# A Convergence Analysis of Approximate Message Passing with Non-Separable Functions and Applications to Multi-Class Classification

arXiv: https://arxiv.org/abs/2402.08676 · HTML: https://mlsanity.com/paper/2402.08676/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions](https://mlsanity.com/paper/2106.03791/) (2021)
- [Estimation of Low-Rank Matrices via Approximate Message Passing](https://mlsanity.com/paper/1711.01682/) (2017)
- [Graph-based Approximate Message Passing Iterations](https://mlsanity.com/paper/2109.11905/) (2021)
- [Theoretical Insights Into Multiclass Classification: A High-dimensional Asymptotic View](https://mlsanity.com/paper/2011.07729/) (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)
- [Finite Sample Analysis of Approximate Message Passing Algorithms](https://mlsanity.com/paper/1606.01800/) (2016)
- [Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initialization](https://mlsanity.com/paper/2110.02318/) (2021)
- [Learning curves for the multi-class teacher-student perceptron](https://mlsanity.com/paper/2203.12094/) (2022)
- [Approximate message passing from random initialization with applications to mathbbZ2 synchronization](https://mlsanity.com/paper/2302.03682/) (2023)
- [Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensembles](https://mlsanity.com/paper/2101.07464/) (2021)
- [Inference in Multi-Layer Networks with Matrix-Valued Unknowns](https://mlsanity.com/paper/2001.09396/) (2020)
- [Exact solution to the random sequential dynamics of a message passing algorithm](https://mlsanity.com/paper/2101.01571/) (2021)
- [Analysis of Random Sequential Message Passing Algorithms for Approximate Inference](https://mlsanity.com/paper/2202.08198/) (2022)

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

- [Implicit Optimization Bias of Next-Token Prediction in Linear Models](https://mlsanity.com/paper/2402.18551/) (2024)

## Abstract (arXiv)

Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable multivariate nonlinearities. As an application, we present a complete (and independent) analysis of the motivated convex optimization problem.