\\
+\lambda\mathbb{E}_{q_{\phi}(z|x,c)}[{||z-g_{\gamma}(x,c)||^2}]]\nonumber\label{eq:lslcvae}\end{gathered}$$ where $\beta$ are parameters of the prior network. In this phase, the labelling network $g_{\gamma}(x,c)$ is fixed to provide a $z_{label}$ corresponding to each $x$.

In the Labeling phase, we minimize the loss function of the labeling network: $$\begin{gathered}
\min_{\gamma}\mathcal{L}_\mathsf{label}=\min_{\gamma}[-p_{\theta}(x|g_{\gamma}(x,c), c)]\label{eq:llabel}\end{gathered}$$ The decoder is fixed at this time to get the good expressive label for current decoder.

See Algorithm \[alg:slcvae\] for the whole training procedure. The Adam[@kingma2015adam] optimizer is adopted to update parameters.

Initialize ${\phi}, {\theta}, {\beta}, {\gamma}$ randomly $c, x \gets$ sample a mini-batch from dataset Sample latent $z \sim q_{\phi}(z|x, c)$ Calculate label $z_{label} \gets g_{\gamma}(x,c)$ Calculate the gradients: $\nabla_{\phi,\theta,\beta}\mathcal{L}_\mathsf{SLCVAE}$ Update CVAE parameters $\theta, \phi, \beta$ by Adam $c, x \gets$ sample a mini-batch from dataset Calculate the gradients: $\nabla_{\gamma}\mathcal{L}_\mathsf{label}$ Update labeling network parameter $\gamma$ by Adam

The EGOODS Dataset
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The text generating problem defined with “one source, multiple targets” is an active research topic and plays important roles in many tasks. However, there still lacks real one-to-many datasets to improve and evaluate the algorithms for this problem. Most current datasets come from dialogue system are essentially one-to-one corpora. Although there may exist various underlying responses for a certain question, these datasets only contain one 