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

arXiv 2402.08676 ↗First posted 13 Feb 2024cs.LG cs.IT math.ITcited by 1

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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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 14 of its 43 references that are in the map. First posted on arXiv 13 Feb 2024.

Builds on

14 of 43 references.

References · 14

  1. 2021Convex optimizationcited by 2,479
  2. 2021Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensionscited by 52
  3. 2017Estimation of Low-Rank Matrices via Approximate Message Passingcited by 41
  4. 2021Graph-based Approximate Message Passing Iterationscited by 35
  5. 2020Theoretical Insights Into Multiclass Classification: A High-dimensional Asymptotic Viewcited by 32
  6. 2020Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)cited by 23
  7. 2016Finite Sample Analysis of Approximate Message Passing Algorithmscited by 20
  8. 2021Approximate Message Passing for orthogonally invariant ensembles: Multivariate non-linearities and spectral initializationcited by 18
  9. 2022Learning curves for the multi-class teacher-student perceptroncited by 17
  10. 2023Approximate message passing from random initialization with applications to mathbbZ2 synchronizationcited by 9
  11. 2021Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensemblescited by 4
  12. 2020Inference in Multi-Layer Networks with Matrix-Valued Unknownscited by 2
2 more
  1. 2021Exact solution to the random sequential dynamics of a message passing algorithmcited by 2
  2. 2022Analysis of Random Sequential Message Passing Algorithms for Approximate Inferencecited by 1

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Citing papers per year: 2024: 1.

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  1. 2024Implicit Optimization Bias of Next-Token Prediction in Linear Modelscited by 14