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Universality of Approximate Message Passing Algorithms

arXiv 2003.10431 ↗First posted 23 Mar 2020math.PR cs.IT math-phcited by 16

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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.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Mar 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 0; 2023: 3; 2024: 3; 2025: 4; 2026: 2.

16 papers.

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  1. 2021Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensionscited by 52
  2. 2021Graph-based Approximate Message Passing Iterationscited by 35
  3. 2021Estimation in Rotationally Invariant Generalized Linear Models via Approximate Message Passingcited by 18
  4. 2021Local convexity of the TAP free energy and AMP convergence for Z2-synchronizationcited by 15
  5. 2023A polynomial-time iterative algorithm for random graph matching with non-vanishing correlationcited by 8
  6. 2024Information limits and Thouless-Anderson-Palmer equations for spiked matrix models with structured noisecited by 6
  7. 2023Mixed Regression via Approximate Message Passingcited by 3
  8. 2024Fast, robust approximate message passingcited by 3
  9. 2023Bayes optimal learning in high-dimensional linear regression with network side informationcited by 2
  10. 2024Fundamental limits of Non-Linear Low-Rank Matrix Estimationcited by 2
  11. 2025Optimal and Provable Calibration in High-Dimensional Binary Classification: Angular Calibration and Platt Scalingcited by 2
  12. 2025Learning with Restricted Boltzmann Machines: Asymptotics of AMP and GD in High Dimensionscited by 0
4 more
  1. 2025Sharp Trade-Offs in High-Dimensional Inference via 2-Level SLOPEcited by 0
  2. 2025Universality of high-dimensional scaling limits of stochastic gradient descentcited by 0
  3. 2026Rigorous Asymptotics for First-Order Algorithms Through the Dynamical Cavity Methodcited by 0
  4. 2026Decoupled Descent: Exact Test Error Tracking Via Approximate Message Passingcited by 0