论文标题
张量网络收缩和信念传播算法
Tensor Networks contraction and the Belief Propagation algorithm
论文作者
论文摘要
信念传播是一种经过良好的消息通讯算法，可通过图形模型运行，可用于近似推断和近似局部边缘。产生的近似值等效于统计力学的伯特 - 佩埃尔斯近似。在这里，我们展示了如何将该算法适应PEPS张量网络的世界并用作近似收缩方案。我们进一步表明，所得近似等效于``平均磁场''近似值，该近似值在简单升级算法中使用，从而表明后者本质上是伯特·皮埃尔斯的近似值。这表明，张量网络的最简单近似收缩算法之一相当于通常在图形模型中近似边缘的最简单的方案之一，并铺平了使用BP作为张量网络算法的改进的方式。
Belief Propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals. The resulting approximations are equivalent to the Bethe-Peierls approximation of statistical mechanics. Here we show how this algorithm can be adapted to the world of PEPS tensor networks and used as an approximate contraction scheme. We further show that the resultant approximation is equivalent to the ``mean field'' approximation that is used in the Simple-Update algorithm, thereby showing that the latter is a essentially the Bethe-Peierls approximation. This shows that one of the simplest approximate contraction algorithms for tensor networks is equivalent to one of the simplest schemes for approximating marginals in graphical models in general, and paves the way for using improvements of BP as tensor networks algorithms.
