Network Dynamics Governed by Lyapunov Functions: From Memory to Classification

In 1982 John Hopfield published a neural network model for memory retrieval, a model that became a cornerstone in theoretical neuroscience. A key ingredient of the Hopfield model was the use of a network dynamics that is governed by a Lyapunov function. In a recent paper, Krotov and Hopfield showed how a Lyapunov function governs a biological plausible learning rule for the neural networks' connectivity. By doing so, they bring an intriguing approach to classification tasks, and show the relevance of the broader framework across decades in the field.