning to learn multiple preferences and adopt different social welfare functions to aggregate the preferences across multiple parties. We focus on the offline learning setting and establish sample complexity bounds, along with efficiency and fairness guarantees, for optimizing diverse social welfare functions such as Nash, Utilitarian, and Leximin welfare functions. Our results show a separation between the sample complexities of multi-party RLHF and traditional single-party RLHF. Furthermore, we consider a reward-free setting, where each individual's preference is no longer consistent with a reward model, and give pessimistic variants of the von Neumann Winner based on offline preference data. Taken together, our work showcases the advantage of multi-party RLHF but also highlights its more demanding statistical complexity.

Haonan Wang, James Zou, Michael Mozer et al.

Creativity serves as a cornerstone for societal progress and innovation. With the rise of advanced generative AI models capable of tasks once reserved for human creativity, the study of AI's creative potential becomes imperative for its responsible development and application. In this paper, we prove in theory that AI can be as creative as humans under the condition that it can properly fit the data generated by human creators. Therefore, the debate on AI's creativity is reduced into the question of its ability to fit a sufficient amount of data. To arrive at this conclusion, this paper first addresses the complexities in defining creativity by introducing a new concept called Relative Creativity. Rather than attempting to define creativity universally, we shift the focus to whether AI can match the creative abilities of a hypothetical human. The methodological shift leads to a statistically quantifiable assessment of AI's creativity, term Statistical Creativity. This concept, statistically comparing the creative abilities of AI with those of specific human groups, facilitates theoretical exploration of AI's creative potential. Our analysis reveals that by fitting extensive conditional data without marginalizing out the generative conditions, AI can emerge as a hypothetical new creator. The creator possesses the same creative abilities on par with the human creators it was trained on. Building on theoretical findings, we discuss the application in prompt-conditioned autoregressive models, providing a practical means for evaluating creative abilities of generative AI models, such as Large Language Models (LLMs). Additionally, this study provides an actionable training guideline, bridging the theoretical quantification of creativity with practical model training.

Xinyu Yang, Jixuan Leng, Geyang Guo et al. · cmu

Current PEFT methods for LLMs can achieve either high quality, efficient training, or scalable serving, but not all three simultaneously. To address this limitation, we investigate sparse fine-tuning and observe a remarkable improvement in generalization ability. Utilizing this key insight, we propose a family of Structured Sparse Fine-Tuning (S$^{2}$FT) methods for LLMs, which concurrently achieve state-of-the-art fine-tuning performance, training efficiency, and inference scalability. S$^{2}$FT accomplishes this by "selecting sparsely and computing densely". It selects a few heads and channels in the MHA and FFN modules for each Transformer block, respectively. Next, it co-permutes weight matrices on both sides of the coupled structures in LLMs to connect the selected components in each layer into a dense submatrix. Finally, S$^{2}$FT performs in-place gradient updates on all submatrices. Through theoretical analysis and empirical results, our method prevents forgetting while simplifying optimization, delivers SOTA performance on both commonsense and arithmetic reasoning with 4.6% and 1.3% average improvements compared to LoRA, and surpasses full FT by 11.5% when generalizing to various domains after instruction tuning. Using our partial backpropagation algorithm, S$^{2}$FT saves training memory up to 3$\times$ and improves latency by 1.5-2.7$\times$ compared to full FT, while delivering an average 10% improvement over LoRA on both metrics. We further demonstrate that the weight updates in S$^{2}$FT can be decoupled into adapters, enabling effective fusion, fast switch, and efficient parallelism for serving multiple fine-tuned models.

Zongbo Han, Yifeng Yang, Changqing Zhang et al.

Miscalibration in deep learning refers to there is a discrepancy between the predicted confidence and performance. This problem usually arises due to the overfitting problem, which is characterized by learning everything presented in the training set, resulting in overconfident predictions during testing. Existing methods typically address overfitting and mitigate the miscalibration by adding a maximum-entropy regularizer to the objective function. The objective can be understood as seeking a model that fits the ground-truth labels by increasing the confidence while also maximizing the entropy of predicted probabilities by decreasing the confidence. However, previous methods lack clear guidance on confidence adjustment, leading to conflicting objectives (increasing but also decreasing confidence). Therefore, we introduce a method called Dynamic Regularization (DReg), which aims to learn what should be learned during training thereby circumventing the confidence adjusting trade-off. At a high level, DReg aims to obtain a more reliable model capable of acknowledging what it knows and does not know. Specifically, DReg effectively fits the labels for in-distribution samples (samples that should be learned) while applying regularization dynamically to samples beyond model capabilities (e.g., outliers), thereby obtaining a robust calibrated model especially on the samples beyond model capabilities. Both theoretical and empirical analyses sufficiently demonstrate the superiority of DReg compared with previous methods.

