TSRUc

TSRUc, or Transformation-based Spatial Recurrent Unit c, is a modification of a ConvGRU used in the TriVD-GAN architecture for video generation.

Instead of computing the reset gate $r$ and resetting $h\_{t−1}$, the TSRUc computes the parameters of a transformation $\theta$, which we use to warp $h\_{t−1}$. The rest of our model is unchanged (with $\hat{h}\_{t-1}$ playing the role of $h'\_{t}$ in $c$’s update equation from ConvGRU. The TSRUc module is described by the following equations:

$\theta\_{h,x} = f\left(h\_{t−1}, x\_{t}\right)$

$\hat{h}\_{t-1} = w\left(h\_{t-1}; \theta\_{h, x}\right)$

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

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

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

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.