Bayesian quadrature is a probabilistic, model-based approach to numerical integration, the estimation of intractable integrals, or expectations. Although Bayesian quadrature was popularised already in the 1980s, no systematic and comprehensive treatment has been published. The purpose of this survey is to fill this gap. We review the mathematical foundations of Bayesian quadrature from different points of view; present a systematic taxonomy for classifying different Bayesian quadrature methods along the three axes of modelling, inference, and sampling; collect general theoretical guarantees; and provide a controlled numerical study that explores and illustrates the effect of different choices along the axes of the taxonomy. We also provide a realistic assessment of practical challenges and limitations to application of Bayesian quadrature methods and include an up-to-date and nearly exhaustive bibliography that covers not only machine learning and statistics literature but all areas of mathematics and engineering in which Bayesian quadrature or equivalent methods have seen use.

This paper addresses the challenging computational problem of estimating intractable expectations over discrete domains. Existing approaches, including Monte Carlo and Russian Roulette estimators, are consistent but often require a large number of samples to achieve accurate results. We propose a novel estimator, \emph{BayesSum}, which is an extension of Bayesian quadrature to discrete domains. It is more sample efficient than alternatives due to its ability to make use of prior information about the integrand through a Gaussian process. We show this through theory, deriving a convergence rate significantly faster than Monte Carlo in a broad range of settings. We also demonstrate empirically that our proposed method does indeed require fewer samples on several synthetic settings as well as for parameter estimation for Conway-Maxwell-Poisson and Potts models.

Generative artificial intelligence (GenAI) has become a transformative approach in bioinformatics that often enables advancements in genomics, proteomics, transcriptomics, structural biology, and drug discovery. To systematically identify and evaluate these growing developments, this review proposed six research questions (RQs), according to the preferred reporting items for systematic reviews and meta-analysis methods. The objective is to evaluate impactful GenAI strategies in methodological advancement, predictive performance, and specialization, and to identify promising approaches for advanced modeling, data-intensive discovery, and integrative biological analysis. RQ1 highlights diverse applications across multiple bioinformatics subfields (sequence analysis, molecular design, and integrative data modeling), which demonstrate superior performance over traditional methods through pattern recognition and output generation. RQ2 reveals that adapted specialized model architectures outperformed general-purpose models, an advantage attributed to targeted pretraining and context-aware strategies. RQ3 identifies significant benefits in the bioinformatics domains, focusing on molecular analysis and data integration, which improves accuracy and reduces errors in complex analysis. RQ4 indicates improvements in structural modeling, functional prediction, and synthetic data generation, validated by established benchmarks. RQ5 suggests the main constraints, such as the lack of scalability and biases in data that impact generalizability, and proposes future directions focused on robust evaluation and biologically grounded modeling. RQ6 examines that molecular datasets (such as UniProtKB and ProteinNet12), cellular datasets (such as CELLxGENE and GTEx) and textual resources (such as PubMedQA and OMIM) broadly support the training and generalization of GenAI models.

Robo-advisors (RAs) are cost-effective, bias-resistant alternatives to human financial advisors, yet adoption remains limited. While prior research has examined user interactions with RAs, less is known about how individuals interpret RA roles and integrate their advice into decision-making. To address this gap, this study employs a multiphase mixed methods design integrating a behavioral experiment (N = 334), thematic analysis, and follow-up quantitative testing. Findings suggest that people tend to rely on RAs, with reliance shaped by information about RA performance and the framing of advice as gains or losses. Thematic analysis reveals three RA roles in decision-making and four user types, each reflecting distinct patterns of advice integration. In addition, a 2 x 2 typology categorizes antecedents of acceptance into enablers and inhibitors at both the individual and algorithmic levels. By combining behavioral, interpretive, and confirmatory evidence, this study advances understanding of human-RA collaboration and provides actionable insights for designing more trustworthy and adaptive RA systems.

Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability and poor convergence, which hinder effective rate coefficient estimation using learning-based approaches. To address this, we propose a Stiff Physics-Informed N eural ODE framework (SPIN-ODE) for chemical reaction modelling. Our method introduces a three-stage optimisation process: first, a black-box neural ODE is trained to fit concentration trajectories; second, a Chemical Reaction Neural Network (CRNN) is pre-trained to learn the mapping between concentrations and their time derivatives; and third, the rate coefficients are fine-tuned by integrating with the pre-trained CRNN. Extensive experiments on both synthetic and newly proposed real-world datasets validate the effectiveness and robustness of our approach. As the first work addressing stiff neural ODE for chemical rate coefficient discovery, our study opens promising directions for integrating neural networks with detailed chemistry.

This paper investigates the enhancement of reasoning capabilities in language models through token-level multi-model collaboration. Our approach selects the optimal tokens from the next token distributions provided by multiple models to perform autoregressive reasoning. Contrary to the assumption that more models yield better results, we introduce a distribution distance-based dynamic selection strategy (DDS) to optimize the multi-model collaboration process. To address the critical challenge of vocabulary misalignment in multi-model collaboration, we propose the concept of minimal complete semantic units (MCSU), which is simple yet enables multiple language models to achieve natural alignment within the linguistic space. Experimental results across various benchmarks demonstrate the superiority of our method. The code will be available at https://github.com/Fanye12/DDS.

--Retrieval-Augmented Generation (RAG) has emerged as a powerful approach to boost the capabilities of large language models (LLMs) by incorporating external, up-to-date knowledge sources. However, this introduces a potential vulnerability to knowledge poisoning attacks, where attackers can compromise the knowledge source to mislead the generation model. One such attack is the PoisonedRAG in which the injected adversarial texts steer the model to generate an attacker chosen response for a target question. In this work, we propose novel defense methods, FilterRAG and ML-FilterRAG, to mitigate the PoisonedRAG attack. First, we propose a new property to uncover distinct properties to differentiate between adversarial and clean texts in the knowledge data source. Next, we employ this property to filter out adversarial texts from clean ones in the design of our proposed approaches. Evaluation of these methods using benchmark datasets demonstrate their effectiveness, with performances close to those of the original RAG systems. KEY challenge associated with large language models (LLMs) [1]-[3] is their tendency of becoming outdated and struggling to integrate the most recent knowledge [4], [5]. This fundamental short-coming is addressed by the recent emergency of retrieval-augmented generation (RAG) [6]-[9].