Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Convolution Properties I

Convolution Properties I

Convolution computations can be simplified by utilizing their inherent properties.
The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output:

Convolution Properties II

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

Convolution: Math, Graphics, and Discrete Signals

Convolution: Math, Graphics, and Discrete Signals

In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time.
To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

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....

Region of Convergence of Laplace Tarnsform

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...

Convergence of Fourier Series

Convergence of Fourier Series

The Fourier series is a powerful mathematical tool for representing periodic signals as an infinite sum of complex exponentials. In practice, this infinite series is truncated to a finite number of terms, yielding a partial sum. This truncation makes the approximation of the signal feasible but introduces certain challenges, particularly near discontinuities, known as the Gibbs phenomenon.
The Gibbs phenomenon refers to the persistent oscillations and overshoots that occur near discontinuities...

You might also read

Related Articles

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

Sort by

Same journal

RETRACTION: Real-Time Modulation of Physical Training Intensity Based on Wavelet Recursive Fuzzy Neural Networks.

Computational intelligence and neuroscience·2026

Same journal

RETRACTION: Multidimensional Heterogeneous Network Link Adaptation Based on Mobile Environment.

Computational intelligence and neuroscience·2026

Same journal

RETRACTION: Framework to Segment and Evaluate Multiple Sclerosis Lesion in MRI Slices Using VGG-UNet.

Computational intelligence and neuroscience·2026

Same journal

RETRACTION: Facial Emotion Recognition Using a Novel Fusion of Convolutional Neural Network and Local Binary Pattern in Crime Investigation.

Computational intelligence and neuroscience·2026

Same journal

RETRACTION: Automatic Intelligent System Using Medical of Things for Multiple Sclerosis Detection.

Computational intelligence and neuroscience·2026

Same journal

RETRACTION: Intangible Cultural Heritage Reproduction and Revitalization: Value Feedback, Practice, and Exploration Based on the IPA Model.

Computational intelligence and neuroscience·2026

Search research articles

Related Experiment Video

Updated: Aug 15, 2025

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy

Published on: January 29, 2022

A Frobenius Norm Regularization Method for Convolutional Kernel Tensors in Neural Networks.

Pei-Chang Guo¹

¹School of Science, China University of Geosciences, Beijing 100083, China.

Computational Intelligence and Neuroscience

|December 29, 2022

Summary

We introduce a new regularization method for convolutional neural networks (CNNs). This technique bounds singular values, improving training stability and model generalizability in deep learning.

More Related Videos

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Related Experiment Videos

Last Updated: Aug 15, 2025

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy

Control of Cell Adhesion using Hydrogel Patterning Techniques for Applications in Traction Force Microscopy

Published on: January 29, 2022

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

Deep Neural Networks for Image-Based Dietary Assessment

Deep Neural Networks for Image-Based Dietary Assessment

Published on: March 13, 2021

Area of Science:

Deep Learning
Machine Learning
Artificial Intelligence

Background:

Convolutional neural networks (CNNs) are crucial deep learning models.
Training stability is often hindered by exploding/vanishing gradients.
Generalizability of neural networks can be improved by bounding Jacobian singular values.

Purpose of the Study:

To propose a novel Frobenius norm penalty function for convolutional kernel tensors.
To ensure singular values of the transformation matrix are bounded around 1 during training.

Main Methods:

Developing a new Frobenius norm penalty function for convolutional kernel tensors.
Implementing gradient-type methods to apply the penalty function.
Analyzing the effect of the penalty on singular values of the transformation matrix.

Main Results:

The proposed penalty function effectively bounds the singular values around 1.
Gradient-type methods are shown to be applicable for implementing this regularization.
The method offers a potentially useful regularization strategy for convolutional layer weights.

Conclusions:

The novel penalty function provides a method to stabilize CNN training.
This approach enhances the generalizability of deep learning models.
It represents a valuable regularization technique for convolutional neural networks.