Biologically Inspired Neural Networks and Optimization: Neural Circuits Meet Contraction Theory

Abstract:
This talk presents novel connections between biologically plausible continuous-time neural networks, optimization problems, and contraction 
theory.
The motivation for this work comes from the growing interest in modeling biologically inspired neural networks, ensuring their stability and robustness, and investigating their functional implications. These models may ultimately inform machine learning models.
We begin by presenting a normative top/down framework for analyzing and designing biologically plausible continuous-time recurrent neural networks for sparse reconstruction problems. We use contraction theory — a powerful control-theoretical tool — to characterize the convergence properties of these dynamics, demonstrating that the convergence is linear-exponential.
We then show that a broader class of continuous-time contracting dynamics solving convex optimization problems also exhibits this convergence behavior.
Finally, we discuss the potential of embedding Hebbian learning in this framework and present related contractivity results for neural-synaptic networks.

Brief Biosketch:
Veronica Centorrino is a Ph.D. student in Modeling and Engineering Risk and Complexity at the Scuola Superiore Meridionale, Naples, where she is advised by Francesco Bullo and Giovanni Russo. She received her B.S. and M.S. degrees in mathematics from the University of Catania, Italy, in 2019.
Her primary research interests include contraction theory, analysis of biologically inspired models, and optimization.