How to compute sparse similarity matrix of L1 distances from a variable efficiently?


I am trying to implement the following architecture which utilizes similarity matrix of size n^2 x n^2 and it is difficult to fit such a huge matrix in GPU. So we are calculating matrix n^2 x M, where is M is some radius of neighborhood pixels then perform the convolution.
Image taken from Convolution RWN


  • How to compute pairwise L1 distance from first Convolution layer efficiently (n^2 x M)?
  • How to multiply sparse matrix with activations output final step of Random Walk Layer i.e. (k x n^2) * (n^2 x M)?

I would appreciate any pointers.


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