Introduction to Neural Networks (Lecture 21)

Описание: #AI #Python #DeepLearning #NeuralNetworks #GradientAccumulation #Micrograd #BugFix

Welcome to the twenty-first lecture of my Deep Learning series! 🧠🐛

In the previous lecture, we successfully implemented the topological sort and automated the backward pass. Our engine seemed complete—but there was a subtle "base case" we missed. Today, we identify a critical flaw in our logic regarding variable reuse and implement the fix: **Gradient Accumulation**.

This lecture focuses on debugging and the Multivariate Chain Rule. What happens when a single node in our graph sends its output to multiple other nodes? Currently, our engine creates a "Gradient Overwriting" problem.

In this video, we cover:
✅ *The "Bug" Observation:* We construct a specific computational graph where an input variable (e.g., `a`) is used in two different operations (multiplication and addition) simultaneously.
✅ *The Overwriting Problem:* We analyze the trace to see that our current `.backward()` implementation calculates the gradient for one path, but then overwrites it with the gradient from the second path, losing information.
✅ *The Mathematical Solution:* We revisit the chain rule for multivariate calculus. If a variable influences the loss through multiple paths, its total gradient must be the *sum* of the local gradients from all those paths.
✅ *Implementing the Fix:* We modify our `Value` class methods (`__add__`, `__mul__`, `tanh`, `relu`, etc.). Instead of setting gradients (`self.grad = ...`), we change them to accumulate (`self.grad += ...`).
✅ *Verification:* We dry run the corrected code against our manual calculations to prove that the gradients (e.g., -3 and -8) are now mathematically accurate.

By the end of this lecture, our Autograd Engine is completely bug-free and robust! We can now handle complex graphs where nodes are reused multiple times, which is essential for modern neural network architectures.

*Resources:*

🔗 GitHub Repository (Code & Notes):
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Now that the engine is solid, we are ready to level up. In the next lecture, we will compare our custom engine against *PyTorch* to see the similarities, and then we will start building our Neuron and Layer classes (`nn.py`). Let's keep building! 📉🔥

#deeplearning #Python #Micrograd #Calculus #Debugging #DataScience #MachineLearning #Hindi #AI #NeuralNetworks #Backpropagation #Coding #Pytorch