Learning in a Multifield Coherent Ising Machine

We introduce a network of coupled oscillators that can learn to solve a classification task from a set of examples -- performing both training and inference through the nonlinear evolution of the system. We accomplish this by combining three key elements to achieve learning: A long-term memory that stores learned responses, analogous to the synapses in biological brains; a short-term memory that stores the neural activations, similar to the firing patterns of neurons; and an evolution law that updates the synapses in response to novel examples, inspired by synaptic plasticity. Achieving all three elements in wave-based information processors such as metamaterials is a significant challenge. Here, we solve it by leveraging the material multistability to implement long-term memory, and harnessing symmetries and thermal noise to realize the learning rule. Our analysis reveals that the learning mechanism, although inspired by synaptic plasticity, also shares parallelisms with bacterial evolution strategies, where mutation rates increase in the presence of noxious stimuli.