arXiv Machine Learning By Tomonaga Okabe, Kazuhiko Komatsu

Knowledge Manifold: A Riemannian Geometric Framework for Semantic Mapping and Geodesic Analysis of Scientific Literature

Read the original on arXiv Machine Learning →

arXiv:2606. 05907v1 Announce Type: cross Abstract: We present the knowledge manifold: a Riemannian geometric space in which a corpus of documents is arranged according to semantic positional relationships derived from character n-gram TF-IDF representations.

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arXiv Machine Learning
1d ago

Iso-Riemannian Optimization on Learned Data Manifolds

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 Machine Learning
Aug 4

GeoFlowVLM: Geometry-Aware Joint Uncertainty for Frozen Vision-Language Embedding

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