---
_id: '1260'
abstract:
- lang: eng
  text: In this work, the Gardner problem of inferring interactions and fields for
    an Ising neural network from given patterns under a local stability hypothesis
    is addressed under a dual perspective. By means of duality arguments, an integer
    linear system is defined whose solution space is the dual of the Gardner space
    and whose solutions represent mutually unstable patterns. We propose and discuss
    Monte Carlo methods in order to find and remove unstable patterns and uniformly
    sample the space of interactions thereafter. We illustrate the problem on a set
    of real data and perform ensemble calculation that shows how the emergence of
    phase dominated by unstable patterns can be triggered in a nonlinear discontinuous
    way.
article_number: '1650067'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniele
  full_name: De Martino, Daniele
  id: 3FF5848A-F248-11E8-B48F-1D18A9856A87
  last_name: De Martino
  orcid: 0000-0002-5214-4706
citation:
  ama: De Martino D. The dual of the space of interactions in neural network models.
    <i>International Journal of Modern Physics C</i>. 2016;27(6). doi:<a href="https://doi.org/10.1142/S0129183116500674">10.1142/S0129183116500674</a>
  apa: De Martino, D. (2016). The dual of the space of interactions in neural network
    models. <i>International Journal of Modern Physics C</i>. World Scientific Publishing.
    <a href="https://doi.org/10.1142/S0129183116500674">https://doi.org/10.1142/S0129183116500674</a>
  chicago: De Martino, Daniele. “The Dual of the Space of Interactions in Neural Network
    Models.” <i>International Journal of Modern Physics C</i>. World Scientific Publishing,
    2016. <a href="https://doi.org/10.1142/S0129183116500674">https://doi.org/10.1142/S0129183116500674</a>.
  ieee: D. De Martino, “The dual of the space of interactions in neural network models,”
    <i>International Journal of Modern Physics C</i>, vol. 27, no. 6. World Scientific
    Publishing, 2016.
  ista: De Martino D. 2016. The dual of the space of interactions in neural network
    models. International Journal of Modern Physics C. 27(6), 1650067.
  mla: De Martino, Daniele. “The Dual of the Space of Interactions in Neural Network
    Models.” <i>International Journal of Modern Physics C</i>, vol. 27, no. 6, 1650067,
    World Scientific Publishing, 2016, doi:<a href="https://doi.org/10.1142/S0129183116500674">10.1142/S0129183116500674</a>.
  short: D. De Martino, International Journal of Modern Physics C 27 (2016).
corr_author: '1'
date_created: 2018-12-11T11:51:00Z
date_published: 2016-06-01T00:00:00Z
date_updated: 2025-09-22T09:01:25Z
day: '01'
department:
- _id: GaTk
doi: 10.1142/S0129183116500674
external_id:
  arxiv:
  - '1505.02963'
  isi:
  - '000377674800010'
intvolume: '        27'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1505.02963
month: '06'
oa: 1
oa_version: Preprint
publication: International Journal of Modern Physics C
publication_status: published
publisher: World Scientific Publishing
publist_id: '6065'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The dual of the space of interactions in neural network models
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 27
year: '2016'
...