We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Label prototype learning has emerged as an effective paradigm in Partial MultiLabel Learning (PML), providing a distinctive framework for modeling structured representations of label semantics while naturally filtering noise through prototypebased label confidence estimation. However, existing prototype-based methods face a critical limitation: class prototypes are the biased estimates due to noisy candidate labels, particularly when positive samples are scarce. To this end, we first propose a mutually class prototype alignment strategy bypassing noise interference by introducing two different transformation matrices, which makes the class prototypes learned by the fuzzy clustering and candidate label set mutually alignment for correcting themselves. Such alignment is also passed on to the fuzzy memberships label in turn. In addition, to eliminate noise interference in the candidate label set during the classifier learning, we use the learned permutation matrix to transform the fuzzy memberships label for learning a label reliability indicator matrix accompanied by the candidate label set. This makes the label reliability indicator matrix absolutely prevent the occurrence of numerical values located in non-label and simultaneously eliminate the introduction of incorrect label as much as possible.

This paper establishes the theoretical limits of graph clustering under the PopularityAdjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex degrees, and to the Degree-Corrected Block Model (DCBM), which applies uniform degree corrections across clusters, PABM introduces separate popularity parameters for intra-and inter-cluster connections. Our main contribution is the characterization of the optimal error rate for clustering under PABM, which provides novel insights on clustering hardness: we demonstrate that unlike SBM and DCBM, cluster recovery remains possible in PABM even when traditional edge-density signals vanish, provided intra-and inter-cluster popularity coefficients differ. This highlights a dimension of degree heterogeneity captured by PABM but overlooked by DCBM: local differences in connectivity patterns can enhance cluster separability independently of global edge densities. Finally, because PABM exhibits a richer structure, its expected adjacency matrix has rank between k and k2, where k is the number of clusters. As a result, spectral embeddings based on the top k eigenvectors may fail to capture important structural information. Our numerical experiments on both synthetic and real datasets confirm that spectral clustering algorithms incorporating k2 eigenvectors outperform traditional spectral approaches.

As machine learning increasingly relies on large, opaque foundation models powering generative and agentic AI, deploying these systems in safety-critical contexts demands rigorous generalization guarantees beyond training data. PAC-Bayes theory provides principled certificates linking training performance to generalization risk, yet existing approaches remain impractical: simple theoretical priors yield vacuous bounds, while data-dependent priors require costly second-stage training or introduce bias. To bridge this critical gap, we propose a localized PAC-Bayes prior--a structured, computationally efficient prior softly concentrated around parameters favored during standard training. By integrating this localized prior directly into the standard training objective, we deliver practically tight generalization certificates with minimal workflow disruption. Under standard neural tangent kernel assumptions, our bound shrinks as networks widen and datasets grow, becoming negligible in realistic regimes. Empirically, we demonstrate tight generalization certificates on tasks ranging from image classification (MNIST, CIFAR, ImageNet) and NLP fine-tuning (GLUE) to semantic segmentation (Cityscapes), typically within three percentage points of test error at ImageNet scale. Additionally, our approach provides rigorous guarantees for individual predictions, selective rejection of uncertain predictions, adversarial robustness, and accurate calibration--directly addressing key requirements for trustworthy AI deployment.

Data attribution methods, which quantify the influence of individual training data points on a machine learning model, have gained increasing popularity in datacentric applications in modern AI. Despite a recent surge of new methods developed in this space, the impact of hyperparameter tuning in these methods remains underexplored. In this work, we present the first large-scale empirical study to understand the hyperparameter sensitivity of common data attribution methods. Our results show that most methods are indeed sensitive to certain key hyperparameters. However, unlike typical machine learning algorithms--whose hyperparameters can be tuned using computationally-cheap validation metrics--evaluating data attribution performance often requires retraining models on subsets of training data, making such metrics prohibitively costly for hyperparameter tuning.

