This paper proves the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point in the large system limit. The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that is guaranteed to converge systematically. The dynamics of Bayes-optimal LM-MP is analyzed via an existing state evolution framework. The obtained state evolution recursions are proved to converge. The convergence of Bayes-optimal orthogonal/vector AMP is proved by confirming an exact reduction of the state evolution recursions to those for Bayes-optimal orthogonal/vector AMP.

翻译：本文证明了 Bayes- 最佳正方位/ 矢量近似信件传递( AMP) 与大系统限制的固定点的趋同。 证明以保证系统趋同的 Bayes- 最佳长模程信件传递( LM) 为基础。 通过现有的州进化框架分析 Bayes- 最佳 LM- MP 的动态。 获得的州进化循环被证明会趋同。 Bayes- 最佳正方位/ 矢量 AMP 的趋同通过确认将州进化周期精确减少到 Bayes- 最佳正方位/ 矢量 AMP 。