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Sigmoid

Published: 2015/02/23

Channel: Udacity

The Sigmoid Curve

Published: 2012/11/11

Channel: Pete Dalgleish

Sigmoid function

Published: 2014/08/16

Channel: Audiopedia

Neural networks [1.2] : Feedforward neural network - activation function

Published: 2013/11/15

Channel: Hugo Larochelle

Julia Programming : The Sigmoid Function Programming Exercise

Published: 2014/03/02

Channel: Stats-Lab Dublin

Mathematical device used in Deep Learning V - Sigmoid function

Published: 2015/10/23

Channel: Vasu Srinivasan

Derivative of the sigmoid activation function, 9/2/2015

Published: 2015/02/10

Channel: Lutfi Al-Sharif

5.3.2 Draw and label a graph showing a sigmoid (S-shaped) population growth curve

Published: 2013/04/05

Channel: Stephanie Castle

Intro to Neural Networks

Published: 2013/06/10

Channel: Michael Zibulevsky

Normalised Tunable Sigmoid Function Demo in Unity3D

Published: 2013/06/26

Channel: Dino Dini

Normalised Tunable Sigmoid Function 2.0

Published: 2013/11/24

Channel: Dino Dini

The Gompertz Sigmoid Function and Its Derivative

Published: 2009/07/16

Channel: wolframmathematica

Logistic function

Published: 2014/08/13

Channel: Audiopedia

Lecture 13.3 — Learning sigmoid belief nets [Neural Networks for Machine Learning]

Published: 2016/02/05

Channel: Colin McDonnell

Sigmoid function displacement time servo control

Published: 2009/05/30

Channel: Devraj Joshi

The Gompertz Sigmoid Function and Its Derivative

Published: 2010/04/13

Channel: wolframmathematica

Introduction to Neural Networks for C#(Class 4/16, Part 2/5) - activation function

Published: 2009/02/07

Channel: Jeff Heaton

Organizational Learning Tool: The Sigmoid Curve

Published: 2013/10/15

Channel: Sigmoid Curve Consulting Group - Experts in Change Leadership

Sigmoid Function and Gradient in Backpropagation

Published: 2016/07/10

Channel: dr3rubens

Impact of Bias on the Sigmoid Activation function

Published: 2014/10/19

Channel: N RS

Equivalence of two activation functions in hidden layer: example

Published: 2014/01/04

Channel: Anish Turlapaty

Neural Network Calculation (Part 2): Activation Functions & Basic Calculation

Published: 2010/10/15

Channel: Jeff Heaton

Mathematical Biology. 19: Sigmoidal Functions, Multisite Systems

Published: 2014/02/25

Channel: UCI Open

Fitting S-Curves with a Boltzmann Equation

Published: 2016/02/02

Channel: Dr. Gerard Verschuuren

Using the Flexible Spline function (FlexSpline) in Excel

Published: 2013/11/13

Channel: SRS1Software

Sigmoid Curve model of Change

Published: 2015/11/17

Channel: Mary-Anne Murphy

Mod-08 Lec-26 Multilayer Feedforward Neural networks with Sigmoidal activation functions;

Published: 2013/12/02

Channel: nptelhrd

Neural network tutorial: The back-propagation algorithm (Part 1)

Published: 2012/01/07

Channel: Ryan Harris

The sigmoid growth curve

Published: 2011/05/18

Channel: IBbiologyBlog

Contrast Enhancement of Color Images using Tunable Sigmoid Function.wmv

Published: 2011/03/16

Channel: VERILOG COURSE TEAM

Logistic growth curve

Published: 2015/09/26

Channel: Shomu's Biology

Logistic Regression Cost Function

Published: 2014/04/28

Channel: Machine Learning

1.6 Sigmoid Emax model - Hill factor

Published: 2012/03/12

Channel: Shankar Lanke

2. Bob Buford explains the Sigmoid Curve

Published: 2012/02/22

Channel: HalftimeOnDemand

The Sigmoid Curve (Positive Psychology)

Published: 2012/10/04

Channel: MrLiveanew

5. RBMs are Infinite Sigmoid Belief Nets

Published: 2013/11/09

Channel: Artificial Intelligence Courses

딥러닝 2. How Artificial Neurons Work (한국어)

Published: 2016/04/30

Channel: J Hong

Octave Tutorial #6 - Functions

Published: 2014/09/11

Channel: DrapsTV

Company Introduction: About Sigmoid Consulting Group

Published: 2013/10/15

Channel: Sigmoid Curve Consulting Group - Experts in Change Leadership

Intorduction to Sigmoid: 1E Simulation

Published: 2008/02/20

Channel: TheSigmoidProject

The Logistic Function

Published: 2014/02/24

Channel: Gregory Chapman

Derivatives of Exponential Functions

Published: 2008/11/29

Channel: patrickJMT

You don't know what you don't know: the sigmoid curve

Published: 2010/03/11

Channel: wiscoach

L3 - Why the Sigmoidal Emax model is Special

Published: 2014/04/04

Channel: Alan Maloney

Logistic Sigmoid Market Model

Published: 2009/07/10

Channel: wolframmathematica

免費統計教學範例39 Sigmoidal Function Fit S曲線回歸

Published: 2013/05/08

Channel: 全傑科技

Neural networks [2.5] : Training neural networks - activation function derivative

