Exploring the holographic entropy cone via reinforcement learning
This work addresses the challenge of characterizing holographic entropy inequalities in theoretical physics, specifically for quantum gravity and holography, by applying machine learning to probe unknown facets, representing an incremental advancement in computational methods for this domain.
The researchers tackled the problem of exploring the holographic entropy cone by developing a reinforcement learning algorithm to search for graph realizations matching target entropy vectors, confirming monogamy of mutual information for N=3 and finding realizations for 3 out of 6 mystery extreme rays for N=6, while providing evidence that the remaining 3 are not realizable.
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 $\sf N=6$.