---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '19065'
abstract:
- lang: eng
  text: 'The identification of the parameters of a neural network from finite samples
    of input-output pairs is often referred to as the teacher-student model, and this
    model has represented a popular framework for understanding training and generalization.
    Even if the problem is NP-complete in the worst case, a rapidly growing literature
    – after adding suitable distributional assumptions – has established finite sample
    identification of two-layer networks with a number of neurons (math. formula),
    D being the input dimension. For the range (math. formula) the problem becomes
    harder, and truly little is known for networks parametrized by biases as well.
    This paper fills the gap by providing efficient algorithms and rigorous theoretical
    guarantees of finite sample identification for such wider shallow networks with
    biases. Our approach is based on a two-step pipeline: first, we recover the direction
    of the weights, by exploiting second order information; next, we identify the
    signs by suitable algebraic evaluations, and we recover the biases by empirical
    risk minimization via gradient descent. Numerical results demonstrate the effectiveness
    of our approach.'
article_number: '101749'
article_processing_charge: No
article_type: original
author:
- first_name: Massimo
  full_name: Fornasier, Massimo
  last_name: Fornasier
- first_name: Timo
  full_name: Klock, Timo
  last_name: Klock
- first_name: Marco
  full_name: Mondelli, Marco
  id: 27EB676C-8706-11E9-9510-7717E6697425
  last_name: Mondelli
  orcid: 0000-0002-3242-7020
- first_name: Michael
  full_name: Rauchensteiner, Michael
  last_name: Rauchensteiner
citation:
  ama: Fornasier M, Klock T, Mondelli M, Rauchensteiner M. Efficient identification
    of wide shallow neural networks with biases. <i>Applied and Computational Harmonic
    Analysis</i>. 2025;77. doi:<a href="https://doi.org/10.1016/j.acha.2025.101749">10.1016/j.acha.2025.101749</a>
  apa: Fornasier, M., Klock, T., Mondelli, M., &#38; Rauchensteiner, M. (2025). Efficient
    identification of wide shallow neural networks with biases. <i>Applied and Computational
    Harmonic Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.acha.2025.101749">https://doi.org/10.1016/j.acha.2025.101749</a>
  chicago: Fornasier, Massimo, Timo Klock, Marco Mondelli, and Michael Rauchensteiner.
    “Efficient Identification of Wide Shallow Neural Networks with Biases.” <i>Applied
    and Computational Harmonic Analysis</i>. Elsevier, 2025. <a href="https://doi.org/10.1016/j.acha.2025.101749">https://doi.org/10.1016/j.acha.2025.101749</a>.
  ieee: M. Fornasier, T. Klock, M. Mondelli, and M. Rauchensteiner, “Efficient identification
    of wide shallow neural networks with biases,” <i>Applied and Computational Harmonic
    Analysis</i>, vol. 77. Elsevier, 2025.
  ista: Fornasier M, Klock T, Mondelli M, Rauchensteiner M. 2025. Efficient identification
    of wide shallow neural networks with biases. Applied and Computational Harmonic
    Analysis. 77, 101749.
  mla: Fornasier, Massimo, et al. “Efficient Identification of Wide Shallow Neural
    Networks with Biases.” <i>Applied and Computational Harmonic Analysis</i>, vol.
    77, 101749, Elsevier, 2025, doi:<a href="https://doi.org/10.1016/j.acha.2025.101749">10.1016/j.acha.2025.101749</a>.
  short: M. Fornasier, T. Klock, M. Mondelli, M. Rauchensteiner, Applied and Computational
    Harmonic Analysis 77 (2025).
corr_author: '1'
date_created: 2025-02-23T23:01:54Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2025-09-30T10:35:09Z
day: '01'
ddc:
- '000'
department:
- _id: MaMo
doi: 10.1016/j.acha.2025.101749
external_id:
  isi:
  - '001430202700001'
file:
- access_level: open_access
  checksum: 657f258af0f7ca135e69959fd13e2d63
  content_type: application/pdf
  creator: dernst
  date_created: 2025-08-05T12:22:04Z
  date_updated: 2025-08-05T12:22:04Z
  file_id: '20131'
  file_name: 2025_ApplCompAnalysis_Fornasier.pdf
  file_size: 2223350
  relation: main_file
  success: 1
file_date_updated: 2025-08-05T12:22:04Z
has_accepted_license: '1'
intvolume: '        77'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '06'
oa: 1
oa_version: Published Version
publication: Applied and Computational Harmonic Analysis
publication_identifier:
  eissn:
  - 1096-603X
  issn:
  - 1063-5203
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Efficient identification of wide shallow neural networks with biases
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 77
year: '2025'
...