# Generalized Memory Approximate Message Passing

arXiv: https://arxiv.org/abs/2110.06069 · HTML: https://mlsanity.com/paper/2110.06069/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [MIMO Detection with Spatial Sigma-Delta ADCs: A Variational Bayesian Approach](https://mlsanity.com/paper/2410.03891/) (2024)

## Abstract (arXiv)

Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed (IID) entries. In this context, generalized vector AMP (GVAMP) is proposed for general unitarily-invariant transformation matrices but it has a high-complexity matrix inverse. To this end, we propose a universal generalized memory AMP (GMAMP) framework including the existing orthogonal AMP/VAMP, GVAMP, and memory AMP (MAMP) as special instances. Due to the characteristics that local processors are all memory, GMAMP requires stricter orthogonality to guarantee the asymptotic IID Gaussianity and state evolution. To satisfy such orthogonality, local orthogonal memory estimators are established. The GMAMP framework provides a principle toward building new advanced AMP-type algorithms. As an example, we construct a Bayes-optimal GMAMP (BO-GMAMP), which uses a low-complexity memory linear estimator to suppress the linear interference, and thus its complexity is comparable to GAMP. Furthermore, we prove that for unitarily-invariant transformation matrices, BO-GMAMP achieves the replica minimum (i.e., Bayes-optimal) MSE if it has a unique fixed point.