1 citations · 1 across the 2 of their papers we have counts for
7 papers
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…
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…