Feature/ml solution articles new

[ahmadbasyouni10]

• File(s) Modified: articles/batch-normalization.md, articles/multi-layer-backpropagation.md, articles/weight-initialization.md, articles/multi-headed-self-attention.md, articles/transformer-block.md
• Language(s) Used: python
• Submission URL: N/A (ML course solution articles, not LeetCode submissions)

Summary

Solution articles for the 3 new ML problems + W_o output projection fix for 2 existing problems:

New articles:

• multi-layer-backpropagation.md — Chain rule through 2-layer MLP with ReLU, covers forward/backward pass, ReLU mask, outer product gradients
• weight-initialization.md — Xavier vs Kaiming initialization, activation stability analysis across layers using raw matrix approach
• batch-normalization.md — Training vs inference modes, running statistics, axis=0 vs axis=1 distinction

Updated articles:

• multi-headed-self-attention.md — Added W_o output projection (nn.Linear(attention_dim, attention_dim, bias=False)) to solution code and explanation
• transformer-block.md — Updated inner MultiHeadedSelfAttention class to include W_o output projection, matching the updated problem

Each new article follows the existing format: Prerequisites → Concept → Solution (Intuition, Implementation, Walkthrough, Time & Space Complexity) → Common Pitfalls → In the GPT Project → Key Takeaways.