Efficient Implementation of Neural Networks

Reasons deep learning researchers have scaled up neural networks:
Neural networks can be vectorized
Can be implemented efficiently using matrix multiplications
“Parallel computing hardware, including GPUs, but also some CPU functions are very good at doing very large matrix multiplications”
“Without these ideas, I don’t think deep learning would be anywhere near a success and scale today”
Traditional Implementation (non-vectorized):
Example code from previous lesson:
- Input X (features)
- W (weights for first, second, third neurons)
- Parameters B (bias)
- Uses for-loop to process each neuron individually
- Example output: [1, 0, 1]
Vectorized Implementation:
Uses different data structure format:
- X with double square brackets (2D array, like in TensorFlow)
- W remains the same
- B becomes a one-by-three 2D array
Replaces entire for-loop with just a couple lines of code:
```
Z = np.matmul(A_in, W) + B
A_out = g(Z)  # g is sigmoid function
return(A_out)
```
- “matmul is how NumPy carries out matrix multiplication”
Key difference:
- All quantities (X/A_in, W, B, Z, A_out) become 2D arrays/matrices
- “This turns out to be a very efficient implementation”
Understanding the mechanics:
What matmul is actually doing requires understanding matrix multiplication
Upcoming optional videos will explain:
- Matrix multiplication basics
- How matmul creates the vectorized implementation

Note: If already familiar with linear algebra concepts (vectors, matrices, transposes, matrix multiplication), you can “safely just quickly skim over these two videos”

Vectorized implementations using matrix multiplication enable neural networks to scale efficiently. By replacing loops with matrix operations, the code runs much faster on modern hardware, especially GPUs, making deep learning practical for large models.