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.

翻译：基于能量的学习算法是反向传播的替代方案，非常适合在模拟电子设备中实现分布式部署。然而，目前缺乏关于其收敛性的严格理论。我们通过分析一种特定的基于能量的学习算法——对比学习，并将其应用于线性可调电阻网络，朝着这一方向迈出了第一步。研究表明，在此设置下，对比学习等价于在具有利普希茨连续梯度的凸函数上进行投影梯度下降，从而为该算法在一定步长范围内提供了收敛性保证。随后，这一收敛结果被推广到对比学习的随机变体。