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.
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.
arXiv:2609.10305v1 Announce Type: new Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transfor...
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
The paper introduces a pullback Riemannian geometry tailored for multimodal data by employing a latent Gaussian mixture model. It defines a smooth, positive‑definite metric based on responsibility‑weighted component precision, extending the standard single‑Gaussian construction. Experiments on synthetic, multi‑view image, and MNIST datasets demonstrate reduced transport distortion, accurate trajectory recovery, and more realistic interpolation.
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.