Tensor network representations of discrete maximum entropy distributions via mean polytopes

2026-09-07

AI Summary

本文通过引入计算激活网络(CompActNets)架构，利用凸多面体几何表示离散最大熵分布，解决了在期望约束下如何高效表示这类分布的问题。

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.

Problem

• tensor network
• maximum entropy distribution
• expectation constraints
• Computation-Activation Networks
• convex polytope

Innovation

• Tensor Network
• Maximum Entropy Distributions
• Exponential Families
• Convex Polytope
• CompActNets