Original: D IALOG WAE: M ULTIMODAL R ESPONSE G ENERATION WITH C ONDITIONAL W ASSERSTEIN A UTO -E NCODER
Revised: D IALOG WAE: M ULTIMODAL R ESPONSE G ENERATION WITH C ONDITIONAL W ASSERSTEIN A UTO -E NCODER

Original: Anonymous authors
Revised: Anonymous authors

Original: Paper under double-blind review
Revised: Paper under double-blind review

Original: A BSTRACT
Revised: A BSTRACT

Original: Variational autoencoders (VAEs) have shown a promise in data-driven conversation modeling.
Revised: Variational autoencoders (VAEs) have shown a promise in data-driven conversation modeling.

Original: However, most VAE conversation models match the approximate posterior distribution over the latent variables to a simple prior such as standard normal distribution, thereby restricting the generated responses to a relatively simple (e.g., single-modal) scope.
Revised: However, most VAE conversation models match the approximate posterior distribution over the latent variables to a simple prior such as standard normal distribution, thereby restricting the generated responses to a relatively simple (e.g., unimodal) scope.

Original: In this paper, we propose DialogWAE, a conditional Wasserstein autoencoder (WAE) specially designed for dialogue modeling.
Revised: In this paper, we propose DialogWAE, a conditional Wasserstein autoencoder (WAE) specially designed for dialogue modeling.

Original: Unlike VAEs that impose a simple distribution over the latent variables, DialogWAE models the distribution of data by training a GAN within the latent variable space.
Revised: Unlike VAEs that impose a simple distribution over the latent variables, DialogWAE models the distribution of data by training a GAN within the latent variable space.

Original: Speciﬁcally, our model samples from the prior and posterior distributions over the latent variables by transforming context-dependent random noise using neural networks and minimizes the Wasserstein distance between the two distributions.
Revised: Speciﬁcally, our model samples from the prior and posterior distributions over the latent variables by transforming context-dependent random noise using neural networks and minimizes the Wasserstein distance between the two distributions.

Original: We further develop a Gaussian mixture prior network to enrich the latent space.
Revised: We further develop a Gaussian mixture prior network to enrich the latent space.

Original: Experiments on two popular datasets show that DialogWAE outperforms the state-of-the-art approaches in generating more coherent, informative and diverse responses.
Revised: Experiments on two popular datasets show that DialogWAE outperforms the state-of-the-art approaches in generating more coherent, informative and diverse responses.

Original:  I NTRODUCTION
Revised:  I NTRODUCTION

Original: Neural response generation has been a long interest of natural language research.
Revised: Neural response generation has been a long interest of natural language research.

Original: Most of the recent approaches to data-driven conversation modeling primarily build upon sequence-to-sequence learning (Cho et al. , 2014; Sutskever et al. , 2014).
Revised: Most of the recent approaches to data-driven conversation modeling primarily build upon sequence-to-sequence learning (Cho et al. , 2014; Sutskever et al. , 2014).

Original: Previous research has demonstrated that sequenceto-sequence conversation models often suffer from the safe response problem and fail to generate meaningful, diverse on-topic responses (Li et al. , 2015;
Revised: Previous research has demonstrated that sequenceto-sequence conversation models often suffer from the safe response problem and fail to generate meaningful, diverse on-topic responses (Li et al. , 2015;

Original: Sato et al. , 2017).
Revised: Sato et al. , 2017).

Original: Conditional variational autoencoders (CVAE) have shown promising results in addressing the safe response issue (Zhao et al. , 2017; Shen et al. , 2018).
Revised: Conditional variational autoencoders (CVAE) have shown promising results in addressing the safe response issue (Zhao et al. , 2017; Shen et al. , 2018).

Original: CVAE generates the response conditioned on a latent variable - representing topics, tones and situations of the response - and approximate the posterior distribution over latent variables using a neural network.
Revised: CVAE generates the response conditioned on a latent variable - representing topics, tones and situations of the response - and approximate the posterior distribution over latent variables using a neural network.

Original: The latent variable captures variabilities in the dialogue and thus generates more diverse responses.
Revised: The latent variable captures variabilities in the dialogue and thus generates more diverse responses.

Original: However, previous studies have shown that VAE models tend to suffer from the posterior collapse problem, where the decoder learns to ignore the latent variable and degrades to a vanilla RNN (Shen et al. , 2018;
Revised: However, previous studies have shown that VAE models tend to suffer from the posterior collapse problem, where the decoder learns to ignore the latent variable and degrades to a vanilla RNN (Shen et al. , 2018;

Original: Park et al. , 2018; Bowman et al. , 2015).
Revised: Park et al. , 2018; Bowman et al. , 2015).

Original: Furthermore, they match the approximate posterior distribution over the latent variables to a simple prior such as standard normal distribution, thereby restricting the generated responses to a relatively simple (e.g., single-mode) scope (Goyal et al. , 2017).
Revised: Furthermore, they match the approximate posterior distribution over the latent variables to a simple prior such as standard normal distribution, thereby restricting the generated responses to a relatively simple (e.g., unimodal) scope (Goyal et al. , 2017).

Original: A number of studies have sought GAN-based approaches (Goodfellow et al. , 2014; Li et al. , 2017a;
Revised: A number of studies have sought GAN-based approaches (Goodfellow et al. , 2014; Li et al. , 2017a;

Original: Xu et al. , 2017) which directly model the distribution of the responses.
Revised: Xu et al. , 2017) which directly model the distribution of the responses.

Original: However, adversarial training over discrete tokens has been known to be difﬁcult due to the non-differentiability.
Revised: However, adversarial training over discrete tokens has been known to be difﬁcult due to the non-differentiability.

