Tensor network representations of discrete maximum entropy distributions via mean polytopes
Abstract
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.
Related
- Tensor Network Moral Graph Recovery of Discrete Probability Distributions
- Truncated Grassmannians: polytopes, representations, and Cauchy formulas
- Maximum Entropy Probability Distributions on Spheres with Fixed Mean Busemann Function and Holomorphic-Information-Geometric Model of Cognition
- Joint Distributions of Minimum and Maximum Angles on High-Dimensional Spheres
- Maximum principle for discrete-time stochastic recursive games driven by fractional noises
BibTeX
@misc{goessmann2026tensor,
title = {{Tensor network representations of discrete maximum entropy distributions via mean polytopes}},
author = {Alex Goessmann and Martin Eigel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07184},
eprint = {2609.07184},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07184},
}
RIS
TY - UNPB
TI - Tensor network representations of discrete maximum entropy distributions via mean polytopes
AU - Alex Goessmann
AU - Martin Eigel
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07184
UR - https://arxiv.org/abs/2609.07184
AB - 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.
ER -