如何在Theano中对选定的尺寸进行逐元素乘法？

Question

I have two tensors and I need to do the following:

C[i, j, k, l, a, b] = A[i, j, k, l] * B[a, b, k, l]

So, as you can see there is not summation over k and l . So, I cannot apply tensordot .

Answer 1

Here is the solution:

C = a.dimshuffle(0, 1, 2, 3, 'x', 'x') * b.dimshuffle('x', 'x', 2, 3, 0, 1)

And here is the explanation:

You try to archive two goals:

1. Pair only some indices of the first tensor with some indices of the second tensor.
2. Do not sum up over the paired indices.

If you use pairwise multiplication, then there will be no summation over the paired indices (unlike in tensordot , which sums up over the paired indices / axes). So, the second goal is achieved by using pairwise multiplication.

Now you need to achieve the first goal. Per default pairwise multiplication pairs all the indices of the first tensor with all the corresponding indices of the second tensor (first with first, second with second and so on). To avoid that use dimshuffle to align indexes that have to be paired and use 'x' to introduce "dummy" axes for the indices that should not be paired. In your particular example it should like like that: