Random Features Hopfield Networks generalize retrieval to previously unseen examples

TL;DR

This paper demonstrates that Hopfield Networks with random features can generalize to unseen examples by forming attractors for new data, expanding their retrieval capabilities beyond stored patterns.

Contribution

It reveals that Hopfield Networks can learn to represent unseen examples through feature mixing, extending their retrieval to previously unencountered data.

Findings

Networks develop attractors for unseen examples.

Spurious states enable generalization to new data.

Phase diagram analysis supports the findings.

Abstract

It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model. In this work we reveal that the network also develops attractors corresponding to previously unseen examples generated with the same set of features. We explain this surprising behaviour in terms of spurious states of the learned features: we argue that, increasing the number of stored examples beyond the learning transition, the model also learns to mix the features to represent both stored and previously unseen examples. We support this claim with the computation of the phase diagram of the model.