1
$\begingroup$

I am reading the paper Convolutional Sequence to Sequence Learning by Facebook AI researchers and having trouble to understand how the dimensions of convolutional filters work here. Please take a look at the relevant part of the paper below.

enter image description here

Let's say the input to the kernel X is k*d (say k=5 words of d=300 embedding dimenisonality). Therefore the input is 5*300. In a computer vision task a kernel would slide over parts of the image, in NLP you usually see kernel taking up the whole width of the input matrix. So I would expect kernel to be m*d (e.g. 3*300 - slide over 3 words and look at their whole embeddiings).

However, the kernel here is of dimensionality 2d x kd which in our hypothetical example would be 600*1500. I don't understand how this massive kernel would slide over an input that is by far lower dimensional (5*300). In computer vision you could zero-pad the input, but here zero-padding would basically turn the input matrix into mostly zeros with only a handful of meaningful numbers.

Thanks for shedding some light on it!

$\endgroup$
0
$\begingroup$

They are doing a matrix multiplication: consider $y = Ax, y \in \mathbb{R}^m, x \in \mathbb{R}^n, A \in M_\mathbb{R}(m,n)$. In the paper $x$ is a concatenation of $k$ elements of $\mathbb{R}^d$, so $x$ is long $kd$; $y$ is long $2d$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.