21 citations · 29 across the 12 of their papers we have counts for
18 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…
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…
Combinatorial Geometry of Threshold-Linear Networks
Carina Curto, Christopher Langdon, Katherine Morrison
The architecture of a neural network constrains the potential dynamics that can emerge. Some architectures may only allow for a single dynamic regime, while others display a great…
Stable fixed points of combinatorial threshold-linear networks
Carina Curto, Jesse Geneson, Katherine Morrison
Combinatorial threshold-linear networks (CTLNs) are a special class of recurrent neural networks whose dynamics are tightly controlled by an underlying directed graph. Recurrent ne…
Robust motifs of threshold-linear networks
Carina Curto, Christopher Langdon, Katherine Morrison
To any inhibition-dominated threshold-linear network (TLN) we can associate a directed graph that captures the pattern of strong and weak inhibition between neurons. Robust motifs…
Algebraic signatures of convex and non-convex codes
Carina Curto, Elizabeth Gross, Jack Jeffries +4
A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as t…
Predicting neural network dynamics via graphical analysis
Katherine Morrison, Carina Curto
Neural network models in neuroscience allow one to study how the connections between neurons shape the activity of neural circuits in the brain. In this chapter, we study Combinato…
Fixed points of competitive threshold-linear networks
Carina Curto, Jesse Geneson, Katherine Morrison
Threshold-linear networks (TLNs) are models of neural networks that consist of simple, perceptron-like neurons and exhibit nonlinear dynamics that are determined by the network's c…
Sobolev subspaces of nowhere bounded functions
Pier Domenico Lamberti, Giorgio Stefani
We prove that in any Sobolev space which is subcritical with respect to the Sobolev Embedding Theorem there exists a closed infinite dimensional linear subspace whose non zero elem…
Pattern completion in symmetric threshold-linear networks
Carina Curto, Katherine Morrison
Threshold-linear networks are a common class of firing rate models that describe recurrent interactions among neurons. Unlike their linear counterparts, these networks generically…
What makes a neural code convex?
Carina Curto, Elizabeth Gross, Jack Jeffries +5
Neural codes allow the brain to represent, process, and store information about the world. Combinatorial codes, comprised of binary patterns of neural activity, encode information…
An Enumeration of the Equivalence Classes of Self-Dual Matrix Codes
Katherine Morrison
As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, th…
Cyclic Orbit Codes and Stabilizer Subfields
Heide Gluesing-Luerssen, Katherine Morrison, Carolyn Troha
Cyclic orbit codes are constant dimension subspace codes that arise as the orbit of a cyclic subgroup of the general linear group acting on subspaces in the given ambient space. Wi…
Equivalence for Rank-metric and Matrix Codes and Automorphism Groups of Gabidulin Codes
Katherine Morrison
For a growing number of applications such as cellular, peer-to-peer, and sensor networks, efficient error-free transmission of data through a network is essential. Toward this end,…
Combinatorial neural codes from a mathematical coding theory perspective
Carina Curto, Vladimir Itskov, Katherine Morrison +2
Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on t…