its variants can be modified to account for the control attribute. Additional gates can be added or the control attribute can be provided as an additional input to the standard gates of RNNS.

@gan2017stylenet propose a variant of the LSTM model, named factored LSTM, which controls style representation in image caption task. The parameters of the LSTM module which are responsible to transform the input ${\mathbf{x}}_t$ are factored into three components ${\mathbf{U}}$, ${\mathbf{S}}$ and ${\mathbf{V}}$. The operations of the input (${\mathbf{i}}_t$), forget (${\mathbf{f}}_t$) and output gate (${\mathbf{o}}_t$) are given by: $$\begin{aligned}
    {\mathbf{i}}_t &=& {\mathtt{sigmoid}}({\mathbf{U}}_{ix} {\mathbf{S}}_{ix} {\mathbf{V}}_{ix} {\mathbf{x}}_t + {\mathbf{W}}_{ih} {\mathbf{h}}_{t-1}) \\
    {\mathbf{f}}_t &=& {\mathtt{sigmoid}}({\mathbf{U}}_{fx} {\mathbf{S}}_{fx} {\mathbf{V}}_{fx} {\mathbf{x}}_t + {\mathbf{W}}_{fh} {\mathbf{h}}_{t-1}) \\
    {\mathbf{o}}_t &=& {\mathtt{sigmoid}}({\mathbf{U}}_{ox} {\mathbf{S}}_{ox} {\mathbf{V}}_{ox} {\mathbf{x}}_t + {\mathbf{W}}_{oh} {\mathbf{h}}_{t-1}) \\
    {\mathbf{\tilde{c}}}_t &=& {\mathtt{tanh}}({\mathbf{U}}_{cx} {\mathbf{S}}_{cx} {\mathbf{V}}_{cx} {\mathbf{x}}_t + {\mathbf{W}}_{ch} {\mathbf{h}}_{t-1})\end{aligned}$$

Particularly, the matrix set $\{{\mathbf{S}}\}$ is specific to each style in the task and is responsible to capture the underlying style features in the data.

In [@kiddon2016globally], the GRU unit is modified to accommodate extra inputs - goal ${\mathbf{g}}$ and agenda items $E^{new}_t$ in the recipe generation task. The operation of the new component ${\mathbf{\tilde{h}}}_t$ is given by: $$\begin{aligned}
    {\mathbf{\tilde{h}}}_t = {\mathtt{tanh}}({\mathbf{W}}_h {\mathbf{x}}_t + {\mathbf{r}}_t \odot {\mathbf{U}}_h {\mathbf{h}}_{t-1} + {\mathbf{s}}_t 