ANN(Artificial Neural Network) in Mathematical Model

Artificial Neural Network (ANN)

An ANN is made up of neurons, and each neuron has its own weights, which help it process information. This model is very important in building intelligent systems.

Let’s break down the main components:

1. Input

Think of this as the data the neuron receives. For example:

x1,x2,…,xnx_1, x_2, …, x_nx1​,x2​,…,xn​ are the inputs coming into the neuron.

Each input represents a specific piece of information or feature.

2. Weight

Each input has its own weight that determines its importance.

For example:

Input x1x_1x1​ will have a weight w1w_1w1​, input x2x_2x2​ will have a weight w2w_2w2​, and so on until xnx_nxn​, which has weight wnw_nwn​.

These weights can be adjusted during learning to improve accuracy.

3. Summation of Weighted Inputs

The neuron sums up all the weighted inputs and adds a bias term bbb, which helps fine-tune the output.

The formula for this step is:

S=∑(wi⋅xi)+bS = sum (w_i cdot x_i) + bS=∑(wi​⋅xi​)+b

Here:

wiw_iwi​: Weight of input xix_ixi​bbb: Bias, a constant value added to the sum to adjust it.

4. Activation Function

This is like the decision-maker for the neuron.

If the total sum SSS is high enough (greater than a threshold), the neuron fires (turns ON).If not, the neuron remains inactive (turns OFF).

The activation function transforms SSS into the neuron’s final output yyy:

y=f(S)y = f(S)y=f(S)

Some common activation functions include:

Sigmoid: Smooth output between 0 and 1.ReLU: Outputs 0 if SSS is negative; otherwise, outputs SSS.Tanh: Outputs values between -1 and 1.Simplified Analogy

Imagine a light switch:

Inputs (x1,x2,… x_1, x_2, …x1​,x2​,…) are the people deciding whether to turn it on.Weights (w1,w2,… w_1, w_2, …w1​,w2​,…) are how much influence each person has.Summation adds up everyone’s opinions.The activation function decides:If the combined opinion is strong, the switch turns ON.Otherwise, it stays OFF.