Peel neighborhoods

2026/03/27 by Steve Huntsman · 1 voice
Mathematics · #math.MG #math.AT

paper · pdf

arxiv published 2026/03/27 · arxiv updated 2026/07/13

Abstract

We introduce the canonical, parameter-free, and efficiently computable notion of peel neighborhoods in a finite metric space of strict negative type. Using a soft threshold to upper bound their radius or cardinality allows peel neighborhoods to be computed at scale, enabling useful microscopic descriptions of geometry and topology. As an example of their utility, peel neighborhoods enable efficient and performant estimates of local dimension and detections of singularities in samples from stratified manifolds.

Citations

• Geometric interpretation of magnitude
• The geometry of magnitude for finite metric spaces
• Peeling metric spaces of strict negative type
• Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform
• A Survey of Dimension Estimation Methods
• Sparsification and Reconstruction from the Perspective of Representation Geometry
• Unraveling the Localized Latents: Learning Stratified Manifold Structures in LLM Embedding Space with Sparse Mixture-of-Experts
• Manifold Diffusion Geometry: Curvature, Tangent Spaces, and Dimension
• The structure of the token space for large language models
• A theory of stratification learning
• HADES: Fast Singularity Detection with Local Measure Comparison
• Topological Singularity Detection at Multiple Scales
• Verifying the Union of Manifolds Hypothesis for Image Data
• Practical applications of metric space magnitude and weighting vectors
• Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs
• A distributed-memory package for dense Hierarchically Semi-Separable matrix computations using randomization
• The magnitude of metric spaces
• Heuristic and computer calculations for the magnitude of metric spaces
• Entropy and diversity

Discussions

• arxiv.org/abs/2603.26645 [bsky, 2 points, 0 comments]