jointly trained with the generator. This technique can be useful with the decompose technique to ensure that the decomposed sub-spaces represent the desired control attributes.

Sequential Input {#sec:bg-dec-inp}
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In this section we discuss the different techniques which can be used to manipulate the sequential input ${\mathbf{x}}_t$ to the decoder at each time step. ${\mathbf{x}}_t$ here is used to denote the word embedding of the token at time step $t$. This is marked as position (2) in Figure \[fig:bg-overview\].

Arithmetic or Linear Transform {#arithmetic-or-linear-transform}
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Similar to changing the initialization, we can change the input to the decoder by concatenating the information at each time step with some additional control vector ${\mathbf{s}}$. Typically, teacher forcing method [@williams1989learning] is used to train the generator. At time step $t$, the generator takes as input the word embedding ${\mathbf{x}}_t$ of the word that was predicted at step $t-1$ and predicts the word to be generated ${\mathbf{y}}_t$ at the current time step. Note that ${\mathbf{x}}_t = {\mathbf{y}}_{t-1}$. The input ${\mathbf{x}}_t$ can be concatenated with ${\mathbf{s}}$ at each time step to control the generation process. Hence, ${\mathbf{\tilde{x}}}_t = [{\mathbf{x}}_t; {\mathbf{s}}]$.

@noraset2017definition, use this technique in the task of definition modeling. They concatenate word embedding vector 