---
_id: '13321'
abstract:
- lang: eng
  text: We consider the problem of reconstructing the signal and the hidden variables
    from observations coming from a multi-layer network with rotationally invariant
    weight matrices. The multi-layer structure models inference from deep generative
    priors, and the rotational invariance imposed on the weights generalizes the i.i.d.
    Gaussian assumption by allowing for a complex correlation structure, which is
    typical in applications. In this work, we present a new class of approximate message
    passing (AMP) algorithms and give a state evolution recursion which precisely
    characterizes their performance in the large system limit. In contrast with the
    existing multi-layer VAMP (ML-VAMP) approach, our proposed AMP – dubbed multilayer
    rotationally invariant generalized AMP (ML-RI-GAMP) – provides a natural generalization
    beyond Gaussian designs, in the sense that it recovers the existing Gaussian AMP
    as a special case. Furthermore, ML-RI-GAMP exhibits a significantly lower complexity
    than ML-VAMP, as the computationally intensive singular value decomposition is
    replaced by an estimation of the moments of the design matrices. Finally, our
    numerical results show that this complexity gain comes at little to no cost in
    the performance of the algorithm.
acknowledgement: Marco Mondelli was partially supported by the 2019 Lopez-Loreta prize.
article_processing_charge: No
arxiv: 1
author:
- first_name: Yizhou
  full_name: Xu, Yizhou
  last_name: Xu
- first_name: Tian Qi
  full_name: Hou, Tian Qi
  last_name: Hou
- first_name: Shan Suo
  full_name: Liang, Shan Suo
  last_name: Liang
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
citation:
  ama: 'Xu Y, Hou TQ, Liang SS, Mondelli M. Approximate message passing for multi-layer
    estimation in rotationally invariant models. In: <i>2023 IEEE Information Theory
    Workshop</i>. Institute of Electrical and Electronics Engineers; 2023:294-298.
    doi:<a href="https://doi.org/10.1109/ITW55543.2023.10160238">10.1109/ITW55543.2023.10160238</a>'
  apa: 'Xu, Y., Hou, T. Q., Liang, S. S., &#38; Mondelli, M. (2023). Approximate message
    passing for multi-layer estimation in rotationally invariant models. In <i>2023
    IEEE Information Theory Workshop</i> (pp. 294–298). Saint-Malo, France: Institute
    of Electrical and Electronics Engineers. <a href="https://doi.org/10.1109/ITW55543.2023.10160238">https://doi.org/10.1109/ITW55543.2023.10160238</a>'
  chicago: Xu, Yizhou, Tian Qi Hou, Shan Suo Liang, and Marco Mondelli. “Approximate
    Message Passing for Multi-Layer Estimation in Rotationally Invariant Models.”
    In <i>2023 IEEE Information Theory Workshop</i>, 294–98. Institute of Electrical
    and Electronics Engineers, 2023. <a href="https://doi.org/10.1109/ITW55543.2023.10160238">https://doi.org/10.1109/ITW55543.2023.10160238</a>.
  ieee: Y. Xu, T. Q. Hou, S. S. Liang, and M. Mondelli, “Approximate message passing
    for multi-layer estimation in rotationally invariant models,” in <i>2023 IEEE
    Information Theory Workshop</i>, Saint-Malo, France, 2023, pp. 294–298.
  ista: 'Xu Y, Hou TQ, Liang SS, Mondelli M. 2023. Approximate message passing for
    multi-layer estimation in rotationally invariant models. 2023 IEEE Information
    Theory Workshop. ITW: Information Theory Workshop, 294–298.'
  mla: Xu, Yizhou, et al. “Approximate Message Passing for Multi-Layer Estimation
    in Rotationally Invariant Models.” <i>2023 IEEE Information Theory Workshop</i>,
    Institute of Electrical and Electronics Engineers, 2023, pp. 294–98, doi:<a href="https://doi.org/10.1109/ITW55543.2023.10160238">10.1109/ITW55543.2023.10160238</a>.
  short: Y. Xu, T.Q. Hou, S.S. Liang, M. Mondelli, in:, 2023 IEEE Information Theory
    Workshop, Institute of Electrical and Electronics Engineers, 2023, pp. 294–298.
conference:
  end_date: 2023-04-28
  location: Saint-Malo, France
  name: 'ITW: Information Theory Workshop'
  start_date: 2023-04-23
corr_author: '1'
date_created: 2023-07-30T22:01:04Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2025-04-15T07:50:16Z
day: '01'
department:
- _id: MaMo
doi: 10.1109/ITW55543.2023.10160238
external_id:
  arxiv:
  - '2212.01572'
  isi:
  - '001031733100053'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2212.01572
month: '05'
oa: 1
oa_version: Preprint
page: 294-298
project:
- _id: 059876FA-7A3F-11EA-A408-12923DDC885E
  name: Prix Lopez-Loretta 2019 - Marco Mondelli
publication: 2023 IEEE Information Theory Workshop
publication_identifier:
  eissn:
  - 2475-4218
  isbn:
  - '9798350301496'
publication_status: published
publisher: Institute of Electrical and Electronics Engineers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Approximate message passing for multi-layer estimation in rotationally invariant
  models
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...