Sparse and Structured Hopfield Networks

Saul José Rodrigues dos Santos, Vlad Niculae, Daniel C McNamee, Andre Martins

Abstract: Modern Hopfield networks have enjoyed recent interest due to their connection to attention in transformers. Our paper provides a unified framework for sparse Hopfield networks by establishing a link with Fenchel-Young losses. The result is a new family of Hopfield-Fenchel-Young energies whose update rules are end-to-end differentiable sparse transformations. We reveal a connection between loss margins, sparsity, and exact memory retrieval. We further extend this framework to structured Hopfield networks via the SparseMAP transformation, which can retrieve pattern associations instead of a single pattern. Experiments on multiple instance learning and text rationalization demonstrate the usefulness of our approach.

Submission Number: 4531