Question: Why is at an Adjustment gate？
Evidence: The proposed semantic RALSTM cell applied for Decoder side consists of three components: a Refinement cell, a traditional LSTM cell, and an Adjustment cell:
Firstly, instead of feeding the original input token $\textbf {w}_{t}$ into the RNN cell, the input is recomputed by using a semantic gate as follows: 
$$\begin{aligned}
\textbf {r}_{t}&=\sigma (\textbf {W}_{rd}\textbf {d}_{t} + \textbf {W}_{rh}\textbf {h}_{t-1})\\
\textbf {x}_{t}&=\textbf {r}_{t} \odot \textbf {w}_{t}
\end{aligned}$$   (Eq. 19) 
where $\textbf {W}_{rd}$ and $\textbf {W}_{rh}$ are weight matrices. Element-wise multiplication $\odot $ plays a part in word-level matching which not only learns the vector similarity, but also preserves information about the two vectors. $\textbf {W}_{rh}$ acts like a key phrase detector that learns to capture the pattern of generation tokens or the relationship between multiple tokens. In other words, the new input $\textbf {x}_{t}$ consists of information of the original input token $\textbf {w}_{t}$ , the DA representation $\textbf {d}_{t}$ , and the hidden context $\textbf {h}_{t-1}$ . $\textbf {r}_{t}$ is called a Refinement gate because the input tokens are refined by a combination gating information of the attentive DA representation $\textbf {d}_{t}$ and the previous hidden state $\textbf {W}_{rh}$0 . By this way, we can represent the whole sentence based on the refined inputs.
Secondly, the traditional LSTM network proposed by BIBREF26 bahdanau2014neural in which the input gate $\textbf {i}_{i}$ , forget gate $\textbf {f}_{t}$ and output gates $\textbf {o}_{t}$ are introduced to control information flow and computed as follows: 
$$\begin{aligned}
\begin{pmatrix}
\textbf {i}_{t}
\\ \textbf {f}_{t}
\\ \textbf {o}_{t}
\\ \hat{\textbf {c}}_{t}
\end{pmatrix}
&=
\begin{pmatrix}\sigma \\ \sigma \\ \sigma \\ \tanh \end{pmatrix}\textbf {W}_{4n,4n}
\begin{pmatrix}
\textbf {x}_{t}
\\ \textbf {d}_{t}
\\ \textbf {h}_{t-1}
\end{pmatrix}\\
\end{aligned}$$   (Eq. 20) 
where $n$ is hidden layer size, $\textbf {W}_{4n,4n}$ is model parameters. The cell memory value $\textbf {c}_{t}$ is modified to depend on the DA representation as: 
$$\begin{aligned}
\textbf {c}_{t}&=\textbf {f}_{t}\odot \textbf {c}_{t-1} +\textbf {i}_{t}\odot \hat{\textbf {c}}_{t} + \tanh (\textbf {W}_{cr}\textbf {r}_{t})
\\ \tilde{\textbf {h}}_{t}&= \textbf {o}_{t} \odot \tanh (\textbf {c}_{t})
\end{aligned}$$   (Eq. 21) 
where $\tilde{\textbf {h}}_{t}$ is the output.
Thirdly, inspired by work of BIBREF4 in which the generator was further conditioned on a 1-hot representation vector $\textbf {s}$ of given dialogue act, and work of BIBREF27 that proposed a visual sentinel gate to make a decision on whether the model should attend to the image or to the sentinel gate, an additional gating cell is introduced on top of the traditional LSTM to gate another controlling vector $\textbf {s}$ . Figure 6 shows how RALSTM controls the DA vector $\textbf {s}$ . First, starting from the 1-hot vector of the DA $\textbf {s}_{0}$ , at each time step $t$ the proposed cell computes how much the LSTM output $\tilde{\textbf {h}}_{t}$ affects the DA vector, which is computed as follows: 
$$\begin{aligned}
\textbf {a}_{t}&=\sigma (\textbf {W}_{ax}\textbf {x}_{t} +\textbf {W}_{ah}\tilde{\textbf {h}}_{t})\\
\textbf {s}_{t}&=\textbf {s}_{t-1} \odot \textbf {a}_{t}
\end{aligned}$$   (Eq. 22) 
where $\textbf {W}_{ax}$ , $\textbf {W}_{ah}$ are weight matrices to be learned. $\textbf {a}_{t}$ is called an $Adjustment$ gate since its task is to control what information of the given DA have been generated and what information should be retained for future time steps. Second, we consider how much the information preserved in the DA $\textbf {s}_{t}$ can be contributed to the output, in which an additional output is computed by applying the output gate $\textbf {o}_{t}$ on the remaining information in $\textbf {s}_{t}$ as follows: 
$$\begin{aligned}
\textbf {c}_{a}&=\sigma (\textbf {W}_{os}\textbf {s}_{t})\\
\tilde{\textbf {h}}_{a}&= \textbf {o}_{t} \odot \tanh (\textbf {c}_{a})
\end{aligned}$$   (Eq. 23) 
where $\textbf {W}_{os}$ is a weight matrix to project the DA presentation into the output space, $\tilde{\textbf {h}}_{a}$ is the Adjustment cell output. Final RALSTM output is a combination of both outputs of the traditional LSTM cell and the Adjustment cell, and computed as follows: 
$$\textbf {h}_{t}=\tilde{\textbf {h}}_{t} + \tilde{\textbf {h}}_{a}$$   (Eq. 24) 
Finally, the output distribution is computed by applying a softmax function $g$ , and the distribution can be sampled to obtain the next token, 
$$\begin{aligned}
& P(w_{t+1}\mid w_{t},...w_{0},\textbf {DA})=g(\textbf {W}_{ho}\textbf {h}_{t}) \\
& w_{t+1} \sim P(w_{t+1}\mid w_{t}, w_{t-1},...w_{0},\textbf {DA})
\end{aligned}$$   (Eq. 25) 
where $\textbf {DA}=(\textbf {s}, \textbf {z})$ .
at is called an Adjustment gate since its task is to control what information of the given DA have been generated and what information should be retained for future time steps.
Answer: Because its task is to control what information of the given DA have been generated and what information should be retained for future time steps.