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

Arthur N. Montanari; Francesco Bullo; Dmitry Krotov; Adilson E. Motter

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arXiv · 2604.05042

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

Arthur N. Montanari·Francesco Bullo·Dmitry Krotov·Adilson E. Motter

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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.

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Arthur N. Montanari, Francesco Bullo, Dmitry Krotov, Adilson E. Motter. 2026-04-06. Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization. https://arxiv.org/abs/2604.05042

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