The growing prevalence of streaming data and increasing concerns over data privacy pose significant challenges for traditional nonparametric regression methods, which are often ill-suited for real-time, privacy-aware learning. In this paper, we tackle these issues by first proposing a novel one-pass online functional stochastic gradient descent algorithm that leverages the Huber loss (H-FSGD), to improve robustness against outliers and heavy-tailed errors in dynamic environments. To further accommodate privacy constraints, we introduce a locally differentially private extension, Private H-FSGD (PH-FSGD), designed to real-time, privacy-preserving estimation. Theoretically, we conduct a comprehensive non-asymptotic convergence analysis of the proposed estimators, establishing finite-sample guarantees and identifying optimal step size schedules that achieve optimal convergence rates. In particular, we provide practical insights into the impact of key hyperparameters, such as step size and privacy budget, on convergence behavior. Extensive experiments validate our theoretical findings, demonstrating that our methods achieve strong robustness and privacy protection without sacrificing efficiency.

This paper investigates approximation-theoretic aspects of the in-context learning capability of the transformers in representing a family of noisy linear dynamical systems. Our first theoretical result establishes an upper bound on the approximation error of multi-layer transformers with respect to an L2-testing loss uniformly defined across tasks. This result demonstrates that transformers with logarithmic depth can achieve error bounds comparable with those of the least-squares estimator. In contrast, our second result establishes a non-diminishing lower bound on the approximation error for a class of single-layer linear transformers, which suggests a depth-separation phenomenon for transformers in the in-context learning of dynamical systems.

Modern foundation models are trained on diverse datasets to enhance generalization across tasks and domains. A central challenge in this process is determining how to effectively mix and sample data from multiple sources. This naturally leads to a multi-task learning (MTL) perspective. While prior work in MTL has emphasized mitigating gradient conflicts, we observe that large-scale pretraining scenarios--such as multilingual or multi-domain training--often exhibit little to no gradient conflict. Motivated by this observation, we propose PiKE (Positive gradient interaction-based K-task weights Estimator), an adaptive data mixing algorithm that dynamically adjusts sampling weights during training. PiKE exploits non-conflicting gradient interactions to minimize a near-tight upper bound on the average loss decrease at each step, while incurring negligible computational overhead. We provide theoretical convergence guarantees and show that PiKE outperforms static and non-adaptive mixing baselines. Furthermore, we extend PiKE to promote balanced learning across tasks. Extensive experiments on largescale language model pretraining confirm that PiKE achieves faster convergence and improved downstream performance compared to existing approaches.

Physiological signals are often corrupted by motion artifacts, baseline drift, and other low-SNR disturbances, which pose significant challenges for analysis. Additionally, these signals exhibit strong non-stationarity, with sharp peaks and abrupt changes that evolve continuously, making them difficult to represent using traditional time-domain or filtering methods. To address these issues, a novel waveletbased approach for physiological signal analysis is presented, aiming to capture multi-scale time-frequency features in various physiological signals. Leveraging this technique, two large-scale pretrained models specific to EMG and ECG are introduced for the first time, achieving superior performance and setting new baselines in downstream tasks. Additionally, a unified multi-modal framework is constructed by integrating pretrained EEG model, where each modality is guided through its dedicated branch and fused via learnable weighted fusion. This design effectively addresses challenges such as low signal-to-noise ratio, high inter-subject variability, and device mismatch, outperforming existing methods on multi-modal tasks. The proposed wavelet-based architecture lays a solid foundation for analysis of diverse physiological signals, while the multi-modal design points to nextgeneration physiological signal processing with potential impact on wearable health monitoring, clinical diagnostics, and broader biomedical applications.

Graph transformers (GTs) have shown strong empirical performance, yet current architectures vary widely in their use of attention mechanisms, positional embeddings (PEs), and expressivity. Existing expressivity results are often tied to specific design choices and lack comprehensive empirical validation on large-scale data. This leaves a gap between theory and practice, preventing generalizable insights that exceed particular application domains. Here, we propose the GeneralizedDistance Transformer (GDT), a GT architecture based on standard attention that incorporates many recent advancements for GTs, and we develop a fine-grained understanding of the GDT's representation power in terms of attention and PEs. Through extensive experiments, we identify design choices that consistently perform well across various applications, tasks, and model scales, demonstrating strong performance in a few-shot transfer setting without fine-tuning. Our evaluation covers over eight million graphs with roughly 270M tokens across diverse domains, including image-based object detection, molecular property prediction, code summarization, and out-of-distribution algorithmic reasoning.