mlsanityData to 7 Oct 2026

Testing the variety hypothesis

arXiv 2507.16705 ↗First posted 22 Jul 2025math.AG math.MG math.STcited by 1

Not on the map. Why?

Abstract (arXiv)

Given a probability measure on the unit disk, we study the problem of deciding whether, for some threshold probability, this measure is supported near a real algebraic variety of given dimension and bounded degree. We call this "testing the variety hypothesis". We prove an upper bound on the so-called "sample complexity" of this problem and show how it can be reduced to a semialgebraic decision problem. This is done by studying in a quantitative way the Hausdorff geometry of the space of real algebraic varieties of a given dimension and degree.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 3 of its 16 references that are in the map. First posted on arXiv 22 Jul 2025.

Builds on

3 of 16 references.

References · 3

  1. 2013The Euclidean distance degree of an algebraic varietycited by 15
  2. 2023Covering Number of Real Algebraic Varieties and Beyond: Improved Bounds and Applicationscited by 7
  3. 2021Hausdorff approximations and volume of tubes of singular algebraic setscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Testing Algebraic Complete Intersectionscited by 0