# Neighborhood Growth Determines Geometric Priors for Relational Representation Learning

arXiv: https://arxiv.org/abs/1910.05565 · HTML: https://mlsanity.com/paper/1910.05565/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2019.

## Built on by (most cited first, 7 of 7)

- [Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature](https://mlsanity.com/paper/2309.09384/) (2023)
- [Curvature-based Clustering on Graphs](https://mlsanity.com/paper/2307.10155/) (2023)
- [Effective Structural Encodings via Local Curvature Profiles](https://mlsanity.com/paper/2311.14864/) (2023)
- [Box Embeddings: An open-source library for representation learning using geometric structures](https://mlsanity.com/paper/2109.04997/) (2021)
- [FMGNN: Fused Manifold Graph Neural Network](https://mlsanity.com/paper/2304.01081/) (2023)
- [Towards Non-Euclidean Foundation Models: Advancing AI Beyond Euclidean Frameworks](https://mlsanity.com/paper/2505.14417/) (2025)
- [Automated Manifold Learning for Reduced Order Modeling](https://mlsanity.com/paper/2506.01741/) (2025)

## Abstract (arXiv)

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or trees, the heterogeneity of the relational data typically encountered in practice limits the applicability of these classical methods. In this paper, we propose a combinatorial approach to evaluating embeddability, i.e., to decide whether a data set is best represented in Euclidean, Hyperbolic or Spherical space. Our method analyzes nearest-neighbor structures and local neighborhood growth rates to identify the geometric priors of suitable embedding spaces. For canonical graphs, the algorithm's prediction provably matches classical results. As for large, heterogeneous graphs, we introduce an efficiently computable statistic that approximates the algorithm's decision rule. We validate our method over a range of benchmark data sets and compare with recently published optimization-based embeddability methods.