TSRUs

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

It largely follows TSRUc, but computes each intermediate output in a fully sequential manner: like in TSRUc, $c$ is given access to $\hat{h}_{t-1}$, but additionally, $u$ is given access to both outputs $\hat{h}_{t-1}$ and $c$, so as to make an informed decision prior to mixing. This yields the following replacement for $u$:

$$ u = \sigma\left(W_{u} \star_{n}\left[\hat{h}_{t-1};c\right] + b_{u} \right) $$

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.