September 20, 2024

# What is the meaning sigmoid function?

Sigmoid function no matter whether you’re developing a neural network from scratch or utilising a pre-existing library, knowing the relevance of a sigmoid function is vital. Understanding how a neural network learns to handle challenging challenges involves familiarity with the sigmoid function. Other functions that lead to effective and desired solutions for supervised learning in deep learning architectures were found by using this one as a starting point.

Sigmoid function no matter whether you’re developing a neural network from scratch or utilising a pre-existing library, knowing the relevance of a sigmoid function is vital. Understanding how a neural network learns to handle challenging challenges involves familiarity with the sigmoid function. Other functions that lead to effective and desired solutions for supervised learning in deep learning architectures were found by using this one as a starting point.

You will study 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 sophisticated decision-making

The time has come to begin.

Context of the Tutorial

### This lesson consists of three sections:

Sigmoidal function

Characteristics of the sigmoid function

The contrast between linear and non-linearly separable issues

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

#### S-shaped function

The sigmoid function, a version of the logistic function, is often denoted by the symbols sigmoidal (sig) or (x) (x) (x). For each real number x, we have x = 1/(1+exp(-x))

#### Sigmoid Function: Definition, Properties, and Applications

The sigmoid function, indicated by the green line in the following graph, has a graph that is S-shaped. Derivative graph is presented in pink as well. On the right, we see the derivative’s statement and a couple of its noteworthy properties.

Domicile: (-, +)

Range: (0, +1)

σ(0) = 0.5

An continuous increasing trend can be seen in the function.

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

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

#### The Suppressing Power of the Sigmoid Function

The squashing sigmoid function has all real numbers as its domain and range (0, 1). (0, 1). Because of this, the outcome 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 negative infinity and plus infinity is admissible.

#### Sigmoid as a Neuronal Network Activation Function

In artificial neural networks, the sigmoid function acts as an activation function.

The image below shows an activation function used in a neural network layer. An activation function applied on a weighted sum of the inputs from the previous layer feeds the next layer.

Sigmoid-activated neurons always output between 0 and 1.

Additionally, the output of this device would be a non-linear function of the weighted sum of inputs, just as the sigmoid is a non-linear function. An example of a neuron that uses a sigmoid activation function is a sigmoid unit.

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

We need to classify a set of data points into one of several classes. A problem is linearly separable if and only if a straight line (or n-dimensional hyperplane) can partition it into two classes (or an n-dimensional hyperplane). Non-linearly separable problems occur when the two groups cannot be divided by a straight line. Below is two-dimensional data. Data points are red or blue.. In the left diagram, we can see an example of an issue that can be remedied by creating a linear boundary, separating the two groups displayed. Graph on the right: a non-linearly separable problem with a non-linear decision boundary

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

Linear activation functions limit a neural network’s 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 gives non-linear bounds.

Neural networks can use only monotonically growing non-linear functions as activation functions. Sin(x) and cos(x) cannot be activation functions. It is also important that the function be differentiable everywhere the real numbers can be.

When training a neural network, the back propagation technique commonly includes gradient descent to calculate acceptable weight values for each neuron.

The activation function’s derivative computes this method.

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.

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