Connectionists: Fwd: New on the VVTNS YouTube channel : Equilibrium Geometry and Chaotic Dynamics in Large Recurrent Neural Networks | Giancarlo La Camera , Stony Brook University

[David Hansel]

[image: VVTNS.png]

>
> <https://84454458.streak-link.com/C_KL58US0gMxir-acw5GfowJ/https%3A%2F%2Fwww.wwtns.online>
>
https://www.wwtns.online
> <https://streaklinks.com/A9c7PbbpKY7PxB6PaAJWGD3-/https%3A%2F%2Fwww.wwtns.online>
> - on twitter: wwtns at TheoreticalWide  and on YouTube
>

New on the VVTNS Website and YouTube Channel
https://www.wwtns.online
<https://streaklinks.com/A9c7PbbpKY7PxB6PaAJWGD3-/https%3A%2F%2Fwww.wwtns.online>


Equilibrium Geometry and Chaotic Dynamics in  Large Recurrent Neural
Networks

lecture delivered on May 27,  2026  by

Giancarlo La Camera

 Stony Brook University

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 : *
*VVTNS  is a weekly digital seminar on Zoom targeting the theoretical
neuroscience community. Launched as the World Wide Neuroscience Seminar
(WWTNS) in November 2020 and renamed in homage to Carl van Vreeswijk in
Memoriam (April 20, 2022), its aim is to be a platform to exchange ideas
among theoreticians, but not only. 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  are 45 min long followed by a discussion and are held on
Wednesdays at 11 am ET. The talks are recorded with authorization of the
speaker and are available to everybody on our YouTube channel.*
ᐧ
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mailman.srv.cs.cmu.edu/pipermail/connectionists/attachments/20260804/bf0fc4ba/attachment.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: VVTNS.png
Type: image/png
Size: 41084 bytes
Desc: not available
URL: <http://mailman.srv.cs.cmu.edu/pipermail/connectionists/attachments/20260804/bf0fc4ba/attachment.png>