I have a matrix of embeddings of size N*d (N inputs each having an embedding of size d) and I have a graph adjacency matrix of size N*N. Assuming the adjacency matrix is as follows (N=4):

[[1,1, 0, 0],
[0, 0, 1, 0],
[1, 0, 0, 0],
[1, 0, 1, 0]]

And the embedding matrix is as follows (d=3):

[[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 11, 12]]

I want to get the following output:

[[18, 21, 24],
[1, 2, 3],
[14, 16, 18],
[0, 0, 0, 0]]

The output is computed as follows: since the first column of the adjacency matrix is 1 at rows 0, 2, and 3, we sum the embeddings at rows 0, 2, 3 and that becomes the first row of the output ([18, 21, 24]). Similarly, since the second column of the adjacency matrix is 1 only at row 0, the second row of the output is just equivalent to row 0 of the embedding. Since the third column of the adjacency matrix is 1 at rows 1 and 3, the third row of the output is the sum of the rows 1 and 3 of the embedding. And since the last column of the adjacency matrix is all zeros, the last row of the output is all zeros.
Can’t figure out how to do it without using a for loop. Thanks for any helps in advance.