ARTIFICIAL NEURAL NETWORK

 

🧠 Artificial Neural Network (ANN)

Interactive ANN Diagram — Click any term to learn its definition and use

ANN Basic Working Structure

🔘 Click Individual ANN Terms

📥 1. Input

Input is the information supplied to an ANN.

Use: Inputs provide the features from which the neural network learns and makes predictions.

🔢 2. X₁, X₂, X₃, X₄

These represent individual input features.

Use: Each input feature contributes to the neuron's calculation through its corresponding weight.

⚖️ 3. Weights

A weight determines how strongly an input influences a neuron.

Use: During training, weights are adjusted so that the network can learn useful relationships in the data.

➕ 4. Bias

Bias is an additional learnable value added to the weighted sum.

Use: It allows the neuron to shift its activation threshold instead of forcing the decision boundary through the origin.

Σ 5. Summation

Summation combines the weighted inputs and bias.

z = Σ(wᵢxᵢ) + b

Use: It produces the value that is passed to the activation function.

🔢 6. Weighted Sum

Weighted sum is the combined contribution of all inputs after multiplying each input by its corresponding weight.

w₁x₁ + w₂x₂ + w₃x₃ + w₄x₄

Use: Determines the neuron's raw pre-activation value.

🧠 7. Neuron

A neuron is the basic computational unit of an ANN.

Use: It receives inputs, multiplies them by weights, adds bias, applies an activation function and produces an output.

⚡ 8. Activation Function

An activation function transforms the neuron's weighted sum into its output.

Use: It introduces non-linearity, allowing neural networks to learn complex patterns.

y = f(z)

🎯 9. Output

Output is the value generated by the neuron or network.

Use: It represents the model's prediction or intermediate result.

ŷ 10. Predicted Output

ŷ represents the value predicted by the neural network.

Use: It can be compared with the actual target value during model evaluation and training.

📐 11. ANN Mathematical Formula

z = w₁x₁ + w₂x₂ + w₃x₃ + ... + wₙxₙ + b

ŷ = f(z)

Use: These equations describe the basic computation performed by a neuron.

🧮 Step-by-Step ANN Calculation

Let's use a simple neuron with four inputs.

Step 1 — Given Inputs

X₁ = 2    X₂ = 3    X₃ = 1    X₄ = 2

Step 2 — Given Weights

W₁ = 0.5    W₂ = 0.4    W₃ = 0.3    W₄ = 0.2

Step 3 — Bias

b = 0.5

Step 4 — Multiply Each Input by Its Weight

W₁X₁ = 0.5 × 2 = 1.0

W₂X₂ = 0.4 × 3 = 1.2

W₃X₃ = 0.3 × 1 = 0.3

W₄X₄ = 0.2 × 2 = 0.4

Step 5 — Calculate Weighted Sum

1.0 + 1.2 + 0.3 + 0.4 = 2.9

Step 6 — Add Bias

z = 2.9 + 0.5 = 3.4

Step 7 — Apply Activation Function

For demonstration, use the Binary Step activation:

f(z) = 1, if z ≥ 0

f(3.4) = 1

Step 8 — Final Prediction

ŷ = 1

🎯 FINAL OUTPUT: ŷ = 1

The neuron produces a positive/binary output.

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