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

Approximation by fully complex multilayer perceptrons.

Taehwan Kim1, Tülay Adali

  • 1MITRE Corporation, McLean, Virginia 22102, USA. tkim@mitre.org

Neural Computation
|June 21, 2003
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

Multimodal subspace independent vector analysis effectively captures latent relationships between brain structure and function.

Imaging neuroscience (Cambridge, Mass.)·2026
Same author

Clinical Utility of AI-Enabled CT-to-MRI Translation for Degenerative Spinal Disorders: A Retrospective Reader Study.

Diagnostics (Basel, Switzerland)·2026
Same author

Microglia modulate concussion biomarkers and cognitive recovery in male mice.

bioRxiv : the preprint server for biology·2026
Same author

HFIP-Promoted PdH-Electrocatalytic Remote Ritter-Type Hydrofunctionalization of Alkenes: Divergent Access to Amides and Tetrazoles.

Organic letters·2026
Same author

Enhanced Visualization: Transforming Non-Contrast into Contrast-Enhanced Computed Tomography Images Through Advanced Generative Adversarial Networks.

Diagnostics (Basel, Switzerland)·2026
Same author

Multidimensional Comparisons Between Constrained ICA/IVA Algorithms for Multi-Subject fMRI Data Analysis.

IEEE access : practical innovations, open solutions·2026
Same journal

A Model-Free Reinforcement Learning Implementation of Decision Making Under Uncertainty by Sequential Sampling.

Neural computation·2026
Same journal

DROP: Distributional and Regular Optimism and Pessimism for Reinforcement Learning.

Neural computation·2026
Same journal

Hierarchical Active Inference Using Successor Representations.

Neural computation·2026
Same journal

W-Kernel and Its Principal Space for Frequentist Evaluation of Bayesian Estimators.

Neural computation·2026
Same journal

A Hidden Markov Model-Inspired Sequence Classification Method for Hyperdimensional Computing.

Neural computation·2026
Same journal

Sparse Graphical Modeling for Electrophysiological Phase-Based Connectivity Using Circular Statistics.

Neural computation·2026
See all related articles

Fully complex multilayer perceptron (MLP) networks using elementary transcendental functions (ETFs) overcome limitations in processing complex data. These networks demonstrate universal approximation capabilities for complex mappings, enhancing neural network efficiency.

Area of Science:

  • Complex analysis
  • Neural networks
  • Machine learning

Background:

  • Processing complex data with neural networks is challenging due to the lack of bounded, analytic complex nonlinear activation functions.
  • Traditional methods use separate real-valued MLPs, leading to inefficient backpropagation and compromised approximation.
  • Liouville's theorem highlights the conflict between boundedness and analyticity for complex functions.

Purpose of the Study:

  • To investigate the approximation ability of multilayer perceptron (MLP) networks extended to the complex domain.
  • To introduce and analyze fully complex activation functions based on elementary transcendental functions (ETFs).
  • To address the limitations of traditional ad hoc MLPs for complex data processing.

Main Methods:

Related Experiment Videos

  • Defined fully complex activation functions using elementary transcendental functions (ETFs) analytic in the complex domain.
  • Developed three proofs for the approximation capability of fully complex MLPs based on ETF singularity characteristics.
  • Extended the complex universal approximation theorem to include ETFs with removable singularities.

    • Main Results:

    • Fully complex MLPs with continuous ETFs are universal approximators of continuous complex mappings over compact sets.
    • The approximation capability extends to bounded measurable ETFs with removable singularities.
    • Complex MLPs using ETFs with isolated and essential singularities uniformly converge to nonlinear mappings in specific regions.

    Conclusions:

    • Fully complex MLPs utilizing analytic ETFs offer a parsimonious and efficient structure for complex data processing.
    • These networks overcome the shortcomings of traditional real-valued MLP approaches.
    • The study proves the universal approximation capability of fully complex MLPs under various conditions involving ETFs.