from scratch

The assign-then-update loop is ten lines; the signal is whether you handle the three things that bite in production: initialization, an empty cluster, and a real convergence test instead of a fixed iteration count.

There is no training, just storage; the work is at query time. The signal is whether you vectorize the distance computation, break ties sensibly, and know when O(n) per query forces you onto an ANN index instead.

softmax(QKᵀ/√d_k)·V in four lines, but the grade is the three details people drop: the √d_k scale, subtracting the row max for numerical stability, and getting the causal mask to add -inf before the softmax, not after.

The whole question is the representation: store only the nonzeros as index→value, then either two-pointer over sorted indices or hash-join. The follow-up that decides the design is what happens when one vector is dense.