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What is: Convolutional GRU?

SourceDelving Deeper into Convolutional Networks for Learning Video Representations
Year2000
Data SourceCC BY-SA - https://paperswithcode.com

A Convolutional Gated Recurrent Unit is a type of GRU that combines GRUs with the convolution operation. The update rule for input x_tx\_{t} and the previous output h_t1h\_{t-1} is given by the following:

r=σ(W_r_n[h_t1;x_t]+b_r)r = \sigma\left(W\_{r} \star\_{n}\left[h\_{t-1};x\_{t}\right] + b\_{r}\right)

u=σ(W_u_n[h_t1;x_t]+b_u)u = \sigma\left(W\_{u} \star\_{n}\left[h\_{t-1};x\_{t}\right] + b\_{u} \right)

c=ρ(W_c_n[x_t;rh_t1]+b_c)c = \rho\left(W\_{c} \star\_{n}\left[x\_{t}; r \odot h\_{t-1}\right] + b\_{c} \right)

h_t=uh_t1+(1u)ch\_{t} = u \odot h\_{t-1} + \left(1-u\right) \odot c

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