Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization

TL;DR

This paper reviews energy-based dynamical models inspired by neuroscience, highlighting their applications in computation, learning, and optimization, and discusses how control theory can guide the development of scalable, robust neurocomputing systems.

Contribution

It introduces a unified energy-based dynamical framework for neuro-inspired computation, extending classical models to modern high-capacity and optimization-oriented systems.

Findings

Energy landscapes encode information via gradient flows.

Modern models include dense associative memories and oscillator networks.

Control principles inform the design of scalable neurocomputing architectures.

Abstract

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and computational ideas, with applications for model learning and training, memory retrieval, data-driven control, and optimization. This tutorial focuses on neuro-inspired approaches to computation that aim to improve scalability, robustness, and energy efficiency across such tasks, bridging the gap between artificial and biological systems. Particular emphasis is placed on energy-based dynamical models that encode information through gradient flows and energy landscapes. We begin by reviewing classical formulations, such as continuous-time Hopfield networks and Boltzmann machines, and then extend the framework to modern developments. These include dense associative memory models for high-capacity storage, oscillator-based networks for large-scale optimization, and proximal-descent dynamics for composite and constrained reconstruction. The tutorial demonstrates how control-theoretic principles can guide the design of next-generation neurocomputing systems, steering the discussion beyond conventional feedforward and backpropagation-based approaches to artificial intelligence.