Neural Circuits as Optimizers: Energy Landscapes and Predictive Coding
Neural circuits are networks of interacting units whose collective dynamics support perception, memory, and decision-making. This talk develops a mathematical perspective in which these dynamics navigate energy landscapes and implement distributed optimization.
The central bridge is an equivalence between recurrent firing-rate networks and proximal gradient dynamics. Starting from an energy or probabilistic objective, the framework provides a top-down explanation for a circuit’s recurrent interactions, activation functions, and prediction-error signals. It encompasses classical predictive coding, sparse reconstruction, and non-Gaussian models, and extends naturally to hierarchical networks that exchange bottom-up errors and top-down predictions. I will illustrate this viewpoint through examples of neural computation and discuss how tools from optimization and dynamical systems can help analyze stability, convergence, and collective behavior. The broader goal is to connect energy-based models of the brain with questions in network science about how local interactions produce global computation.
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