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.
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.
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.
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.
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).
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.
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
arXiv:2512. 07355v2 Announce Type: replace Abstract: Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge.
arXiv:2209. 15130v3 Announce Type: replace-cross Abstract: We study a general matrix optimization problem with a fixed-rank positive semidefinite (PSD) constraint.
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
Many representation learning problems involve directed relations, such as lexical entailment, sentence entailment, ontology hierarchy, and citation links. Standard Euclidean, cosine, and Mahalanobis heads are symmetric, while generic neural scorers can model directionality but provide limited geometric structure.
Multimodal large language models (MLLMs) have advanced image geolocalization mainly by improving how they reason about geographic cues. How that reasoning isdecoded into coordinates, however, has lagged behind.
arXiv:2608. 01283v1 Announce Type: new Abstract: All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al.