Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Function approximation on non-Euclidean spaces.

Pierre Courrieu1

  • 1Laboratoire de Psychologie Cognitive, CNRS-UMR 6146, Université de Provence, 29 avenue Robert Schuman, 13621 Aix-en-Provence cedex 1, France. courrieu@up.univ-mrs.fr

Neural Networks : the Official Journal of the International Neural Network Society
|January 15, 2005
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Spelling performance on the web and in the lab.

PloS one·2019
Same author

The primacy order effect in complex decision making.

Psychological research·2019
Same author

Brain correlates of phonological recoding of visual symbols.

NeuroImage·2016
Same author

The time course of visual influences in letter recognition.

Cognitive, affective & behavioral neuroscience·2016
Same author

General or idiosyncratic item effects: What is the good target for models?

Journal of experimental psychology. Learning, memory, and cognition·2015
Same author

The unbearable articulatory nature of naming: on the reliability of word naming responses at the item level.

Psychonomic bulletin & review·2012
Same journal

Exploiting audio-visual modalities in videos: Object detection via multi-stage bilateral coupling network.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Reliability-aware modality completion with cross-modal distillation for federated learning with missing modalities.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

IGFD-Net: Illumination-guided frequency decoupling for polarization image fusion.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Multiple-Strategies dung beetle optimizer and its applications in engineering optimization and bankruptcy prediction.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Aggregating global-scale pixel-wise forgery cues within a graph.

Neural networks : the official journal of the International Neural Network Society·2026
Same journal

Finite-Time intermittent control for secure synchronization of Neutral-Type stochastic delayed neural networks under aperiodic DoS attacks.

Neural networks : the official journal of the International Neural Network Society·2026
See all related articles

This study introduces novel feed-forward networks capable of function approximation across diverse metric and non-metric spaces. These networks extend universal approximation capabilities beyond traditional Euclidean domains, offering broader applicability.

Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Function Approximation Theory

Background:

  • Standard approximation schemes are limited to Euclidean metric spaces.
  • Non-Euclidean input spaces are common in real-world applications.
  • Existing methods lack universal approximation capabilities for diverse spaces.

Purpose of the Study:

  • To present a family of layered feed-forward networks.
  • To enable uniform function approximation on metric and non-metric spaces.
  • To extend the concept of universal approximation capability.

Main Methods:

  • Development of layered feed-forward neural network architectures.
  • Theoretical analysis of approximation properties on various spaces.
  • Design of practical algorithms and illustrative examples.

Related Experiment Videos

Main Results:

  • Demonstrated uniform approximation on any metric space.
  • Extended approximation capabilities to a wide range of non-metric spaces.
  • Provided theoretical foundations, algorithms, and examples.

Conclusions:

  • The proposed networks offer a significant advancement in function approximation.
  • This approach broadens the applicability of neural networks to non-Euclidean and non-metric data.
  • The findings enhance the theoretical and practical understanding of universal approximation.