Personalized Bayesian federated learning (PBFL) handles non-i.i.d.

The present article studies the minimization of convex, L-smooth functions defined on a separable real Hilbert space. We analyze regularized stochastic gradient descent (reg-SGD), a variant of stochastic gradient descent that uses a Tikhonov regularization with time-dependent, vanishing regularization parameter. We prove strong convergence of reg-SGD to the minimum-norm solution of the original problem without additional boundedness assumptions. Moreover, we quantify the rate of convergence and optimize the interplay between step-sizes and regularization decay. Our analysis reveals how vanishing Tikhonov regularization controls the flow of SGD and yields stable learning dynamics, offering new insights into the design of iterative algorithms for convex problems, including those that arise in ill-posed inverse problems.

Learning robust representations from unlabeled time series is crucial, and contrastive learning offers a promising avenue. However, existing contrastive learning approaches for time series often struggle to define meaningful similarities, tending to overlook inherent physical correlations and diverse, sequence-varying non-stationarity. This limits their representational quality and real-world adaptability. To address these limitations, we introduce AdaTS, a novel adaptive soft contrastive learning strategy. AdaTS offers a computationally efficient solution centered on dynamic instance-wise and temporal assignments that enhance time series representations by: (i) leveraging Time-Frequency Coherence to provide robust, physics-guided similarity measurements; (ii) preserving relative instance similarities through ordinal consistency learning; and (iii) adapting to sequencespecific non-stationarity with dynamic temporal assignments. AdaTS is designed as a pluggable module for standard contrastive frameworks, achieving accuracy improvements of up to 13.7% across diverse time series datasets and three state-ofthe-art contrastive frameworks while enhancing robustness under label scarcity.

Contrastive learning is a powerful framework for learning discriminative representations from image-text pairs. Despite its success, its theoretical foundations, especially when the image-text pair exhibits misalignment, remain underexplored. This paper provides the first theoretical analysis of contrastive learning under data misalignment, proving how the ground-truth modality-paired features are amplified while spurious features are suppressed through the training dynamics analysis. Specifically, we study two nonlinear encoders trained jointly with a contrastive loss and demonstrate that noisy (or misaligned) data pairs result in mixed representations and degrade the model's generalization ability. In contrast, recaptioning and filtering improve the data alignment, which in turn purifies the features learned by neurons and subsequently enhances generalization. Our analysis identifies feature purity as a key factor in the success of contrastive learning and offers insights into how data quality and training procedures impact representation learning and downstream generalization. Theoretical insights are supported by experiments on standard benchmarks.

Existing methods for differentiable structure learning in discrete data typically assume that the data are generated from specific structural equation models. However, these assumptions may not align with the true data-generating process, which limits the general applicability of such methods. Furthermore, current approaches often ignore the complex dependence structure inherent in discrete data and consider only linear effects. We propose a differentiable structure learning framework that is capable of capturing arbitrary dependencies among discrete variables. We show that although general discrete models are unidentifiable from purely observational data, it is possible to characterize the complete set of compatible parameters and structures. Additionally, we establish identifiability up to Markov equivalence under mild assumptions. We formulate the learning problem as a single differentiable optimization task in the most general form, thereby avoiding the unrealistic simplifications adopted by previous methods. Empirical results demonstrate that our approach effectively captures complex relationships in discrete data.

Yet, modern machine learning pipelines offer a promising solution--provided their predictions yield correct conclusions. We focus on Prediction-Powered Causal Inferences (PPCI), i.e., estimating the treatment effect in an unlabeled target experiment, relying on training data with the same outcome annotated but potentially different treatment or effect modifiers.

Decentralized training removes the centralized server, making it a communicationefficient approach that can significantly improve training efficiency, but it often suffers from degraded performance compared to centralized training. Multi-Gossip Steps (MGS) serve as a simple yet effective bridge between decentralized and centralized training, significantly reducing experiment performance gaps. However, the theoretical reasons for its effectiveness and whether this gap can be fully eliminated by MGS remain open questions. In this paper, we derive upper bounds on the generalization error and excess error of MGS using stability analysis, systematically answering these two key questions.

In recent developments in scientific machine learning (SciML), neural surrogate solvers for partial differential equations (PDEs) have become powerful tools for accelerating scientific computation for various science and engineering applications. However, training neural PDE solvers often demands a large amount of high-fidelity PDE simulation data, which are expensive to generate. Active learning (AL) offers a promising solution by adaptively selecting training data from the PDE settings-including parameters, initial and boundary conditions-that are expected to be most informative to help reduce this data burden. In this work, we introduce PaPQS, a Plug-and-Play Query Synthesis AL framework that synthesizes informative PDE settings directly in the continuous design space.

The gradient descent (GD) has been one of the most common optimizer in machine learning. In particular, the loss landscape of a neural network is typically sharpened during the initial phase of training, making the training dynamics hover on the edge of stability. This is beyond our standard understanding of GD convergence in the stable regime where stepsize is chosen sufficiently smaller. Recently, Wu et al. [63] have shown that GD converges with much larger stepsize under linearly separable logistic regression. Although their analysis hinges on the self-bounding property of the logistic loss, which seems to be a cornerstone to establish a modified descent lemma, our pilot study shows that other loss functions without the selfbounding property can make GD attain arbitrarily small loss with large stepsize.

With the increasing need to safeguard data privacy in machine learning models, differential privacy (DP) is one of the major frameworks to build privacy-preserving models. Support Vector Machines (SVMs) are widely used traditional machine learning models due to their robust margin guarantees and strong empirical performance in binary classification. However, applying DP to multi-class SVMs is inadequate, as the standard one-versus-rest (OvR) and one-versus-one (OvO) approaches repeatedly query each data sample when building multiple binary classifiers, thus consuming the privacy budget proportionally to the number of classes. To overcome this limitation, we explore all-in-one SVM approaches for DP, which access each data sample only once to construct multi-class SVM boundaries with margin maximization properties. We propose a novel differentially Private Multi-class SVM (PMSVM) with weight and gradient perturbation methods, providing rigorous sensitivity and convergence analyses to ensure DP in all-in-one SVMs. Empirical results demonstrate that our approach surpasses existing DP-SVM methods in multi-class scenarios.