Convergence of energy-based learning in linear resistive networks

Anne-Men Huijzer; Thomas Chaffey; Bart Besselink; Henk J. van Waarde

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arXiv · 2503.00349

Convergence of energy-based learning in linear resistive networks

Anne-Men Huijzer·Thomas Chaffey·Bart Besselink·Henk J. van Waarde

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Abstract

Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this direction by analysing a particular energybased learning algorithm, Contrastive Learning, applied to a network of linear adjustable resistors. It is shown that, in this setup, Contrastive Learning is equivalent to projected gradient descent on a convex function with Lipschitz continuous gradient, giving a guarantee of convergence of the algorithm for a range of stepsizes. This convergence result is then extended to a stochastic variant of Contrastive Learning.

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Anne-Men Huijzer, Thomas Chaffey, Bart Besselink, Henk J. van Waarde. 2025-03-01. Convergence of energy-based learning in linear resistive networks. https://arxiv.org/abs/2503.00349

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