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 Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

116
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
116
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

107
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
107
Classification of Systems-II01:31

Classification of Systems-II

183
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
183
Classification of Systems-I01:26

Classification of Systems-I

221
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
221
Aggregates Classification01:29

Aggregates Classification

350
Aggregate classification is generally based on its size, petrographic characteristics, weight, and source. Size classification ranges from coarse to fine aggregates, defined by the size of the particles. Coarse aggregates are particles that do not pass through ASTM sieve No. 4, and aggregates that pass through the sieve are fine aggregates.
Petrographic classification groups aggregates based on common mineralogical characteristics. Some of the common mineral groups found in aggregates are...
350
Classification of Signals01:30

Classification of Signals

556
In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where...
556

You might also read

Related Articles

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

Sort by
Same author

The rise of <i>Candidozyma auris</i> in Czechia: three clades, prosthetic joint infection and fluconazole resistance development, 2022 to 2024.

Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin·2025
Same author

Exploratory drilling: how to set up, carry out, and evaluate a seroprevalence study.

Casopis lekaru ceskych·2020
Same author

Translation-Invariant Kernels for Multivariable Approximation.

IEEE transactions on neural networks and learning systems·2020
Same author

Kolmogorov's Theorem Is Relevant.

Neural computation·2019
Same author

Some insights from high-dimensional spheres: Comment on "The unreasonable effectiveness of small neural ensembles in high-dimensional brain" by Alexander N. Gorban et al.

Physics of life reviews·2019
Same author

Classification by Sparse Neural Networks.

IEEE transactions on neural networks and learning systems·2019
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

Related Experiment Video

Updated: Jul 25, 2025

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

9.2K

Approximation of classifiers by deep perceptron networks.

Věra Kůrková1, Marcello Sanguineti2

  • 1Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 18207 Prague, Czech Republic.

Neural Networks : the Official Journal of the International Neural Network Society
|June 26, 2023
PubMed
Summary
This summary is machine-generated.

Deep perceptron networks can classify large datasets effectively. High-dimensional geometry reveals conditions for deterministic approximation errors in deep learning models, using statistical learning theory.

Keywords:
Approximation by deep networksConcentration of measureGrowth functionsMethod of bounded differencesProbabilistic bounds on approximation errorsRandom classifiers

More Related Videos

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
03:31

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

Published on: December 15, 2023

585
P300-Based Brain-Computer Interface Speller Performance Estimation with Classifier-Based Latency Estimation
06:09

P300-Based Brain-Computer Interface Speller Performance Estimation with Classifier-Based Latency Estimation

Published on: September 8, 2023

617

Related Experiment Videos

Last Updated: Jul 25, 2025

Deep Neural Networks for Image-Based Dietary Assessment
13:19

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

9.2K
Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
03:31

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications

Published on: December 15, 2023

585
P300-Based Brain-Computer Interface Speller Performance Estimation with Classifier-Based Latency Estimation
06:09

P300-Based Brain-Computer Interface Speller Performance Estimation with Classifier-Based Latency Estimation

Published on: September 8, 2023

617

Area of Science:

  • Computational mathematics
  • Machine learning theory
  • High-dimensional geometry

Background:

  • Deep perceptron networks are crucial for large dataset classification.
  • Understanding their approximation error behavior is key to improving performance.

Purpose of the Study:

  • To derive conditions for deterministic approximation errors in deep perceptron networks.
  • To provide insights into network depth, activation functions, and parameter impact on classification accuracy.

Main Methods:

  • Employing high-dimensional geometry principles.
  • Utilizing concentration of measure inequalities (method of bounded differences).
  • Applying concepts from statistical learning theory.

Main Results:

  • Derived conditions on network architecture and activation functions (Heaviside, ramp sigmoid, rectified linear, rectified power) for deterministic error behavior.
  • Established probabilistic bounds on approximation errors.

Conclusions:

  • Network properties significantly influence classification accuracy and error predictability.
  • Theoretical insights can guide the design of more effective deep learning models for large-scale data.