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Measure-to-measure interpolation using Transformers

arXiv:2411.04551v2 Announce Type: replace-cross Abstract: Transformers are deep neural network architectures that underpin the recent successes of large language models. Unlike more classical architectures that can be viewed as point-to-point maps, a Transformer acts as a measure-to-measure map implemented as…

Kernel K-means clustering of distributional data

arXiv:2509.18037v1 Announce Type: new Abstract: We consider the problem of clustering a sample of probability distributions from a random distribution on $mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing kernel…

Learning Centre Partitions from Summaries

arXiv:2509.16337v1 Announce Type: cross Abstract: Multi-centre studies increasingly rely on distributed inference, where sites share only centre-level summaries. Homogeneity of parameters across centres is often violated, motivating methods that both emph{test} for equality and emph{learn} centre groupings before estimation. We…

Hierarchical Retrieval: The Geometry and a Pretrain-Finetune Recipe

arXiv:2509.16411v1 Announce Type: cross Abstract: Dual encoder (DE) models, where a pair of matching query and document are embedded into similar vector representations, are widely used in information retrieval due to their simplicity and scalability. However, the Euclidean geometry of…

Overfitting in Adaptive Robust Optimization

arXiv:2509.16451v1 Announce Type: cross Abstract: Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty – weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous constraints that were independent…