Tianxi Cai, Feiqing Huang, Ryumei Nakada et al.

Electronic health record (EHR) systems contain a wealth of multimodal clinical data including structured data like clinical codes and unstructured data such as clinical notes. However, many existing EHR-focused studies has traditionally either concentrated on an individual modality or merged different modalities in a rather rudimentary fashion. This approach often results in the perception of structured and unstructured data as separate entities, neglecting the inherent synergy between them. Specifically, the two important modalities contain clinically relevant, inextricably linked and complementary health information. A more complete picture of a patient's medical history is captured by the joint analysis of the two modalities of data. Despite the great success of multimodal contrastive learning on vision-language, its potential remains under-explored in the realm of multimodal EHR, particularly in terms of its theoretical understanding. To accommodate the statistical analysis of multimodal EHR data, in this paper, we propose a novel multimodal feature embedding generative model and design a multimodal contrastive loss to obtain the multimodal EHR feature representation. Our theoretical analysis demonstrates the effectiveness of multimodal learning compared to single-modality learning and connects the solution of the loss function to the singular value decomposition of a pointwise mutual information matrix. This connection paves the way for a privacy-preserving algorithm tailored for multimodal EHR feature representation learning. Simulation studies show that the proposed algorithm performs well under a variety of configurations. We further validate the clinical utility of the proposed algorithm in real-world EHR data.

Zhe Zhang, Ryumei Nakada, Linjun Zhang

Differentially private federated learning is crucial for maintaining privacy in distributed environments. This paper investigates the challenges of high-dimensional estimation and inference under the constraints of differential privacy. First, we study scenarios involving an untrusted central server, demonstrating the inherent difficulties of accurate estimation in high-dimensional problems. Our findings indicate that the tight minimax rates depends on the high-dimensionality of the data even with sparsity assumptions. Second, we consider a scenario with a trusted central server and introduce a novel federated estimation algorithm tailored for linear regression models. This algorithm effectively handles the slight variations among models distributed across different machines. We also propose methods for statistical inference, including coordinate-wise confidence intervals for individual parameters and strategies for simultaneous inference. Extensive simulation experiments support our theoretical advances, underscoring the efficacy and reliability of our approaches.

Ryumei Nakada, Wenlong Ji, Tianxi Cai et al.

Prompt engineering has emerged as a powerful technique for guiding large language models (LLMs) toward desired responses, significantly enhancing their performance across diverse tasks. Beyond their role as static predictors, LLMs increasingly function as intelligent agents, capable of reasoning, decision-making, and adapting dynamically to complex environments. However, the theoretical underpinnings of prompt engineering remain largely unexplored. In this paper, we introduce a formal framework demonstrating that transformer models, when provided with carefully designed prompts, can act as a configurable computational system by emulating a ``virtual'' neural network during inference. Specifically, input prompts effectively translate into the corresponding network configuration, enabling LLMs to adjust their internal computations dynamically. Building on this construction, we establish an approximation theory for $β$-times differentiable functions, proving that transformers can approximate such functions with arbitrary precision when guided by appropriately structured prompts. Moreover, our framework provides theoretical justification for several empirically successful prompt engineering techniques, including the use of longer, structured prompts, filtering irrelevant information, enhancing prompt token diversity, and leveraging multi-agent interactions. By framing LLMs as adaptable agents rather than static models, our findings underscore their potential for autonomous reasoning and problem-solving, paving the way for more robust and theoretically grounded advancements in prompt engineering and AI agent design.

Qichuan Yin, Zexian Wang, Junzhou Huang et al.

