Mathematics > Optimization and Control
[Submitted on 1 Mar 2025
]
Title: Convergence of energy-based learning in linear resistive networks
Title: 基于能量的线性电阻网络学习收敛性
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 energy-based 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, for any step size, giving a guarantee of convergence for the algorithm.
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