Connectionists: World wide VVTNS series (6th season): Equilibrium Geometry and Chaotic Dynamics in Large Recurrent Neural Networks | Giancarlo La Camera, Stonybrook University| Wednesday, May 27, 2026, at 11:00 am ET

[David Hansel]

[image: VVTNS.png]
https://www.wwtns.online
<https://streaklinks.com/A9c7PbbpKY7PxB6PaAJWGD3-/https%3A%2F%2Fwww.wwtns.online>
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on twitter: wwtns at TheoreticalWide

You are cordially invited to the lecture

Giancarlo La Camera

Stonybrook University

 on the topic of

 Equilibrium Geometry and Chaotic Dynamics in Large Recurrent Neural
Networks



The lecture will be held on Zoom on May 27, 2026 at *11:00 am ET *

> To receive the link: https://www.wwtns.online/register-page
>

*Abstract: *Large recurrent networks are important models in several
fields, including neuroscience, machine learning, physics, and applied
mathematics. Yet their dynamics are difficult to study directly, because
high-dimensional nonlinear systems can exhibit rich behavior that is hard
to summarize in terms of individual trajectories. In this talk, I will
discuss an approach that seeks to understand such dynamics through the
structure of the network’s equilibria. I will focus on a random balanced
network of threshold-linear units that undergoes a transition from a single
stable equilibrium to extensive chaos as the disorder strength crosses a
critical value. Using a combination of Kac–Rice theory, replica
calculations, numerical root-finding, and dynamical mean-field theory, we
show that the chaotic regime contains an exponentially large number of
equilibria. These equilibria are all saddles, but with only a fractionally
small number of unstable directions. Surprisingly, despite the completely
random connectivity, the equilibria are not scattered randomly through
phase space. Instead, they are strongly correlated and confined to a
comparatively small region. The chaotic attractor lies within this same
region, suggesting a direct geometric link between the organization of
unstable equilibria and the collective structure of the dynamics. This
picture helps explain why networks with extensive chaos can nevertheless
display dynamics dominated by a relatively small number of collective
modes. More broadly, the results suggest that the geometry of equilibria
provides a useful complementary perspective to dynamical mean-field theory
for understanding high-dimensional neural dynamics.


*About VVTNS : Launched as the World Wide  Theoretical Neuroscience Seminar
(WWTNS) in November 2020 and renamed in homage to Carl van Vreeswijk in
Memoriam (April 20, 2022), Speakers have the occasion to talk about
theoretical aspects of their work which cannot be discussed in a setting
where the majority of the audience consists of experimentalists. The
seminars, **held on Wednesdays at 11 am ET,**  are 45-50 min long followed
by a discussion. The talks are recorded with authorization of the speaker
and are available to everybody on our YouTube channel.*


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