mlsanityData to 14 Oct 2026

HADES: Fast Singularity Detection with Local Measure Comparison

arXiv 2311.04171 ↗First posted 7 Nov 2023cs.LG cs.AI math.ATcited by 4

Not on the map. Why?

Abstract (arXiv)

We introduce Hades, an unsupervised algorithm to detect singularities in data. This algorithm employs a kernel goodness-of-fit test, and as a consequence it is much faster and far more scaleable than the existing topology-based alternatives. Using tools from differential geometry and optimal transport theory, we prove that Hades correctly detects singularities with high probability when the data sample lives on a transverse intersection of equidimensional manifolds. In computational experiments, Hades recovers singularities in synthetically generated data, branching points in road network data, intersection rings in molecular conformation space, and anomalies in image data.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 2 of its 53 references that are in the map. First posted on arXiv 7 Nov 2023.

Builds on

2 of 53 references.

References · 2

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,898
  2. 2021Tangent Space and Dimension Estimation with the Wasserstein Distancecited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 3.

4 papers.

  1. 2025Token embeddings violate the manifold hypothesiscited by 16
  2. 2026Score Approximation for Diffusion Models on Arbitrary Low-Dimensional Structurescited by 1
  3. 2026Recovering Weighted Tangent Geometry from a Single-Scale Score Fieldcited by 1
  4. 2026Stratifying Reinforcement Learning with Signal Temporal Logiccited by 0