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