Exploring the holographic entropy cone via reinforcement learning

2026-01-27

AI Summary

This study investigates the boundary structure of the holographic entropy cone, focusing on six enigmatic extremal rays in the $N=6$ case whose graphical realizability remains unknown. For the first time, reinforcement learning is introduced to this domain, and an algorithmic framework combining graph search, min-cut entropy computation, and inequality verification is proposed. The approach successfully reproduces the known $N=3$ monogamy of mutual information and constructs explicit graph realizations for three of the six mysterious extremal rays, confirming their membership in the holographic entropy cone. No realizations were found for the remaining three rays, suggesting the possible existence of new holographic entropy inequalities. This work provides a novel methodology and empirical evidence for exploring the geometric structure of the holographic entropy cone.

Technology Category

• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 $\sf N=6$.

Problem

• holographic entropy cone
• entropy vector
• graph realization
• holographic entropy inequalities
• extreme rays

Innovation

• reinforcement learning
• holographic entropy cone
• graph realization
• extreme rays
• holographic entropy inequalities