Vision-language pre-trained models, such as CLIP, have established new benchmarks in multimodal data mining. In such models, few-shot fine-tuning is a major challenge to achieve optimal performance on both in-distribution (ID) and out-of-distribution (OOD) datasets, especially when labeled data is scarce. Most existing fine-tuning approaches rely on first-order gradient-based optimizers, which typically suffer from slow convergence, sensitivity to step-size hyperparameters, and poor generalization in OOD settings. In contrast, second-order methods utilize local curvature information of the loss landscape to adjust the update step size. This is particularly beneficial for CLIP models, whose non-convex loss functions often contain sharp critical points. In such cases, natural gradient direction can offer more substantial and efficient per-iteration updates when fine-tuning with limited data. Natural Gradient Descent (NGD) is obtained by preconditioning the standard gradient with the inverse Fisher Information Matrix (FIM), which is computationally expensive for large models. To address this, we propose a Bayesian approximation of NGD using a Kalman filter for CLIP models. Our method combines the benefits of second-order optimization with Bayesian inference, which enhances generalization while providing uncertainty quantification. Extensive experiments conducted on diverse image classification datasets demonstrate that our algorithm consistently achieves superior--or comparable--ID performance and improved OOD robustness compared to state-of-the-art baselines. To the best of our knowledge, this work represents the first successful application of Kalman filtering to fine-tuning CLIP-based models, which enables more robust and efficient learning in vision-language tasks.

Bayesian Optimization (BO) is an efficient tool for optimizing black-box functions, but its theoretical guarantees typically hold in the asymptotic regime. In many critical real-world applications such as drug discovery or materials design, where each evaluation can be very costly and time-consuming, BO becomes impractical for many evaluations. In this paper, we introduce the Procedure-inFormed BO (ProfBO) algorithm, which solves black-box optimization with remarkably few function evaluations. At the heart of our algorithmic design are Markov Decision Process (MDP) priors that model optimization trajectories from related source tasks, thereby capturing procedural knowledge on efficient optimization. We embed these MDP priors into a prior-fitted neural network and employ model-agnostic meta-learning for fast adaptation to new target tasks. Experiments on real-world Covid and Cancer benchmarks and hyperparameter tuning tasks demonstrate that ProfBO consistently outperforms state-of-the-art methods by achieving high-quality solutions with significantly fewer evaluations, making it ready for practical deployment.

Understanding probabilistic relationships among variables is crucial for analyzing complex systems. Traditional structure learning methods often require extensive observational data and incur high computational costs. Recent studies have explored using large language models (LLMs) for structure learning, but most treat LLMs as auxiliary tools for pre-processing or post-processing, leaving the core learning process data-driven. In this work, we propose a unified framework for Bayesian network structure discovery that places LLMs at the center, supporting both data-free and data-aware settings. In the data-free case, we introduce \textbf{PromptBN} to query LLMs with metadata and efficiently uncover valid probabilistic relationships. When observational data are available, we introduce \textbf{ReActBN}, which integrates the ReAct reasoning paradigm with structure scores such as the Bayesian Information Criterion (BIC) for iterative refinement. Unlike prior methods that offload refinement to external algorithms, our framework maintains the LLM actively in the loop throughout the discovery process. Experiments demonstrate that our method significantly outperforms both existing LLM-based approaches and traditional data-driven algorithms, particularly in the low- or no-data scenario. Code is publicly available at {\texttt{\textcolor{magenta}{https://github.com/sherryzyh/prompt2bn}}}.

Sliding window-factor graph optimization (SW-FGO) has gained more and more attention in navigation research due to its robust approximation to non-Gaussian noises and nonlinearity of measuring models. There are lots of works focusing on its application performance compared to extended Kalman filter (EKF) but there is still a myth at the theoretical relationship between the SW-FGO and EKF. In this paper, we find the necessarily fair condition to connect SW-FGO and Kalman filter variants (KFV) (e.g., EKF, iterative EKF (IEKF), robust EKF (REKF) and robust iterative EKF (RIEKF)). Based on the conditions, we propose a recursive FGO (Re-FGO) framework to represent KFV under SW-FGO formulation. Under explicit conditions (Markov assumption, Gaussian noise with L2 loss, and a one-state window), Re-FGO regenerates exactly to EKF/IEKF/REKF/RIEKF, while SW-FGO shows measurable benefits in nonlinear, non-Gaussian regimes at a predictable compute cost. Finally, after clarifying the connection between them, we highlight the unique advantages of SW-FGO in practical phases, especially on numerical estimation and deep learning integration. The code and data used in this work is open sourced at https://github.com/Baoshan-Song/KFV-FGO-Comparison.

Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural networks (PaTraC BNNs) that enable uncertainty quantification comparable to standard BNNs but use significantly fewer Bayesian parameters. These PaTraC BNNs have computational and statistical advantages over standard Bayesian neural networks in terms of speed and memory requirements. Our proposed methodology therefore facilitates reliable, robust, and scalable uncertainty quantification in neural networks. The three architectures build on trace-class neural network priors which induce an ordering of the neural network parameters, and are thus a natural choice in our framework. In a numerical simulation study, we verify the claimed benefits, and further illustrate the performance of our proposed methodology on a real-world dataset.

