Coercivity and Local Convergence of Physical Learning in Linear Circuits
Researchers have developed a new theoretical framework for analyzing the convergence of physical learning methods in linear circuits. The study focuses on Equilibrium Propagation (EP), Coupled Learning (CL), and a novel method called Adjoint Coupled Learning (AL). The paper introduces a coercivity condition, based on a rank condition of a matrix derived from the network's structure, which guarantees exponential decay of the training loss and parameter convergence to the solution manifold, provided a solution exists. While a specific kite circuit example demonstrates potential failure due to symmetry, the research concludes that such degeneracies are non-generic, with coercivity generally holding for most desired outputs. AI
IMPACT Provides theoretical groundwork for understanding physical learning methods, potentially influencing future hardware-based AI development.