Introduction to Neural Networks (Lecture 18)

#AI #Python #DeepLearning #NeuralNetworks #Backpropagation #Micrograd #Calculus

Welcome to the eighteenth lecture of my Deep Learning series! 🧠📉

In the previous lecture, we conquered the activation function by deriving the analytical gradient for Tanh. Now, we move further back into the neuron to find the gradients for our *weights (w), inputs (x), and bias (b).*

This lecture is a deep dive into the fundamental "rules of thumb" for backpropagation through the most common operations in any computational graph: *Addition and Multiplication.*

In this video, we cover:
✅ *Backpropagation through Addition:* We prove analytically that when two values are added, the gradient simply "flows" through them unchanged. We demonstrate why dL/db and dL/d(weighted_sum) are identical to the incoming gradient.
✅ *Backpropagation through Multiplication:* We derive the local derivative for the product x.w. You’ll see the "swap" rule in action: the gradient with respect to one input is the value of the other input multiplied by the incoming gradient.
✅ *The "Gradient Flow" Intuition:* We build a mental model for how gradients behave—addition acts as a distributor, while multiplication acts as a scaler/interactor.
✅ *Manual Calculation vs. Chain Rule:* We use step-by-step calculus to verify these properties, ensuring you understand the "why" before we automate the "how."
✅ *Python Code Verification:* As always, we don't just trust the math. we jump into our Jupyter Notebook to verify that our manual calculations perfectly match the numerical results from our code.

By the end of this lecture, we will have manually calculated the gradient for every single parameter in our artificial neuron!

*Resources:*

🔗 *GitHub Repository (Code & Notes):* https://github.com/gautamgoel962/Yout...
🔗 *Follow me on Instagram:*   / gautamgoel978  

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We have successfully completed the manual backward pass. In the upcoming lectures, we will step away from the pen and paper and start implementing an automated `backward()` function using *Topological Sort* to handle complex graphs. Let's keep building! 📉🔥

#deeplearning #Python #Micrograd #Calculus #ChainRule #Gradients #WeightsAndBiases #DataScience #MachineLearning #Hindi #AI #Backpropagation #MathForAI #NeuralNetworks