# Universality of Approximate Message Passing Algorithms

arXiv: https://arxiv.org/abs/2003.10431 · HTML: https://mlsanity.com/paper/2003.10431/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 16 of 16)

- [Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions](https://mlsanity.com/paper/2106.03791/) (2021)
- [Graph-based Approximate Message Passing Iterations](https://mlsanity.com/paper/2109.11905/) (2021)
- [Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passing](https://mlsanity.com/paper/2112.04330/) (2021)
- [Local convexity of the TAP free energy and AMP convergence for Z2-synchronization](https://mlsanity.com/paper/2106.11428/) (2021)
- [A polynomial-time iterative algorithm for random graph matching with non-vanishing correlation](https://mlsanity.com/paper/2306.00266/) (2023)
- [Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noise](https://mlsanity.com/paper/2405.20993/) (2024)
- [Mixed Regression via Approximate Message Passing](https://mlsanity.com/paper/2304.02229/) (2023)
- [Fast, robust approximate message passing](https://mlsanity.com/paper/2411.02764/) (2024)
- [Universality of high-dimensional scaling limits of stochastic gradient descent](https://mlsanity.com/paper/2512.13634/) (2025)
- [Bayes optimal learning in high-dimensional linear regression with network side information](https://mlsanity.com/paper/2306.05679/) (2023)
- [Fundamental limits of Non-Linear Low-Rank Matrix Estimation](https://mlsanity.com/paper/2403.04234/) (2024)
- [Optimal and Provable Calibration in High-Dimensional Binary Classification: Angular Calibration and Platt Scaling](https://mlsanity.com/paper/2502.15131/) (2025)
- [Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensions](https://mlsanity.com/paper/2505.18046/) (2025)
- [Sharp Trade-Offs in High-Dimensional Inference via 2-Level SLOPE](https://mlsanity.com/paper/2507.09110/) (2025)
- [Rigorous Asymptotics for First-Order Algorithms Through the Dynamical Cavity Method](https://mlsanity.com/paper/2603.14573/) (2026)
- [Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passing](https://mlsanity.com/paper/2604.27883/) (2026)

## Abstract (arXiv)

We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an n× n random symmetric matrix A. We establish universality in noise for this AMP in the n-limit and validate this behavior in a number of AMPs popularly adapted in compressed sensing, statistical inferences, and optimizations in spin glasses.