Exploring the holographic entropy cone via reinforcement learning

TL;DR

This paper introduces a reinforcement learning approach to explore the holographic entropy cone, identifying realizations for certain extreme rays and suggesting the existence of new holographic inequalities.

Contribution

The authors develop a RL algorithm to find graph realizations of entropy vectors, confirming some extreme rays and indicating the presence of unknown inequalities.

Findings

Successfully rediscovered monogamy of mutual information for N=3.

Found realizations for 3 of 6 mystery extreme rays at N=6.

Provided evidence that 3 extreme rays are not realizable, implying new inequalities.

Abstract

We develop a reinforcement learning algorithm to study the holographic entropy cone. Given a target entropy vector, our algorithm searches for a graph realization whose min-cut entropies match the target vector. If the target vector does not admit such a graph realization, it must lie outside the cone, in which case the algorithm finds a graph whose corresponding entropy vector most nearly approximates the target and allows us to probe the location of the facets. For the $\sf N=3$ cone, we confirm that our algorithm successfully rediscovers monogamy of mutual information beginning with a target vector outside the holographic entropy cone. We then apply the algorithm to the $\sf N=6$ cone, analyzing the 6 "mystery" extreme rays of the subadditivity cone from arXiv:2412.15364 that satisfy all known holographic entropy inequalities yet lacked graph realizations. We found realizations for 3 of them, proving they are genuine extreme rays of the holographic entropy cone, while providing evidence that the remaining 3 are not realizable, implying unknown holographic inequalities exist for $\sf N=6$.