Machine Learning Day 10 (Activation Functions & Universal Approximation Theory | Deep Learning

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In this session, we dive deep into Activation Functions and the Universal Approximation Theory, two crucial concepts in deep learning. We’ll explore how different activation functions impact neural network performance and why neural networks can approximate any function with enough complexity.

🔹 Topics Covered:

⏳ Timeframe Breakdown:

📌 0:00 - 2:30 | Introduction to Activation Functions

What are activation functions in neural networks?

Why are they necessary for deep learning models?

Role of non-linearity in deep learning

📌 2:30 - 7:00 | Types of Activation Functions (With Graphs & Examples)
✅ Sigmoid Function – Used in binary classification, smooth gradient, but prone to vanishing gradient problem. (Graph: Sigmoid curve showing smooth transitions between 0 and 1.)
✅ Tanh Function – Centered around zero, better than sigmoid but still suffers from vanishing gradient. (Graph: Tanh curve illustrating values between -1 and 1.)
✅ ReLU (Rectified Linear Unit) – Popular in deep networks due to efficiency, but can suffer from "dying ReLU" problem. (Graph: ReLU function showing zero for negative inputs and linear for positives.)
✅ Leaky ReLU & Parametric ReLU – Solutions to the dying ReLU problem. (Graph: Leaky ReLU with a small slope for negative values.)
✅ Softmax Function – Used in multi-class classification. (Graph: Softmax curve showing probability distribution across multiple classes.)

📌 7:00 - 12:30 | Universal Approximation Theory Explained

The theorem states that a neural network with a single hidden layer and sufficient neurons can approximate any continuous function.

Why depth and width of networks matter.

Practical applications in AI and deep learning. (Graph: Visualization of a neural network approximating a complex function.)

📌 12:30 - 18:00 | Practical Examples & Intuition

Implementing activation functions in Python/TensorFlow.

How activation function choices impact training.

Example: Image classification model with different activations. (Graph: Comparison of training loss with different activation functions.)

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