# Exploring the holographic entropy cone via reinforcement learning

arXiv: https://arxiv.org/abs/2601.19979 · HTML: https://mlsanity.com/paper/2601.19979/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 5 of 5)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Hindsight Experience Replay](https://mlsanity.com/paper/1707.01495/) (2017)
- [Learning to Unknot](https://mlsanity.com/paper/2010.16263/) (2020)
- [Bit threads and holographic entanglement](https://mlsanity.com/paper/1604.00354/) (2016)
- [Crossing versus locking: Bit threads and continuum multiflows](https://mlsanity.com/paper/2008.03197/) (2020)

## Abstract (arXiv)

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.