Fixed points of competitive threshold-linear networks

04/01/2018
by   Carina Curto, et al.
0

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 connectivity. The set of fixed points of a TLN, including both stable and unstable equilibria, plays a critical role in shaping its emergent dynamics. In this work, we provide two novel characterizations for the set of fixed points of competitive TLNs: the first is in terms of a simple sign condition corresponding to each fixed point support; while the second introduces the concept of domination. We then apply these results to a special family of TLNs, called combinatorial threshold-linear networks (CTLNs), whose connectivity matrix is defined from just two continuous parameters and a directed graph. This leads us to a set of graph rules that enable us to determine fixed points for a CTLN that are independent of the parameters, and can be inferred directly from the underlying graph. Our results thus provide the foundation for a kind of "graphical calculus" to infer features of the dynamics from a network's connectivity.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/15/2022

Fixed-Point Centrality for Networks

This paper proposes a family of network centralities called fixed-point ...
research
02/04/2022

Fixed-Point Code Synthesis For Neural Networks

Over the last few years, neural networks have started penetrating safety...
research
12/04/2019

On stability of users equilibria in heterogeneous routing games

The asymptotic behaviour of deterministic logit dynamics in heterogeneou...
research
01/12/2020

Distributed Fixed Point Method for Solving Systems of Linear Algebraic Equations

We present a class of iterative fully distributed fixed point methods to...
research
09/04/2023

Dynamical Stability of Threshold Networks over Undirected Signed Graphs

In this paper we study the dynamic behavior of threshold networks on und...
research
02/12/2002

Threshold Disorder as a Source of Diverse and Complex Behavior in Random Nets

We study the diversity of complex spatio-temporal patterns in the behavi...
research
04/04/2019

Boolean analysis of lateral inhibition

We study Boolean networks which are simple spatial models of the highly ...

Please sign up or login with your details

Forgot password? Click here to reset