Shows that forwad and backward operations of SpatialConvolution and SpatialFullConvolution are swapped...

2d_conv_test.lua

require 'nn'

x = torch.rand(1,5,5)
a = nn.SpatialConvolution(1,1,3,3)
a.bias:zero()
ay1 =torch.xcorr2(x,a.weight,'V')
ay2 = a:forward(x)

b = nn.SpatialFullConvolution(1,1,3,3)
b.bias:zero()
by1 = torch.conv2(x, b.weight, 'F')
by2 = b:forward(x)

print(ay1)
print(ay2)
print(by1)
print(by2)

deconv_test.lua

require 'nn'
a = nn.SpatialConvolution(7,5,3,3)
a.bias:zero()

b = nn.SpatialFullConvolution(5,7,3,3)
b.bias:zero()

b.weight = a.weight

test = torch.rand(7, 12, 12)
test2 = torch.rand(5, 10, 10)

y1 = a:forward(test)
y2 = b:backward(torch.zeros(5,10,10), test)

z1 = a:backward(torch.zeros(7,12,12), test2)
z2 = b:forward(test2)

-- prints 0 twice
print((y1-y2):abs():sum())
print((z1-z2):abs():sum())

So a SpatialFullConvolution layer is just doing "deconvolution" / "fractionally-strided convolution" / "upconvolution" / ... ?

Here's a fun question: if the stride is 1, is a SpatialFullConvolution layer equivalent to the SpatialConvolution layer? or are there tricks like transposing the kernel matrix?