Here’s the basic idea. I want to compute some distance metric (Euclidian, cosine, etc) between a vector and a matrix of vectors. In the case of a single vector, this is fairly straightforward.
a1 = torch.randn(1,5) a2 = torch.randn(12,5) distances = distance_function(a1.expand_as(a2), a2) # returns vector of size 12
However things get tricky in the batch case where the sizes of the second matrix can vary. For example:
a1 = torch.randn(1,5) b1 = torch.randn(1,5) c1 = torch.randn(1,5) a2 = torch.randn(12,5) b2 = torch.randn(7,5) c2 = torch.randn(2,5)
I’d like to compute all distance comparisons (a1 to a2, b1 to b2, c1 to c2, etc) in a way that is fast and memory efficient. Memory efficiency is important because sometimes the x_2 matrices can be large.
The first approach that comes to mind is something like this:
distances = distance_function(torch.cat([a1.expand_as(a2), b1.expand_as(b2), c1.expand_as(c2)]), torch.cat([a2,b2,c2]))
This works but I have concerns about the memory implications. I know
expand_as does not allocate new memory. However (to my knowledge), using
torch.cat will result in new memory allocation.
Is there a better/more efficient approach to this?