Francesco Bullo - Neural Circuits as Distributed Optimizers - Distinguished Lecture Series

Artificial and biological neural networks both perform complex computations through large collections of interacting units, yet they are designed and understood in very different ways. This talk develops a normative perspective in which recurrent neural circuits act as distributed optimizers, navigating energy landscapes to construct explanations of sensory input. The mathematical bridge is proximal gradient dynamics. Starting from a probabilistic model or regularized optimization objective, this framework derives the circuit’s prediction errors, recurrent interactions, and activation functions. It encompasses classical predictive coding as well as sparse, nonnegative, categorical, and non-Gaussian models, and extends naturally from single populations to hierarchical networks exchanging bottom-up errors and top-down predictions. I will illustrate the framework through examples from sensory coding, decision-making, and learning, and discuss what energy-based analysis can reveal about stability, learning, and design in biological and artificial networks. Francesco Bullo is Distinguished Professor and Mosher Endowed Chair of Mechanical Engineering at the University of California, Santa Barbara, CA, USA. He received the Laurea degree in Electrical Engineering from the University of Padova, Italy, in 1994, and the Ph.D. degree in Control and Dynamical Systems from the California Institute of Technology, Pasadena, CA, in 1998. His research interests include contraction theory, network systems, neural networks, and mathematical neuroscience. He is the author or coauthor of Geometric Control of Mechanical Systems (Springer, 2004), Distributed Control of Robotic Networks (Princeton, 2009), Lectures on Network Systems (KDP, v1.7, 2024), and Contraction Theory for Dynamical Systems (KDP, v1.3 2026). He served as IEEE CSS President and SIAG CST Chair. He is a Fellow of ASME, IEEE, IFAC, NetSci, and SIAM