arXiv:2602. 23665v5 Announce Type: replace-cross Abstract: We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search.
By Brandon Yee, Lucas Wang, Kundana Kommini
arXiv:2510. 21033v3 Announce Type: replace-cross Abstract: We develop a theory of iso-Riemannian optimization for problems constrained to learned data manifolds, a setting in which classical Riemannian optimization - and Riemannian gradient descent in particular - can be poorly suited.
By Willem Diepeveen, Melanie Weber
arXiv:2606. 03307v1 Announce Type: cross Abstract: Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference.
By Yifan Jin, Qirui Ji, Bin Qin, Jiangmeng Li, Lixiang Liu, Fuchun Sun, Changwen Zheng
arXiv:2605. 13352v2 Announce Type: replace Abstract: Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support).
By Mayank Nautiyal, Li Ju, Andreas Hellander, Ekta Vats, Prashant Singh
arXiv:2607. 13660v1 Announce Type: new Abstract: Contrastive Language-Image Pretraining (CLIP) representations form a semantic embedding space governed by cosine similarity, reflecting an intrinsic hyperspherical geometry.
By Zijie Yu, Gaowen Liu, Ramana Rao Kompella, Philip S. Yu, Yue Song
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
By Szczepan Konior, Alexandre Quemy, Przemys{\l}aw Klocek, Gr\'egoire Cattan, Bart{\l}omiej Sobieski