As federated learning gains increasing importance in real-world applications due to its capacity for decentralized data training, addressing fairness concerns across demographic groups becomes critically important. However, most existing machine learning algorithms for ensuring fairness are designed for centralized data environments and generally require large-sample and distributional assumptions, underscoring the urgent need for fairness techniques adapted for decentralized and heterogeneous systems with finite-sample and distribution-free guarantees. To address this issue, this paper introduces FedFaiREE, a post-processing algorithm developed specifically for distribution-free fair learning in decentralized settings with small samples. Our approach accounts for unique challenges in decentralized environments, such as client heterogeneity, communication costs, and small sample sizes. We provide rigorous theoretical guarantees for both fairness and accuracy, and our experimental results further provide robust empirical validation for our proposed method.

Zihan Dong, Xin Zhou, Ryumei Nakada et al.

Network representation learning seeks to embed networks into a low-dimensional space while preserving the structural and semantic properties, thereby facilitating downstream tasks such as classification, trait prediction, edge identification, and community detection. Motivated by challenges in brain connectivity data analysis that is characterized by subject-specific, high-dimensional, and sparse networks that lack node or edge covariates, we propose a novel contrastive learning-based statistical approach for network edge embedding, which we name as Adaptive Contrastive Edge Representation Learning (ACERL). It builds on two key components: contrastive learning of augmented network pairs, and a data-driven adaptive random masking mechanism. We establish the non-asymptotic error bounds, and show that our method achieves the minimax optimal convergence rate for edge representation learning. We further demonstrate the applicability of the learned representation in multiple downstream tasks, including network classification, important edge detection, and community detection, and establish the corresponding theoretical guarantees. We validate our method through both synthetic data and real brain connectivities studies, and show its competitive performance compared to the baseline method of sparse principal components analysis.

Yichen Xu, Ryumei Nakada, Linjun Zhang et al.

Transfer learning typically leverages representations learned from a source domain to improve performance on a target task. A common approach is to extract features from a pre-trained model and directly apply them for target prediction. However, this strategy is prone to negative transfer where the source representation fails to align with the target distribution. In this article, we propose Residual Feature Integration (REFINE), a simple yet effective method designed to mitigate negative transfer. Our approach combines a fixed source-side representation with a trainable target-side encoder and fits a shallow neural network on the resulting joint representation, which adapts to the target domain while preserving transferable knowledge from the source domain. Theoretically, we prove that REFINE is sufficient to prevent negative transfer under mild conditions, and derive the generalization bound demonstrating its theoretical benefit. Empirically, we show that REFINE consistently enhances performance across diverse application and data modalities including vision, text, and tabular data, and outperforms numerous alternative solutions. Our method is lightweight, architecture-agnostic, and robust, making it a valuable addition to the existing transfer learning toolbox.

Mert Yuksekgonul, Linjun Zhang, James Zou et al.

While most machine learning models can provide confidence in their predictions, confidence is insufficient to understand a prediction's reliability. For instance, the model may have a low confidence prediction if the input is not well-represented in the training dataset or if the input is inherently ambiguous. In this work, we investigate the relationship between how atypical(rare) a sample or a class is and the reliability of a model's predictions. We first demonstrate that atypicality is strongly related to miscalibration and accuracy. In particular, we empirically show that predictions for atypical inputs or atypical classes are more overconfident and have lower accuracy. Using these insights, we show incorporating atypicality improves uncertainty quantification and model performance for discriminative neural networks and large language models. In a case study, we show that using atypicality improves the performance of a skin lesion classifier across different skin tone groups without having access to the group attributes. Overall, we propose that models should use not only confidence but also atypicality to improve uncertainty quantification and performance. Our results demonstrate that simple post-hoc atypicality estimators can provide significant value.

Huaxiu Yao, Yu Wang, Sai Li et al.

Machine learning algorithms typically assume that training and test examples are drawn from the same distribution. However, distribution shift is a common problem in real-world applications and can cause models to perform dramatically worse at test time. In this paper, we specifically consider the problems of subpopulation shifts (e.g., imbalanced data) and domain shifts. While prior works often seek to explicitly regularize internal representations or predictors of the model to be domain invariant, we instead aim to learn invariant predictors without restricting the model's internal representations or predictors. This leads to a simple mixup-based technique which learns invariant predictors via selective augmentation called LISA. LISA selectively interpolates samples either with the same labels but different domains or with the same domain but different labels. Empirically, we study the effectiveness of LISA on nine benchmarks ranging from subpopulation shifts to domain shifts, and we find that LISA consistently outperforms other state-of-the-art methods and leads to more invariant predictors. We further analyze a linear setting and theoretically show how LISA leads to a smaller worst-group error.

