Why Most Attention Tutorials Miss the Point
The attention formula looks deceptively simple: $\text{Attention}(Q, K, V) = \text{softmax}\left(\frac{QK^T}{\sqrt{d_k}}\right)V$. But when I actually implemented it from scratch, the numerical instability caught me off guard. My first attempt produced NaN values within 10 forward passes.
Here's the thing: understanding the math is one step. Making it numerically stable is another. And making it fast enough to be useful? That's where most tutorials stop short.
I'm going to build self-attention twice — once in pure NumPy to understand every matrix operation, then in PyTorch to see what the framework handles for us. The NumPy version will break in interesting ways. The PyTorch version will show us why those guardrails exist.
Self-Attention: The Core Mechanism
Self-attention lets each position in a sequence look at every other position to decide what's relevant. For a sequence of $n$ tokens with embedding dimension $d_{model}$, we create three projections:
$$Q = XW_Q, \quad K = XW_K, \quad V = XW_V$$
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