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For use when discussing the commutative and linear, but not associative operator interpreted on functions and distributions.
8
votes
What are deconvolutional layers?
(\mathbf{q} * \mathbf{x})$,
a dilated convolution with factor $k$ is $(\uparrow_k\!\mathbf{q}) * \mathbf{x}$,
a transposed convolution with stride $k$ is $ \mathbf{q} * (\uparrow_k\! … q_2\;\;q_2),$$
i.e. we can replace a repeat upsampler with factor 2 and a convolution with a kernel of size 3 by a transposed convolution with kernel size 4. …