arXiv:2512.16875v3 Announce Type: replace-cross Abstract: We study the problem of finding confidence ellipsoids for an arbitrary distribution in high dimensions. Given samples from a distribution $mathcal{D}$ and a confidence parameter $alpha$, the goal is to find the smallest volume ellipsoid $E$ which has probability mass $Pr_{mathcal{D}}[E] ge 1-alpha$. Ellipsoids are a highly expressive class of confidence sets as they can capture correlations in the distribution, and can approximate any convex set. This problem has been studied in many […]

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Bayesian principal component analysis (BPCA), a probabilistic reformulation of PCA with Bayesian model selection, is a systematic approach to determining the number of essential principal components (PCs) for data representation. However, it assumes that data are Gaussian distributed and thus it cannot handle all types of practical observations, e.g. integers and binary values. In this paper, we propose simple exponential family PCA (SePCA), a generalised family of probabilistic principal component analysers. SePCA employs exponential family distributions to handle […]

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The capabilities of generative AI in mathematics education are rapidly evolving, posing significant challenges for research to keep pace. Research syntheses remain scarce and risk being outdated by the time of publication. To address this issue, we present a Living Meta-Analysis (LIMA) on the effects of generative AI-based interventions for learning mathematics. Following PRISMA-LSR guidelines, we continuously update the literature base, apply a Bayesian multilevel meta-regression model to account for cumulative data, and publish updated versions on a […]

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14.ai also launched a consumer brand to understand how much AI can handle customer support tasks.

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In this tutorial, we build a hierarchical planner agent using an open-source instruct model. We design a structured multi-agent architecture comprising a planner agent, an executor agent, and an aggregator agent, where each component plays a specialized role in solving complex tasks. We use the planner agent to decompose high-level goals into actionable steps, the executor agent to execute those steps using reasoning or Python tool execution, and the aggregator agent to synthesize results into a coherent final […]

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A new approach to regression regularization called the Pairwise Elastic Net is proposed. Like the Elastic Net, it simultaneously performs automatic variable selection and continuous shrinkage. In addition, the Pairwise Elastic Net encourages the grouping of strongly correlated predictors based on a pairwise similarity measure. We give examples of how the Pairwise Elastic Net can be used to achieve the objectives of Ridge regression, the Lasso, the Elastic Net, and Group Lasso. Finally, we present a coordinate descent […]

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arXiv:2602.18532v1 Announce Type: new Abstract: Following the rise of large foundation models, Vision-Language-Action models (VLAs) emerged, leveraging strong visual and language understanding for general-purpose policy learning. Yet, the current VLA landscape remains fragmented and exploratory. Although many groups have proposed their own VLA models, inconsistencies in training protocols and evaluation settings make it difficult to identify which design choices truly matter. To bring structure to this evolving space, we reexamine the VLA design space under a unified framework […]

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arXiv:2601.22364v1 Announce Type: new Abstract: Large Language Models (LLMs) have been shown to organize the representations of input sequences into straighter neural trajectories in their deep layers, which has been hypothesized to facilitate next-token prediction via linear extrapolation. Language models can also adapt to diverse tasks and learn new structure in context, and recent work has shown that this in-context learning (ICL) can be reflected in representational changes. Here we bring these two lines of research together to […]

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arXiv:2601.02540v1 Announce Type: new Abstract: We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry for both periodic and reflecting boundary conditions. The hyperbolic formulation avoids the costly inversion of an elliptic operator present in the classical model. Our schemes combine split forms with summation-by-parts (SBP) operators to construct semidiscretizations that conserve the total water mass and the total energy. We provide analytical proofs of these conservation properties and also verify […]

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arXiv:2602.15568v1 Announce Type: cross Abstract: The scenario approach is an established data-driven design framework that comes equipped with a powerful theory linking design complexity to generalization properties. In this approach, data are simultaneously used both for design and for certifying the design’s reliability, without resorting to a separate test dataset. This paper takes a step further by guaranteeing additional properties, useful in post-design usage but not considered during the design phase. To this end, we introduce a two-level […]

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