Chapter 11.4 - Backpropagation

loss.backward()

After computing the batch loss, we still don't know how to improve the model.

The batch loss only tells us the loss value

It doesn't tell us which weights should increase or decrease.

loss.backward() does this for each single weight in every weight in the weights matrix

$$\text{Gradient} = \frac{\partial \text{Loss}} {\partial \text{Weight}}$$

This value is called the gradient. it calculates

"If I slightly change each weight in the model, how will the loss change?"

Gradient	Meaning
Positive ($> 0$)	Increasing the weight increases the loss. ❌
Negative ($< 0$)	Increasing the weight decreases the loss. ✅
Zero ($= 0$)	A tiny change in the weight does not change the loss (locally flat).

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backpropogation attaches the information to these tensors about how they "should change" in order to achieve targets . how it attaches the information we will learn in ch 8.6 Tensors The Backpropogation step will calculate this for each type of weight matrix there is these are the matrix:

Layer	Weight Matrix	Purpose	Updated by Backprop?
Token Embedding	Embedding Matrix	Converts token IDs → vectors	✅ Yes
Positional Embedding	Position Embedding Matrix	Adds position information	✅ Yes
Query Projection	(W_Q)	Creates Query vectors	✅ Yes
Key Projection	(W_K)	Creates Key vectors	✅ Yes
Value Projection	(W_V)	Creates Value vectors	✅ Yes
Attention Output Projection	(W_O)	Combines attention heads	✅ Yes
Feed Forward Layer 1	(W_1)	Expands hidden dimension	✅ Yes
Feed Forward Layer 2	(W_2)	Compresses back to model dimension	✅ Yes
Final Output Layer (LM Head)	(W_out)	Produces vocabulary logits	✅ Yes
LayerNorm Scale	(\gamma)	Learns feature scaling	✅ Yes
LayerNorm Bias	(\beta)	Learns feature shifting	✅ Yes

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