Attention Weighted Sum

Compute the output of the last step of attention: the weighted sum of the value vectors using precomputed attention weights. weights has shape (n_queries, n_keys) and values has shape (n_keys, d_v).

Implement solve(weights, values).

Returns. Return a NumPy array of shape (n_queries, d_v): row $ii$ is ${\sum }_j{w}_{ij}{v}_j\backslash sum\_j\; w\_\{ij\}v\_j$.

Examples

Example 1

Input:

solve([[0.5, 0.5]], [[1.0, 2.0], [3.0, 4.0]])

Output:

[[2.0, 3.0]]

Example 2

Input:

solve([[1.0, 0.0], [0.25, 0.75]], [[10.0], [20.0]])

Output:

[[10.0], [17.5]]