Wenlong Ji, Zhun Deng, Ryumei Nakada et al.

Contrastive learning has achieved state-of-the-art performance in various self-supervised learning tasks and even outperforms its supervised counterpart. Despite its empirical success, theoretical understanding of the superiority of contrastive learning is still limited. In this paper, under linear representation settings, (i) we provably show that contrastive learning outperforms the standard autoencoders and generative adversarial networks, two classical generative unsupervised learning methods, for both feature recovery and in-domain downstream tasks; (ii) we also illustrate the impact of labeled data in supervised contrastive learning. This provides theoretical support for recent findings that contrastive learning with labels improves the performance of learned representations in the in-domain downstream task, but it can harm the performance in transfer learning. We verify our theory with numerical experiments.

Kenji Kawaguchi, Linjun Zhang, Zhun Deng

Representations of the world environment play a crucial role in artificial intelligence. It is often inefficient to conduct reasoning and inference directly in the space of raw sensory representations, such as pixel values of images. Representation learning allows us to automatically discover suitable representations from raw sensory data. For example, given raw sensory data, a deep neural network learns nonlinear representations at its hidden layers, which are subsequently used for classification (or regression) at its output layer. This happens implicitly during training through minimizing a supervised or unsupervised loss in common practical regimes of deep learning, unlike the neural tangent kernel (NTK) regime. In this paper, we study the dynamics of such implicit nonlinear representation learning, which is beyond the NTK regime. We identify a pair of a new assumption and a novel condition, called the common model structure assumption and the data-architecture alignment condition. Under the common model structure assumption, the data-architecture alignment condition is shown to be sufficient for the global convergence and necessary for the global optimality. Moreover, our theory explains how and when increasing the network size does and does not improve the training behaviors in the practical regime. Our results provide practical guidance for designing a model structure: e.g., the common model structure assumption can be used as a justification for using a particular model structure instead of others. We also derive a new training framework based on the theory. The proposed framework is empirically shown to maintain competitive (practical) test performances while providing global convergence guarantees for deep residual neural networks with convolutions, skip connections, and batch normalization with standard benchmark datasets, including CIFAR-10, CIFAR-100, and SVHN.

Zhun Deng, Linjun Zhang, Kailas Vodrahalli et al.

Transfer learning aims to leverage models pre-trained on source data to efficiently adapt to target setting, where only limited data are available for model fine-tuning. Recent works empirically demonstrate that adversarial training in the source data can improve the ability of models to transfer to new domains. However, why this happens is not known. In this paper, we provide a theoretical model to rigorously analyze how adversarial training helps transfer learning. We show that adversarial training in the source data generates provably better representations, so fine-tuning on top of this representation leads to a more accurate predictor of the target data. We further demonstrate both theoretically and empirically that semi-supervised learning in the source data can also improve transfer learning by similarly improving the representation. Moreover, performing adversarial training on top of semi-supervised learning can further improve transferability, suggesting that the two approaches have complementary benefits on representations. We support our theories with experiments on popular data sets and deep learning architectures.

Huaxiu Yao, Linjun Zhang, Chelsea Finn

Meta-learning enables algorithms to quickly learn a newly encountered task with just a few labeled examples by transferring previously learned knowledge. However, the bottleneck of current meta-learning algorithms is the requirement of a large number of meta-training tasks, which may not be accessible in real-world scenarios. To address the challenge that available tasks may not densely sample the space of tasks, we propose to augment the task set through interpolation. By meta-learning with task interpolation (MLTI), our approach effectively generates additional tasks by randomly sampling a pair of tasks and interpolating the corresponding features and labels. Under both gradient-based and metric-based meta-learning settings, our theoretical analysis shows MLTI corresponds to a data-adaptive meta-regularization and further improves the generalization. Empirically, in our experiments on eight datasets from diverse domains including image recognition, pose prediction, molecule property prediction, and medical image classification, we find that the proposed general MLTI framework is compatible with representative meta-learning algorithms and consistently outperforms other state-of-the-art strategies.

Linjun Zhang, Zhun Deng, Kenji Kawaguchi et al.

