413 citations · 466 across the 22 of their papers we have counts for
29 papers
Graph rules for recurrent neural network dynamics: extended version
Carina Curto, Katherine Morrison
This is an extended version of our survey article, "Graph rules for recurrent neural network dynamics," to appear in the April 2023 edition of the Notices of the AMS. It includes a…
Sequence generation in inhibition-dominated neural networks
Caitlyn Parmelee, Juliana Londono Alvarez, Carina Curto +1
This is a brief overview of results from [arXiv:2107.10244, ref 11], on network architectures that produce sequential dynamics in a special family of inhibition-dominated neural ne…
Core motifs predict dynamic attractors in combinatorial threshold-linear networks
Caitlyn Parmelee, Samantha Moore, Katherine Morrison +1
Combinatorial threshold-linear networks (CTLNs) are a special class of inhibition-dominated TLNs defined from directed graphs. Like more general TLNs, they display a wide variety o…
Sequential attractors in combinatorial threshold-linear networks
Caitlyn Parmelee, Juliana Londono Alvarez, Carina Curto +1
Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. Whil…
Betti Curves of Rank One Symmetric Matrices
Carina Curto, Joshua Paik, Igor Rivin
Betti curves of symmetric matrices were introduced in (Giusti et. al., 2015) as a new class of matrix invariants that depend only on the relative ordering of matrix entries. These…
Nerve theorems for fixed points of neural networks
Daniela Egas Santander, Stefania Ebli, Alice Patania +4
Nonlinear network dynamics are notoriously difficult to understand. Here we study a class of recurrent neural networks called combinatorial threshold-linear networks (CTLNs) whose…