5 papers
Spectral origin of the topological gap exponent d + η: mechanism, kernel, decomposition, and scope
Matthew Loftus
The topological gap -- the excess total persistence of a critical point cloud over a density-matched null -- scales as . We derive this analytically: the s…
The topological gap at criticality: scaling exponent d + η, universality, and scope
Matthew Loftus
The topological gap -- the excess total persistence of the majority-spin alpha complex over a density-matched null -- encodes critical…
How much of persistent homology is topology? A quantitative decomposition for spin model phase transitions
Matthew Loftus
Point-cloud persistent homology (PH) -- computing alpha or Rips complexes on spin-position point clouds -- has been widely applied to detect phase transitions in classical spin mod…
Persistence diagrams of random matrices via Morse theory: universality and a new spectral diagnostic
Matthew Loftus
We prove that the persistence diagram of the sublevel set filtration of the quadratic form f(x) = x^T M x restricted to the unit sphere S^{n-1} is analytically determined by the ei…
Spectral Signatures of Data Quality: Eigenvalue Tail Index as a Diagnostic for Label Noise in Neural Networks
Matthew Loftus
We investigate whether spectral properties of neural network weight matrices can predict test accuracy. Under controlled label noise variation, the tail index alpha of the eigenval…