What is: Convolutional GRU?

A Convolutional Gated Recurrent Unit is a type of GRU that combines GRUs with the convolution operation. The update rule for input $x\_{t}$ and the previous output $h\_{t-1}$ is given by the following:

$r = \sigma\left(W\_{r} \star\_{n}\left[h\_{t-1};x\_{t}\right] + b\_{r}\right)$

$u = \sigma\left(W\_{u} \star\_{n}\left[h\_{t-1};x\_{t}\right] + b\_{u} \right)$

$c = \rho\left(W\_{c} \star\_{n}\left[x\_{t}; r \odot h\_{t-1}\right] + b\_{c} \right)$

$h\_{t} = u \odot h\_{t-1} + \left(1-u\right) \odot c$

In these equations $\sigma$ and $\rho$ are the elementwise sigmoid and ReLU functions respectively and the $\star\_{n}$ represents a convolution with a kernel of size $n \times n$. Brackets are used to represent a feature concatenation.