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## Meaning of sigmoid function?

Sigmoid function no matter whether you’re building a neural network from scratch or using a pre-existing library, grasping the relevance of a sigmoid function is crucial. Understanding how a neural network learns to solve difficult issues requires familiarity with the sigmoid function. This function led to other effective and desirable supervised learning methods in deep learning architectures.

You will learn about the sigmoid function and its application in neural network example-based learning in this course.

## Once you’ve finished this guide, you’ll be able to:

Inverse of the hyperbolic sine

Comparing linear and non-linear separability

How the employment of a sigmoid unit in a neural network allows for more nuanced decision-making

The time has come to begin.

Context of the Tutorial

## This tutorial consists of three sections:

Sigmoidal function

Characteristics of the sigmoid function

The distinction between linear and non-linearly separable problems

For use as an activation function in neural networks, the sigmoid is a popular choice.

### S-shaped function

Sigmoidal (sig) or (x) symbols denote the, a logistic function version (x). For each real number x, we have x = 1/(1+exp(-x))

## The Sigmoid Function and Its Characteristics and Identities

The green line in the following graph represents the S-shaped sigmoid function. Pink represents derivative graph.. On the right, we see the derivative’s statement and a few of its salient qualities.

Domicile: (-, +)

Range: (0, +1)

σ(0) = 0.5

An unbroken upward trend can be seen in the function.

#### It’s true that the function is continuous in all regions.

Calculating the value of this function over a narrow interval, such as [-10, +10], is sufficient for numerical purposes. Values of the function below -10 are close to zero. Over the range 11–100, the function values approach 1.

#### The Suppressing Power of the Sigmoid Function

The squashing sigmoid function has all real numbers as its domain and range (0, 1). Because of this, the result of the function is always between 0 and 1 even whether the input is a very large negative number or a very large positive number. In the same vein, any number between minus infinity and plus infinity is acceptable.

#### Sigmoid as a Neuronal Network Activation Function

The graphic below shows an activation function used in a neural network layer. An activation function applied to a weighted sum of the preceding layer’s inputs feeds the next layer.

Sigmoid-activated neurons always output between 0 and 1.

##### Which Is Better: Linear or Nonlinear Separability?

Let’s say we have to classify a set of data points into multiple groups. Straight lines divide linearly separable issues into two classes (or an n-dimensional hyperplane). Non-linearly separable problems occur when two groups cannot be separated by a straight line. Below is two-dimensional data.. Each data point is classified as either red or blue. In the left diagram, a linear border separates the two groups, solving the problem. Right diagram: non-linearly separable problem with non-linear decision boundary.

##### In Neural Networks, Why Is The Sigmoid Function Crucial?

A neural network’s linear activation function limits learning to linearly separable scenarios. A neural network with one hidden layer and a sigmoid activation function can learn a non-linearly separable issue.The sigmoid function is useful in neural networks for learning non-trivial decision-making procedures because it provides non-linear boundaries.

Neural network activation functions must be monotonically rising non-linear functions. Sin(x) and cos(x) cannot be activation functions. The activation function must also be continuous over the real number line. It is also necessary that the function be differentiable everywhere the real numbers can be.

When training a neural network, the back propagation technique often employs gradient descent to determine appropriate weight values for each neuron. This algorithm can be computed with the help of the activation function’s derivative.

The sigmoid function’s properties—monotonic, continuous, differentiable everywhere, and self-derivative—make it easy to calculate the update equations for learning neural network weights using a back propagation approach.

#### The activation functions of neural networks

Are required to be non-linear functions that rise monotonically. In addition to this, the activation function needs to maintain its continuity across the real number line. In addition to this, the function must be differentiable in every possible location.

#### where the real numbers can be found.

When training a neural network, the back propagation technique frequently uses gradient descent to find appropriate weight values for each neuron.

Because of its qualities, which include being monotonic, continuous, differentiable everywhere, and self-derivative, the sigmoid function makes it simple to compute the update equations that are necessary for learning the weights of neural networks by an approach known as back propagation.

Non-linear neural network activation functions must rise monotonically. Sin(x) and cos(x) cannot activate. The real number line activation function must be continuous.

##### The function must be differentiable everywhere real numbers are.

Gradient descent is used in back propagation to estimate neuron weights. The activation function’s derivative computes this algorithm.

The sigmoid function’s properties—monotonic, continuous, differentiable everywhere, and self-derivative—make it easy to build update equations for learning neural network weights using back propagation.