Mixup is a popular data augmentation technique based on taking convex combinations of pairs of examples and their labels. This simple technique has been shown to substantially improve both the robustness and the generalization of the trained model. However, it is not well-understood why such improvement occurs. In this paper, we provide theoretical analysis to demonstrate how using Mixup in training helps model robustness and generalization. For robustness, we show that minimizing the Mixup loss corresponds to approximately minimizing an upper bound of the adversarial loss. This explains why models obtained by Mixup training exhibits robustness to several kinds of adversarial attacks such as Fast Gradient Sign Method (FGSM). For generalization, we prove that Mixup augmentation corresponds to a specific type of data-adaptive regularization which reduces overfitting. Our analysis provides new insights and a framework to understand Mixup.

Huaxiu Yao, Longkai Huang, Linjun Zhang et al.

Meta-learning has proven to be a powerful paradigm for transferring the knowledge from previous tasks to facilitate the learning of a novel task. Current dominant algorithms train a well-generalized model initialization which is adapted to each task via the support set. The crux lies in optimizing the generalization capability of the initialization, which is measured by the performance of the adapted model on the query set of each task. Unfortunately, this generalization measure, evidenced by empirical results, pushes the initialization to overfit the meta-training tasks, which significantly impairs the generalization and adaptation to novel tasks. To address this issue, we actively augment a meta-training task with "more data" when evaluating the generalization. Concretely, we propose two task augmentation methods, including MetaMix and Channel Shuffle. MetaMix linearly combines features and labels of samples from both the support and query sets. For each class of samples, Channel Shuffle randomly replaces a subset of their channels with the corresponding ones from a different class. Theoretical studies show how task augmentation improves the generalization of meta-learning. Moreover, both MetaMix and Channel Shuffle outperform state-of-the-art results by a large margin across many datasets and are compatible with existing meta-learning algorithms.

Zhun Deng, Linjun Zhang, Amirata Ghorbani et al.

Data augmentation by incorporating cheap unlabeled data from multiple domains is a powerful way to improve prediction especially when there is limited labeled data. In this work, we investigate how adversarial robustness can be enhanced by leveraging out-of-domain unlabeled data. We demonstrate that for broad classes of distributions and classifiers, there exists a sample complexity gap between standard and robust classification. We quantify to what degree this gap can be bridged via leveraging unlabeled samples from a shifted domain by providing both upper and lower bounds. Moreover, we show settings where we achieve better adversarial robustness when the unlabeled data come from a shifted domain rather than the same domain as the labeled data. We also investigate how to leverage out-of-domain data when some structural information, such as sparsity, is shared between labeled and unlabeled domains. Experimentally, we augment two object recognition datasets (CIFAR-10 and SVHN) with easy to obtain and unlabeled out-of-domain data and demonstrate substantial improvement in the model's robustness against $\ell_\infty$ adversarial attacks on the original domain.

T. Tony Cai, Yichen Wang, Linjun Zhang

Privacy-preserving data analysis is a rising challenge in contemporary statistics, as the privacy guarantees of statistical methods are often achieved at the expense of accuracy. In this paper, we investigate the tradeoff between statistical accuracy and privacy in mean estimation and linear regression, under both the classical low-dimensional and modern high-dimensional settings. A primary focus is to establish minimax optimality for statistical estimation with the $(\varepsilon,δ)$-differential privacy constraint. To this end, we find that classical lower bound arguments fail to yield sharp results, and new technical tools are called for. By refining the "tracing adversary" technique for lower bounds in the theoretical computer science literature, we formulate a general lower bound argument for minimax risks with differential privacy constraints, and apply this argument to high-dimensional mean estimation and linear regression problems. We also design computationally efficient algorithms that attain the minimax lower bounds up to a logarithmic factor. In particular, for the high-dimensional linear regression, a novel private iterative hard thresholding pursuit algorithm is proposed, based on a privately truncated version of stochastic gradient descent. The numerical performance of these algorithms is demonstrated by simulation studies and applications to real data containing sensitive information, for which privacy-preserving statistical methods are necessary.

T. Tony Cai, Linjun Zhang

We discuss a clustering method for Gaussian mixture model based on the sparse principal component analysis (SPCA) method and compare it with the IF-PCA method. We also discuss the dependent case where the covariance matrix $Σ$ is not necessarily diagonal.