What are activation functions, and why are they used?

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What are Activation Functions?

An activation function is a mathematical function applied to the output of a neuron in a neural network.

• It decides whether a neuron should be activated or not (i.e., whether information should pass forward).

• It introduces non-linearity into the model, which allows the network to learn complex patterns.

Why Are They Used?

1. Introduce Non-linearity → Without activation functions, neural networks would just be linear models (like simple regression), unable to handle images, text, or speech.

2. Control Output Range → They map values into specific ranges (e.g., 0–1, -1–1).

3. Enable Deep Learning → Allow stacking of multiple layers to extract features.

4. Improve Training → Help gradients flow properly during backpropagation.

Types of Activation Functions

1. Sigmoid Function

   • Output: (0 to 1)

   • Good for probabilities.

   • Problem: vanishing gradients.

   $$f(x) = \frac{1}{1+e^{-x}}$$

2. Tanh (Hyperbolic Tangent)

   • Output: (-1 to 1)

   • Centered at 0, better than sigmoid.

   $$f(x) = \tanh(x)$$

3. ReLU (Rectified Linear Unit)

   • Output: 0 if x < 0, else x.

   • Very popular in deep learning.

   • Fast, reduces vanishing gradient problem.

   $$f(x) = \max(0, x)$$

4. Leaky ReLU

   • Fixes ReLU’s “dead neuron” problem by allowing small negative values.

5. Softmax

   • Converts outputs into probabilities (used in classification problems with multiple classes).

In short:

• Activation functions = the “switches” of neurons.

• They decide what information passes forward and allow networks to learn non-linear relationships.

• Common ones: Sigmoid, Tanh, ReLU, Softmax.

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