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
The paper investigates whether natural language text possesses an intrinsic curvature, proposing a new metric called Texture that captures word-level discrete curvature. Texture is defined as a signed two-axis curvature of the word-in-context belief field, measuring how context from one side contracts or expands the semantic effect of context from the other side. The authors provide empirical and theoretical evidence of non-flat semantic inference, define Texture formally, and demonstrate its practical utility in improving long-context inference and retrieval-augmented generation.
By Karish Grover, Hanqing Zeng, Yinglong Xia, Christos Faloutsos, Geoffrey J. Gordon