Convergence of energy-based learning in linear resistive networks
This provides a foundational convergence guarantee for energy-based learning, which is incremental but important for distributed analog implementations.
The paper tackled the lack of rigorous convergence theory for energy-based learning algorithms by analyzing Contrastive Learning in linear resistive networks, showing it is equivalent to projected gradient descent on a convex function, which guarantees convergence for any step size.
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.