ImplementCore implementation

Attention: scaled dot-product output

Implement `run(q, k, v)` returning the attention output for a single query. q, k, v are lists of lists (one row per position). Compute scores = Q·K^T / sqrt(d_k) where d_k = len(q), apply softmax along the last axis, then take the weighted sum with V. Return the output vector as a list of floats (rows must sum to 1 in the attention weights).

python15 mindifficulty 3/4

From Attention Is All You Need

Sample tests

run([[1,0],[[1,0],[0,1]],[[1,0],[0,1]]])→[0.669762,0.330238]
run([[1,0],[[0,0],[0,0]],[[2,3],[5,7]]])→[3.5,5]

Hints

Attention(Q,K,V) = softmax(QK^T / sqrt(d_k)) V — the sqrt(d_k) scale keeps dot products from growing with dimension.
For a single query, scores[i] = dot(q, k[i]) / sqrt(d_k).
Softmax normalizes the score vector so attention weights sum to 1.
Output[j] = sum over positions i of weight[i] * v[i][j].

Hints

Code runs in an isolated sandbox on the OpenSandbox judge. No model key required.