Published: 2013/11/15

Channel: Hugo Larochelle

Convolutional Neural Network Part-1

Published: 2016/08/15

Channel: Be Expert in Minutes

SIGMOID COLON : DR SAMEH GHAZY

Published: 2014/06/11

Channel: Sameh Ghazy

Jump Your Sigmoid Curve

Published: 2014/04/24

Channel: Vic Lindal

From Wikipedia, the free encyclopedia

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A **sigmoid function** is a mathematical function having an "S" shaped curve (**sigmoid curve**). Often, *sigmoid function* refers to the special case of the logistic function shown in the first figure and defined by the formula

Other examples of similar shapes include the Gompertz curve (used in modeling systems that saturate at large values of t) and the ogee curve (used in the spillway of some dams). Sigmoid functions have finite limits at negative infinity and infinity, most often going either from 0 to 1 or from −1 to 1, depending on convention.

A wide variety of sigmoid functions have been used as the activation function of artificial neurons, including the logistic and hyperbolic tangent functions. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic distribution, the normal distribution, and Student's *t* probability density functions.

A sigmoid function is a bounded differentiable real function that is defined for all real input values and has a positive derivative at each point.^{[1]}

In general, a sigmoid function is real-valued and differentiable, having either a non-negative or non-positive first derivative^{[citation needed]} which is bell shaped. There are also a pair of horizontal asymptotes as . The differential equation , with the inclusion of a boundary condition providing a third degree of freedom, , provides a class of functions of this type.

The logistic function has this further, important property, that its derivative can be expressed by the function itself,

Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a detailed description is lacking, a sigmoid function is often used.^{[2]}

Besides the logistic function, sigmoid functions include the ordinary arctangent, the hyperbolic tangent, the Gudermannian function, and the error function, but also the generalised logistic function and algebraic functions like .

The integral of any smooth, positive, "bump-shaped" function will be sigmoidal, thus the cumulative distribution functions for many common probability distributions are sigmoidal. The most famous such example is the error function, which is related to the cumulative distribution function (CDF) of a normal distribution.

Simpler approximations of smooth sigmoid functions, especially piecewise linear functions or piecewise constant functions, are preferred in some applications, where speed of computation is more important than precision; extreme forms are known as a **hard sigmoid**.^{[3]}^{[4]} These are particularly found in artificial intelligence, especially computer vision and artificial neural networks. The most extreme examples are the sign function or Heaviside step function, which go from −1 to 1 or 0 to 1 (which to use depends on normalization) at 0.^{[5]} For example, the Theano library provides two approximations: `ultra_fast_sigmoid`

and `hard_sigmoid`

, which is a 3-part linear approximation (output 0, line with slope 5, output 1).^{[6]}

Wikimedia Commons has media related to .Sigmoid functions |

- Cumulative distribution function
- Generalized logistic curve
- Gompertz function
- Heaviside step function
- Hyperbolic function
- Logistic distribution
- Logistic function
- Logistic regression
- Logit
- Modified hyperbolic tangent
- Softplus function
- Smoothstep function (Graphics)
- Softmax function
- Weibull distribution
- Netoid function

**^**Han, Jun; Morag, Claudio (1995). "The influence of the sigmoid function parameters on the speed of backpropagation learning". In Mira, José; Sandoval, Francisco.*From Natural to Artificial Neural Computation*. pp. 195–201.**^**Gibbs, M.N. (Nov 2000). "Variational Gaussian process classifiers".*IEEE Transactions on Neural Networks*.**11**(6): 1458–1464. doi:10.1109/72.883477.**^**Quora, "What is hard sigmoid in artificial neural networks? Why is it faster than standard sigmoid? Are there any disadvantages over the standard sigmoid?", Leo Mauro's answer**^**How is Hard Sigmoid defined**^**Curves and Surfaces in Computer Vision and Graphics, Volume 1610, SPIE, 1992, "hard+sigmoid" p. 301**^**nnet – Ops for neural networks

- Mitchell, Tom M. (1997).
*Machine Learning*. WCB–McGraw–Hill. ISBN 0-07-042807-7.. In particular see "Chapter 4: Artificial Neural Networks" (in particular pp. 96–97) where Mitchell uses the word "logistic function" and the "sigmoid function" synonymously – this function he also calls the "squashing function" – and the sigmoid (aka logistic) function is used to compress the outputs of the "neurons" in multi-layer neural nets. - Humphrys, Mark. "Continuous output, the sigmoid function". Properties of the sigmoid, including how it can shift along axes and how its domain may be transformed.

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