Work

Identifiability of points and rigidity of hypergraphs under algebraic constraints

Year: 2026

Type: article

Abstract: The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially‐filled tensors subject to rank conditions. The identifiability of points on secant varieties has also been a topic of much research in algebraic geometry. It is often formulated as the problem of identifying a set of points satisfying a given set of algebraic relations. A key question then is to prove sufficient conditions for relations to guarantee the identifiability of the points. This paper proposes a new general framework for capturing the identifiability problem when a set of algebraic relations has a combinatorial structure and develops tools to analyse the impact of the underlying combinatorics on the local or global identifiability of points. Our framework is built on the language of graph rigidity, where the measurements are Euclidean distances between two points, but applicable in the generality of hypergraphs with arbitrary algebraic measurements. We establish necessary and sufficient (hyper)graph‐theoretical conditions for identifiability by exploiting techniques from graph rigidity theory and algebraic geometry of secant varieties. In particular our work analyses combinatorially the effect of non‐generic projections of secant varieties.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70633

Authors: James Cruickshank, Fatemeh Mohammadi, Anthony Nixon, Shin‐ichi Tanigawa

Institutions: Ollscoil na Gaillimhe – University of Galway, KU Leuven, Lancaster University, Tokyo University of Science

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930