How does Pytorch's "Fold" and "Unfold" work?

unfold imagines a tensor as a longer tensor with repeated columns/rows of values 'folded' on top of each other, which is then "unfolded":

• size determines how large the folds are
• step determines how often it is folded

E.g. for a 2x5 tensor, unfolding it with step=1, and patch size=2 across dim=1:

x = torch.tensor([[1,2,3,4,5],
                  [6,7,8,9,10]])

>>> x.unfold(1,2,1)
tensor([[[ 1,  2], [ 2,  3], [ 3,  4], [ 4,  5]],
        [[ 6,  7], [ 7,  8], [ 8,  9], [ 9, 10]]])

fold is roughly the opposite of this operation, but "overlapping" values are summed in the output.

The unfold and fold are used to facilitate "sliding window" operations (like convolutions). Suppose you want to apply a function foo to every 5x5 window in a feature map/image:

from torch.nn import functional as f
windows = f.unfold(x, kernel_size=5)

Now windows has size of batch-(55x.size(1))-num_windows, you can apply foo on windows:

processed = foo(windows)

Now you need to "fold" processed back to the original size of x:

out = f.fold(processed, x.shape[-2:], kernel_size=5)

You need to take care of padding, and kernel_size that may affect your ability to "fold" back processed to the size of x. Moreover, fold sums over overlapping elements, so you might want to divide the output of fold by patch size.

Please note that torch.unfold performs a different operation than nn.Unfold. See this thread for details.

One dimensional unfolding is easy:

x = torch.arange(1, 9).float()
print(x)
# dimension, size, step
print(x.unfold(0, 2, 1))
print(x.unfold(0, 3, 2))

Out:

tensor([1., 2., 3., 4., 5., 6., 7., 8.])
tensor([[1., 2.],
        [2., 3.],
        [3., 4.],
        [4., 5.],
        [5., 6.],
        [6., 7.],
        [7., 8.]])
tensor([[1., 2., 3.],
        [3., 4., 5.],
        [5., 6., 7.]])

Two dimensional unfolding (also called patching)

import torch
patch=(3,3)
x=torch.arange(16).float()
print(x, x.shape)
x2d = x.reshape(1,1,4,4)
print(x2d, x2d.shape)
h,w = patch
c=x2d.size(1)
print(c) # channels
# unfold(dimension, size, step)
r = x2d.unfold(2,h,1).unfold(3,w,1).transpose(1,3).reshape(-1, c, h, w)
print(r.shape)
print(r) # result

tensor([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10., 11., 12., 13.,
        14., 15.]) torch.Size([16])
tensor([[[[ 0.,  1.,  2.,  3.],
          [ 4.,  5.,  6.,  7.],
          [ 8.,  9., 10., 11.],
          [12., 13., 14., 15.]]]]) torch.Size([1, 1, 4, 4])
1
torch.Size([4, 1, 3, 3])

tensor([[[[ 0.,  1.,  2.],
          [ 4.,  5.,  6.],
          [ 8.,  9., 10.]]],


        [[[ 4.,  5.,  6.],
          [ 8.,  9., 10.],
          [12., 13., 14.]]],


        [[[ 1.,  2.,  3.],
          [ 5.,  6.,  7.],
          [ 9., 10., 11.]]],


        [[[ 5.,  6.,  7.],
          [ 9., 10., 11.],
          [13., 14., 15.]]]])