Outer product in tensorflow

Question

In tensorflow, there are nice functions for entrywise and matrix multiplication, but after looking through the docs, I cannot find any internal function for taking an outer product of two tensors, i.e., making a bigger tensor by all possible products of elements of smaller tensors (like numpy.outer):

v_{i,j} = x_i*h_j

or

M_{ij,kl} = A_{ij}*B_{kl}

Does tensorflow have such a function?

Answer 1

Yes, you can do this by taking advantage of the broadcast semantics of tensorflow. Size the first out to size 1xN of itself, and the second to size Mx1 of itself, and you'll get a broadcast to MxN of all of the results when you multiply them.

(You can play around with the same thing in numpy to see how it behaves in a simpler context, btw:

a = np.array([1, 2, 3, 4, 5]).reshape([5,1])
b = np.array([6, 7, 8, 9, 10]).reshape([1,5])
a*b

How exactly you do it in tensorflow depends a bit on which axes you want to use and what semantics you want for the resulting multiply, but the general idea applies.