Medical imaging relies heavily on large, labeled datasets. But, unfortunately, they are not always easily accessible in clinical settings. Additionally, many practitioners often face various structural obstacles like limited data availability, fragmented data systems, and unbalanced datasets. These barriers often lead to the increased diagnostic uncertainty, underrepresentation of certain conditions, reduced model robustness, and biased diagnostic decisions. In response to these challenges, approaches such as transfer learning, meta-learning, and multimodal fusion have made great strides. However, they still need a solid theoretical justification for why they succeed or fail in situations where data is scarce. To address this gap, we propose a unified theoretical framework that characterizes learning and inference under low-resource medical imaging conditions. We first formalize the learning objective under few-shot conditions and compute sample complexity constraints to estimate the smallest quantity of data needed to achieve clinically reliable accuracy. Then based on ideas from PAC-learning and PAC-Bayesian theory, we explain how multimodal integration encourages generalization and quantifies uncertainty under sparse supervision. We further propose a formal metric for explanation stability, offering interpretability guarantees under low-data conditions. Taken together, the proposed framework establishes a principled foundation for constructing dependable, data-efficient diagnostic systems by jointly characterizing sample efficiency, uncertainty quantification, and interpretability in a unified theoretical setting.

Data for training structural health monitoring (SHM) systems are often expensive and/or impractical to obtain, particularly for labelled data. Population-based SHM (PBSHM) aims to address this limitation by leveraging data from multiple structures. However, data from different structures will follow distinct distributions, potentially leading to large generalisation errors for models learnt via conventional machine learning methods. To address this issue, transfer learning -- in the form of domain adaptation (DA) -- can be used to align the data distributions. Most previous approaches have only considered \emph{unsupervised} DA, where no labelled target data are available; they do not consider how to incorporate these technologies in an online framework -- updating as labels are obtained throughout the monitoring campaign. This paper proposes a Bayesian framework for DA in PBSHM, that can improve unsupervised DA mappings using a limited quantity of labelled target data. In addition, this model is integrated into an active sampling strategy to guide inspections to select the most informative observations to label -- leading to further reductions in the required labelled data to learn a target classifier. The effectiveness of this methodology is evaluated on a population of experimental bridges. Specifically, this population includes data corresponding to several damage states, as well as, a comprehensive set of environmental conditions. It is found that combining transfer learning and active learning can improve data efficiency when learning classification models in label-scarce scenarios. This result has implications for data-informed operation and maintenance of structures, suggesting a reduction in inspections over the operational lifetime of a structure -- and therefore a reduction in operational costs -- can be achieved.

Harmful fine-tuning poses critical safety risks to fine-tuning-as-a-service for large language models. Existing defense strategies preemptively build robustness via attack simulation but suffer from fundamental limitations: (i) the infeasibility of extending attack simulations beyond bounded threat models due to the inherent difficulty of anticipating unknown attacks, and (ii) limited adaptability to varying attack settings, as simulation fails to capture their variability and complexity. To address these challenges, we propose Bayesian Data Scheduler (BDS), an adaptive tuning-stage defense strategy with no need for attack simulation. BDS formulates harmful fine-tuning defense as a Bayesian inference problem, learning the posterior distribution of each data point's safety attribute, conditioned on the fine-tuning and alignment datasets. The fine-tuning process is then constrained by weighting data with their safety attributes sampled from the posterior, thus mitigating the influence of harmful data. By leveraging the post hoc nature of Bayesian inference, the posterior is conditioned on the fine-tuning dataset, enabling BDS to tailor its defense to the specific dataset, thereby achieving adaptive defense. Furthermore, we introduce a neural scheduler based on amortized Bayesian learning, enabling efficient transfer to new data without retraining. Comprehensive results across diverse attack and defense settings demonstrate the state-of-the-art performance of our approach. Code is available at https://github.com/Egg-Hu/Bayesian-Data-Scheduler.

Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered optimal? We propose a theoretical framework that casts learning rules as policies for navigating (partially observable) loss landscapes, and identifies optimal rules as solutions to an associated optimal control problem. A range of well-known rules emerge naturally within this framework under different assumptions: gradient descent from short-horizon optimization, momentum from longer-horizon planning, natural gradients from accounting for parameter space geometry, non-gradient rules from partial controllability, and adaptive optimizers like Adam from online Bayesian inference of loss landscape shape. We further show that continual learning strategies like weight resetting can be understood as optimal responses to task uncertainty. By unifying these phenomena under a single objective, our framework clarifies the computational structure of learning and offers a principled foundation for designing adaptive algorithms.

Generative Adversarial Networks (GANs) are proficient at generating synthetic data but continue to suffer from mode collapse, where the generator produces a narrow range of outputs that fool the discriminator but fail to capture the full data distribution. This limitation is particularly problematic, as generative models are increasingly deployed in real-world applications that demand both diversity and uncertainty awareness. In response, we introduce BI-DCGAN, a Bayesian extension of DCGAN that incorporates model uncertainty into the generative process while maintaining computational efficiency. BI-DCGAN integrates Bayes by Backprop to learn a distribution over network weights and employs mean-field variational inference to efficiently approximate the posterior distribution during GAN training. We establishes the first theoretical proof, based on covariance matrix analysis, that Bayesian modeling enhances sample diversity in GANs. We validate this theoretical result through extensive experiments on standard generative benchmarks, demonstrating that BI-DCGAN produces more diverse and robust outputs than conventional DCGANs, while maintaining training efficiency. These findings position BI-DCGAN as a scalable and timely solution for applications where both diversity and uncertainty are critical, and where modern alternatives like diffusion models remain too resource-intensive.