# Sufficient Statistic Memory Approximate Message Passing

arXiv: https://arxiv.org/abs/2206.11674 · HTML: https://mlsanity.com/paper/2206.11674/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 7 of 7)

- [Approximate Message Passing algorithms for rotationally invariant matrices](https://mlsanity.com/paper/2008.11892/) (2020)
- [Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)](https://mlsanity.com/paper/2006.06581/) (2020)
- [PCA Initialization for Approximate Message Passing in Rotationally Invariant Models](https://mlsanity.com/paper/2106.02356/) (2021)
- [Memory AMP](https://mlsanity.com/paper/2012.10861/) (2020)
- [Memory Approximate Message Passing](https://mlsanity.com/paper/2106.02237/) (2021)
- [On Capacity Optimality of OAMP: Beyond IID Sensing Matrices and Gaussian Signaling](https://mlsanity.com/paper/2108.08503/) (2021)
- [Sufficient-Statistic Memory AMP](https://mlsanity.com/paper/2112.15327/) (2021)

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

- [Random Multiplexing](https://mlsanity.com/paper/2512.24087/) (2025)

## Abstract (arXiv)

Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state evolution. However, state evolution does not necessarily guarantee the convergence of iterative algorithms. To solve the convergence problem of AMP-type algorithms in principle, this paper proposes a memory AMP (MAMP) under a sufficient statistic condition, named sufficient statistic MAMP (SS-MAMP). We show that the covariance matrices of SS-MAMP are L-banded and convergent. Given an arbitrary MAMP, we can construct the SS-MAMP by damping, which not only ensures the convergence, but also preserves the orthogonality, i.e., its dynamics can be correctly described by state evolution.