Foundations for Machine Learning

Currently Playing: Chain rule for Machine Learning | Calculus for ML | Mathematical Foundations for ML [Lecture 18]

Understanding Chain Rule does not have to be complex, even if it is at the heart of machine learning! In machine learning, especially in neural networks, chain rule helps determine how changes in one layer affect the next. But let us simplify that further: Imagine a cat that "meows" 3 times. A dog repeats the cat’s sound twice. Then a cow repeats the dog’s output 1 time. Finally a duck repeats cow's output 5 times At the end, how many "quacks" will the duck produce? The answer comes from multiplying these steps: 3 (cat) × 2 (dog) × 1 (cow) × 5 (cow) = 30 quacks. This is exactly how chain rule works: small changes propagate step-by-step through multiple layers by multiplying the derivatives. In my latest lecture, "Calculus for Machine Learning – Chain Rule Simplified", I explore: 1) The chain rule explained with logical intuition and real-world examples. 2) Why multiplication (not addition) drives changes in composite functions. 3) Practical applications of chain rule in neural networks and beyond. I have also included step-by-step practice problems to help you master this concept. Watch the full lecture here: https://youtu.be/VFg7WlMlIQs Let me know if this explanation clicks for you—or if you have a better analogy to describe the chain rule!