Graphical Domination and Inhibitory Control in Neural Networks

Explore the mathematical foundations of recurrent neural networks through the lens of graph theory in this Coxeter Lecture Series presentation. Discover how directed graphs model neural network dynamics and learn about the crucial concept of graphical domination that shapes emergent behaviors in these systems. Examine key theorems demonstrating how domination principles enable the reduction of complex graphs to smaller equivalent networks while maintaining their essential dynamical properties. Investigate the construction of larger, predictable networks by chaining together reducible graph modules and understand how these architectures respond to inhibitory pulse control. Delve into the application of these theoretical frameworks, originally developed for threshold-linear networks with effective inhibition, to excitatory-inhibitory (E-I) networks featuring global inhibition, revealing universal principles that govern neural network dynamics across different architectural paradigms.