Data-driven Learning and Control - DDLC

Deep learning models, despite their power, lag behind the biological brain in interpretability, energy efficiency, and physical plausibility. This presentation explores the mathematical design principles of biological neural circuits -- building upon the classic concept that neural activity is fundamentally driven by cost minimization and energy landscapes. 

We demonstrate a direct mathematical equivalence between the firing dynamics of recurrent neural networks and "proximal gradient descent," a novel dynamical system used to solve optimization problems. This framework provides a top-down explanation for how biological networks process information, illustrated through examples such as sparse signal reconstruction in the visual cortex and decision-making via the free energy principle. Finally, we extend these concepts to complex excitatory-inhibitory circuits, modeling neurons as players in a mathematical game. We conclude by briefly discussing how these biological insights can inspire next-generation analog and neuromorphic computing.