David Clark, PhD

Group Leader and Associate Research Scientist
Flatiron Institute, Center for Computational Neuroscience
Simons Foundation 

Host: Larry Abbott (Faculty)

Wrapping our minds around high-dimensional neural circuit dynamics

Neural circuits are high-dimensional nonlinear dynamical systems, and such systems are notoriously difficult to understand. I will discuss one such system that we can understand: the chaotic random neural network introduced by Sompolinsky, Crisanti, and Sommers in 1988, whose activity can be analyzed in the limit of many neurons using methods from theoretical physics. Nearly four decades after its introduction, this model, much like the biological circuits it approximates, remains an incredibly rich source of theoretical discoveries. I will review several of these discoveries, from the transition to chaos to the dimensionality of the network’s activity. I will then describe work posted less than two weeks ago in which AI models and I unraveled a central problem posed in the original 1988 paper: the calculation of the network’s full Lyapunov spectrum. I will conclude by speculating on how human–AI collaboration may shape our efforts to wrap our minds around the high-dimensional dynamics of the brain.

Relevant Publications: 
Chaos in Random Neural Networks
Lyapunov spectrum of random neural networks

Tuesdays@10 is a signature Zuckerman Institute initiative that aims to expose researchers at all levels to high-quality science and stimulate scientific discourse. The speakers featured in this series represent various fields and techniques in neuroscience, and include invited guests of the Columbia Neuroscience Seminars, the Zuckerman Institute's Local Circuits Affiliates Program, and other special seminar series through a combined, collaborative effort of one or more of the following: Columbia's Zuckerman Institute, the Center for Precision Psychiatry, the Center for Theoretical Neuroscience, the Department of Neuroscience, the Doctoral Program in Neurobiology and Behavior and the Columbia Translational Neuroscience Initiative, and with support from the Kavli Institute for Brain Science. 

More information and a full schedule can be found here.