Introduction to Neural Networks (Lecture 7)

Описание: Here is the description for the current video, tailored to match the format and style of the previous lecture's description:

Welcome to the seventh lecture of my Deep Learning series! 🧠

In this video, we reach the heart of neural network training: **Backward Propagation**. Building upon the complex computational graph we visualized in the last lecture, we now manually calculate the gradients for every node in our network.

The goal is to understand exactly how a change in any input (like a, b, c, d, e, f) impacts the final Loss (L). To ensure our understanding is rock solid, we don't just rely on calculus formulas; we verify every single gradient using code and the fundamental definition of a derivative (the limit as h approaches 0). This lecture bridges the gap between high-school calculus and the algorithms that power modern AI.

We dissect the "Chain Rule," demonstrating how gradients flow backward through the graph. We learn that the global gradient of a node is simply its *Local Gradient* multiplied by the **Upstream Gradient**. By the end of this video, you will intuitively understand why we multiply gradients during backprop.

In this video, we cover:
✅ *Manual Backpropagation:* Going backward from the output (Loss) to the inputs to calculate gradients step-by-step.
✅ *Numerical Verification:* Writing Python code to calculate the "slope" using the definition of a derivative ((f(x+h) - f(x))/h) to prove our analytical math is correct.
✅ *Derivatives of Operations:* Understanding the gradient behavior of Addition (distributes the gradient) and Multiplication (swaps the values).
✅ *The Chain Rule:* The "Heart of Backpropagation"—learning how to combine local derivatives with global derivatives to propagate information backward.
✅ *Gradient Assignment:* Manually updating `self.grad` in our Python objects to verify the values against our numerical checks.

*Resources:*

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

*Prerequisites:*

Lecture 6 (Visualizing the Forward Pass & Graphviz)
Lecture 5 (The Value Class)
Basic understanding of Derivatives (Slope)

Subscribe to continue the journey. In this lecture, we did the math manually; in the next lecture, we will write the code to automate this entire process by implementing the `backward()` function! 📉🚀

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