Unfold¶
- class torch.nn.Unfold(kernel_size, dilation=1, padding=0, stride=1)[source]¶
Extracts sliding local blocks from a batched input tensor.
Consider a batched
input
tensor of shape $(N, C, *)$, where $N$ is the batch dimension, $C$ is the channel dimension, and $*$ represent arbitrary spatial dimensions. This operation flattens each slidingkernel_size
-sized block within the spatial dimensions ofinput
into a column (i.e., last dimension) of a 3-Doutput
tensor of shape $(N, C \times \prod(\text{kernel\_size}), L)$, where $C \times \prod(\text{kernel\_size})$ is the total number of values within each block (a block has $\prod(\text{kernel\_size})$ spatial locations each containing a $C$-channeled vector), and $L$ is the total number of such blocks:$L = \prod_d \left\lfloor\frac{\text{spatial\_size}[d] + 2 \times \text{padding}[d] % - \text{dilation}[d] \times (\text{kernel\_size}[d] - 1) - 1}{\text{stride}[d]} + 1\right\rfloor,$where $\text{spatial\_size}$ is formed by the spatial dimensions of
input
($*$ above), and $d$ is over all spatial dimensions.Therefore, indexing
output
at the last dimension (column dimension) gives all values within a certain block.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
dilation (int or tuple, optional) – a parameter that controls the stride of elements within the neighborhood. Default: 1
padding (int or tuple, optional) – implicit zero padding to be added on both sides of input. Default: 0
stride (int or tuple, optional) – the stride of the sliding blocks in the input spatial dimensions. Default: 1
If
kernel_size
,dilation
,padding
orstride
is an int or a tuple of length 1, their values will be replicated across all spatial dimensions.For the case of two input spatial dimensions this operation is sometimes called
im2col
.
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 4-D input tensors (batched image-like tensors) are supported.
- Shape:
Input: $(N, C, *)$
Output: $(N, C \times \prod(\text{kernel\_size}), L)$ as described above
Examples:
>>> unfold = nn.Unfold(kernel_size=(2, 3)) >>> input = torch.randn(2, 5, 3, 4) >>> output = unfold(input) >>> # each patch contains 30 values (2x3=6 vectors, each of 5 channels) >>> # 4 blocks (2x3 kernels) in total in the 3x4 input >>> output.size() torch.Size([2, 30, 4]) >>> # Convolution is equivalent with Unfold + Matrix Multiplication + Fold (or view to output shape) >>> inp = torch.randn(1, 3, 10, 12) >>> w = torch.randn(2, 3, 4, 5) >>> inp_unf = torch.nn.functional.unfold(inp, (4, 5)) >>> out_unf = inp_unf.transpose(1, 2).matmul(w.view(w.size(0), -1).t()).transpose(1, 2) >>> out = torch.nn.functional.fold(out_unf, (7, 8), (1, 1)) >>> # or equivalently (and avoiding a copy), >>> # out = out_unf.view(1, 2, 7, 8) >>> (torch.nn.functional.conv2d(inp, w) - out).abs().max() tensor(1.9073e-06)