Fold¶
- class torch.nn.Fold(output_size, kernel_size, dilation=1, padding=0, stride=1)[source]¶
Combines an array of sliding local blocks into a large containing tensor.
Consider a batched
input
tensor containing sliding local blocks, e.g., patches of images, of shape $(N, C \times \prod(\text{kernel\_size}), L)$, where $N$ is batch dimension, $C \times \prod(\text{kernel\_size})$ is the number of values within a block (a block has $\prod(\text{kernel\_size})$ spatial locations each containing a $C$-channeled vector), and $L$ is the total number of blocks. (This is exactly the same specification as the output shape ofUnfold
.) This operation combines these local blocks into the largeoutput
tensor of shape $(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)$ by summing the overlapping values. Similar toUnfold
, the arguments must satisfy$L = \prod_d \left\lfloor\frac{\text{output\_size}[d] + 2 \times \text{padding}[d] % - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor,$where $d$ is over all spatial dimensions.
output_size
describes the spatial shape of the large containing tensor of the sliding local blocks. It is useful to resolve the ambiguity when multiple input shapes map to same number of sliding blocks, e.g., withstride > 0
.
The
padding
,stride
anddilation
arguments specify how the sliding blocks are retrieved.stride
controls the stride for the sliding blocks.padding
controls the amount of implicit zero-paddings on both sides forpadding
number of points for each dimension before reshaping.dilation
controls the spacing between the kernel points; also known as the à trous algorithm. It is harder to describe, but this link has a nice visualization of whatdilation
does.
- Parameters:
output_size (int or tuple) – the shape of the spatial dimensions of the output (i.e.,
output.sizes()[2:]
)stride (int or tuple) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
padding (int or tuple, optional) – implicit zero padding to be added on both sides of input. Default: 0
dilation (int or tuple, optional) – a parameter that controls the stride of elements within the neighborhood. Default: 1
If
output_size
,kernel_size
,dilation
,padding
orstride
is an int or a tuple of length 1 then their values will be replicated across all spatial dimensions.For the case of two output spatial dimensions this operation is sometimes called
col2im
.
Note
Fold
calculates each combined value in the resulting large tensor by summing all values from all containing blocks.Unfold
extracts the values in the local blocks by copying from the large tensor. So, if the blocks overlap, they are not inverses of each other.In general, folding and unfolding operations are related as follows. Consider
Fold
andUnfold
instances created with the same parameters:>>> fold_params = dict(kernel_size=..., dilation=..., padding=..., stride=...) >>> fold = nn.Fold(output_size=..., **fold_params) >>> unfold = nn.Unfold(**fold_params)
Then for any (supported)
input
tensor the following equality holds:fold(unfold(input)) == divisor * input
where
divisor
is a tensor that depends only on the shape and dtype of theinput
:>>> input_ones = torch.ones(input.shape, dtype=input.dtype) >>> divisor = fold(unfold(input_ones))
When the
divisor
tensor contains no zero elements, thenfold
andunfold
operations are inverses of each other (up to constant divisor).Warning
Currently, only unbatched (3D) or batched (4D) image-like output tensors are supported.
- Shape:
Input: $(N, C \times \prod(\text{kernel\_size}), L)$ or $(C \times \prod(\text{kernel\_size}), L)$
Output: $(N, C, \text{output\_size}[0], \text{output\_size}[1], \dots)$ or $(C, \text{output\_size}[0], \text{output\_size}[1], \dots)$ as described above
Examples:
>>> fold = nn.Fold(output_size=(4, 5), kernel_size=(2, 2)) >>> input = torch.randn(1, 3 * 2 * 2, 12) >>> output = fold(input) >>> output.size() torch.Size([1, 3, 4, 5])