166 citations · 655 across the 82 of their papers we have counts for
118 papers
Incoherent filter banks
William J. Brinkley, Matthew Fickus, John Jasper +1
Equi-isoclinic (EI) and equichordal (EC) tight fusion frames (TFFs) are types of minimally coherent (maximally orthogonal) subspace packings that arise in several applications, suc…
Transversal Pooling Neural Networks
Emily J. King, Dustin G. Mixon, Michael Perlmutter +1
Many learning tasks require stability to small transformations while retaining sensitivity to larger ones. We introduce \emph{transversal pooling neural networks}, which generalize…
Towards a mathematical theory of superposition
Michael I. Ivanitskiy, John Jasper, Emily J. King +1
We develop a mathematical theory of superposition in neural networks using tools from frame theory and compressed sensing. In our model, a sparse binary vector \(x\) of active feat…
HRT counterexamples with exponential tails
John Jasper, Dustin G. Mixon
We build on the recent breakthrough of Faulhuber, Petersen, van Velthoven, and Voigtlaender that disproved the HRT conjecture with a Schwartz function and a -point configuratio…
Short spherical -design curves
Emily J. King, Dustin G. Mixon
We study the minimum arclength of spherical -design curves, i.e., closed rectifiable curves on whose normalized arclength measure exactly integrates every polynomial of de…
The Singer-Zauner gap for equiangular tight frames
Matthew Fickus, John Jasper, Dustin G. Mixon
We show that there does not exist a complex equiangular tight frame with \[ d^2-d+1<n<d^2. \] The proof, which originated from an internal model at OpenAI, mimics the r…