[2604.05042] Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization

Computer Science > Machine Learning arXiv:2604.05042 (cs) [Submitted on 6 Apr 2026] Title:Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization Authors:Arthur N. Montanari, Francesco Bullo, Dmitry Krotov, Adilson E. Motter View a PDF of the paper titled Energy-Based Dynamical Models for Neurocomputation, Learning, and Optimization, by Arthur N. Montanari and 3 other authors View PDF HTML (experimental) 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 ...