State sampling dependence of the Hopfield network inference

TL;DR

This paper investigates how the method of state sampling affects the accuracy of inferring Hopfield networks, revealing that sampling with state transitions significantly improves inference accuracy in the glassy phase.

Contribution

It demonstrates the dependence of inference error on state sampling methods in Hopfield networks, especially highlighting the benefits of using state transition data.

Findings

Inference error is insensitive when sampling a single state.

Sampling with state transitions reduces inference error.

Results are consistent across different disorder samples.

Abstract

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the form of state sampling. When a single state is sampled to compute magnetizations and correlations, the inference error is almost indistinguishable irrespective of the sampled state. However, the error can be greatly reduced if the data is collected with state transitions. Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.