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

Multilayer perceptrons to approximate complex valued functions

P Arena1, L Fortuna, R Re

  • 1Dipartimento Elettrico, Elettronico e Sistemistico University of Cantania, Italy.

International Journal of Neural Systems
|December 1, 1995
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

The transcriptomic immune profiling across the different ileal layers highlights the relevant role of neutrophils and the active involvement of healthy mucosa in human Crohn's Disease.

Immunology letters·2026
Same author

Exploring the physiological limits of aging: a case study of the male 50-km world record in the 80+ age category.

Frontiers in physiology·2026
Same author

Consistent efficacy and safety of automated insulin delivery in children aged 2-6 years: results from the LENNY trial continuation phase.

Diabetes research and clinical practice·2025
Same author

A personalized clinical assessment: multi-sensor approach for understanding musculoskeletal health in the frail population.

Biomedical engineering online·2024
Same author

Ureteral stricture rate after endoscopic treatments for urolithiasis and related risk factors: systematic review and meta-analysis.

World journal of urology·2024
Same author

No Difference in Muscle Basal Oxygenation in a Bedridden Population Pre and Post Rehabilitation.

Advances in experimental medicine and biology·2023
Same journal

Latent Space Projections and Atlases, a Cautionary Tale in Deep Neuroimaging using Autoencoders.

International journal of neural systems·2026
Same journal

Transformer-Based Anomaly Detection for Neurodegenerative Screening in MRI Images.

International journal of neural systems·2026
Same journal

Discrete Wavelet Convolution for Learnable Time-Frequency Representation with Application to Seizure Prediction.

International journal of neural systems·2026
Same journal

Automatic Seizure Detection using Hierarchical Spectral-Temporal Feature Learning with an Imbalance-Aware Transformer.

International journal of neural systems·2026
Same journal

Pyramid Vision Transformer-Enhanced Conformer Network for Epileptic Seizure Recognition Using MultiChannel EEG Signals.

International journal of neural systems·2026
Same journal

A Time-Frequency Decoupled Contrastive Learning Framework for Electroencephalography-Based Parkinson's Disease Diagnosis.

International journal of neural systems·2026
See all related articles

Complex feedforward neural networks, specifically Complex Multilayer Perceptrons, are proven universal interpolators for continuous complex functions. This research highlights their computational advantages over traditional real-valued networks.

Area of Science:

  • Computational Intelligence
  • Artificial Neural Networks
  • Complex-Valued Machine Learning

Background:

  • Existing literature on complex feedforward neural networks (CFNNs) lacks a comprehensive theoretical analysis of their approximation capabilities.
  • Understanding the function approximation properties of CFNNs is crucial for advancing complex-valued machine learning.

Purpose of the Study:

  • To theoretically analyze the approximation capabilities of various CFNN structures.
  • To establish a new density theorem for Complex Multilayer Perceptrons (CMLPs) with non-analytical activation functions.
  • To investigate the approximation properties of superpositions of analytic activation functions in CMLPs.

Main Methods:

  • Theoretical analysis of CFNN structures.
  • Development and proof of a new density theorem for CMLPs.

Related Experiment Videos

  • Investigation of approximation properties using analytic activation functions.
  • Numerical simulations comparing CMLPs with real-valued MLPs.

    • Main Results:

    • A new density theorem proves that CMLPs with complex-valued non-analytical sigmoidal activation functions are universal interpolators of continuous complex-valued functions.
    • Superpositions of analytic activation functions in CMLPs were shown not to be dense in the set of continuous complex-valued functions.
    • Numerical examples demonstrate the superior computational efficiency of CMLPs compared to classical real MLPs.

    Conclusions:

    • CMLPs with non-analytical activation functions possess universal approximation capabilities for complex-valued functions.
    • The choice of activation function significantly impacts the density and approximation properties of CMLPs.
    • CMLPs offer significant advantages in computational complexity for complex-valued function approximation tasks.