# Tensor network representations of discrete maximum entropy distributions via mean polytopes

arXiv: https://arxiv.org/abs/2609.07184 · HTML: https://mlsanity.com/paper/2609.07184/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 48 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 3 of 3)

- [Tensor Logic: The Language of AI](https://mlsanity.com/paper/2510.12269/) (2025)
- [A new pathway to generative artificial intelligence by minimizing the maximum entropy](https://mlsanity.com/paper/2502.13287/) (2025)
- [A tensor network formalism for neuro-symbolic AI](https://mlsanity.com/paper/2601.15442/) (2026)

## Abstract (arXiv)

We present tensor network representations for discrete maximum entropy distributions under expectation constraints. To this end, we introduce Computation-Activation Networks (CompActNets), a tensor network architecture that subsumes exponential families. By leveraging the geometry of the convex polytope of realizable expectation vectors, we represent any maximum entropy distribution in the same architecture. We exploit the fact that proper faces of this polytope correspond to the boundary closure of exponential families, which restricts the distribution's support. We then derive explicit representations for the support within the CompActNet architecture. The proposed framework suggests tensor network ranks as complexity measures for faces. Finally, a case study on Boolean statistics links the geometry of 0/1-polytopes directly to propositional formulas.