They asked me to explain the formula before coding, which I actually appreciated because I'd fumbled this before by jumping straight to implementation and getting the matrix dimensions wrong.
First, explain the mathematical formulation of scaled dot-product attention, including the role of the scaling factor and optional causal masking. Then, implement it step-by-step in NumPy or PyTorch, ensuring numerical stability and efficiency. Finally, discuss trade-offs and potential optimizations.
Pro tip: Mention that using `torch.softmax` or `np.exp` with max subtraction improves numerical stability, and that causal masking can be implemented by setting future positions to -inf before softmax.
Describe the formula: Attention(Q, K, V) = softmax(QK^T / sqrt(d_k)) V. Explain each component: Q, K, V shapes, scaling factor, softmax, and optional causal mask.
List the steps: compute QK^T, scale by sqrt(d_k), apply causal mask if needed, apply softmax, and multiply by V. Mention handling batch dimensions.
Implement in NumPy or PyTorch, using efficient matrix operations. For PyTorch, use torch.matmul and torch.softmax; for NumPy, use np.matmul and stable softmax.
Explain how to avoid overflow in softmax by subtracting the max, and how to apply causal masking by setting masked positions to -inf before softmax.
Discuss time and space complexity, and mention optimizations like using fused kernels or memory-efficient attention for large sequences.
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