Original: Li et al.
Revised: Li et al.

Original: (2017a) proposed a hybrid model of GAN and reinforcement learning (RL) where the score predicted by a discriminator is used as a reward to train the generator.
Revised: (2017a) proposed a hybrid model of GAN and reinforcement learning (RL) where the score predicted by a discriminator is used as a reward to train the generator.

Original: However, training with REINFORCE has been observed to be unstable due to the high variance of the gradient estimate (Shen et al. , 2017).
Revised: However, training with REINFORCE has been observed to be unstable due to the high variance of the gradient estimate (Shen et al. , 2017).

Original: Xu et al.
Revised: Xu et al.

Original: (2017) make the GAN model differentiable with an approximate word embedding layer.
Revised: (2017) make the GAN model differentiable with an approximate word embedding layer.

Original: However, their model only injects variability at the word level, thus limited to represent high-level response variabilities such as topics and situations.
Revised: However, their model only injects variability at the word level, thus limited to represent high-level response variabilities such as topics and situations.

Original: In this paper, we propose DialogWAE, a novel variant of GAN for neural conversation modeling.
Revised: In this paper, we propose DialogWAE, a novel variant of GAN for neural conversation modeling.

Original: Unlike VAE conversation models that impose a simple distribution over latent variables, DialogWAE models the data distribution by training a GAN within the latent variable space.
Revised: Unlike VAE conversation models that impose a simple distribution over latent variables, DialogWAE models the data distribution by training a GAN within the latent variable space.

Original: Speciﬁcally, it samples from the prior and posterior distributions over the latent variables by transforming contextdependent random noise with neural networks, and minimizes the Wasserstein distance (Arjovsky et al. , 2017) between the prior and the approximate posterior distributions.
Revised: Speciﬁcally, it samples from the prior and posterior distributions over the latent variables by transforming contextdependent random noise with neural networks, and minimizes the Wasserstein distance (Arjovsky et al. , 2017) between the prior and the approximate posterior distributions.

Original: Furthermore, our model takes into account a multimodal 1 nature of responses by using a Gaussian mixture prior network.
Revised: Furthermore, our model takes into account a multimodal 1 nature of responses by using a Gaussian mixture prior network.

Original: Adversarial training with the Gaussian mixture prior network enables DialogWAE to capture a richer latent space, yielding more coherent, informative and diverse responses.
Revised: Adversarial training with the Gaussian mixture prior network enables DialogWAE to capture a richer latent space, yielding more coherent, informative and diverse responses.

Original: Our main contributions are two-fold: (1) A novel GAN-based model for neural dialogue modeling, which employs GAN to generate samples of latent variables.
Revised: Our main contributions are two-fold: (1) A novel GAN-based model for neural dialogue modeling, which employs GAN to generate samples of latent variables.

Original: (2) A Gaussian mixture prior network to sample random noise from a multimodal prior distribution.
Revised: (2) A Gaussian mixture prior network to sample random noise from a multimodal prior distribution.

Original: To the best of our knowledge, the proposed DialogWAE is the ﬁrst GAN conversation model that exploits multimodal latent structures.
Revised: To the best of our knowledge, the proposed DialogWAE is the ﬁrst GAN conversation model that exploits multimodal latent structures.

Original: We evaluate our model on two benchmark datasets, SwitchBoard (Godfrey and Holliman, 1997) and
Revised: We evaluate our model on two benchmark datasets, SwitchBoard (Godfrey and Holliman, 1997) and

Original: DailyDialog (Li et al. , 2017b).
Revised: DailyDialog (Li et al. , 2017b).

Original: The results demonstrate that our model substantially outperforms the state-of-the-art methods in terms of BLEU, word embedding similarity, and distinct.
Revised: The results demonstrate that our model substantially outperforms the state-of-the-art methods in terms of BLEU, word embedding similarity, and distinct.

Original: Furthermore, we highlight how the GAN architecture with a Gaussian mixture prior network
Revised: Furthermore, we highlight how the GAN architecture with a Gaussian mixture prior network

Original: facilitates the generation of more diverse and informative responses.
Revised: facilitates the generation of more diverse and informative responses.

Original:  R ELATED W ORK
Revised:  R ELATED W ORK

Original: Encoder-decoder variants To address the “safe response” problem of the naive encoder-decoder conversation model, a number of variants have been proposed.
Revised: Encoder-decoder variants To address the “safe response” problem of the naive encoder-decoder conversation model, a number of variants have been proposed.

Original: Li et al.
Revised: Li et al.

Original: (2015) proposed a diversitypromoting objective function to encourage more various responses.
Revised: (2015) proposed a diversitypromoting objective function to encourage more various responses.

Original: Sato et al.
Revised: Sato et al.

Original: (2017) propose to incorporate various types of situations behind conversations when encoding utterances and decoding their responses, respectively.
Revised: (2017) propose to incorporate various types of situations behind conversations when encoding utterances and decoding their responses, respectively.

Original: Xing et al.
Revised: Xing et al.

Original: (2017) incorporate topic information into the sequence-tosequence framework to generate informative and interesting responses.
Revised: (2017) incorporate topic information into the sequence-tosequence framework to generate informative and interesting responses.

Original: Our work is different from the aforementioned studies, as it does not rely on extra information such as situations and topics.
Revised: Our work is different from the aforementioned studies, as it does not rely on extra information such as situations and topics.

Original: VAE conversation models
Revised: VAE conversation models

Original: The variational autoencoder (VAE) (Kingma and Welling, 2014) is among the most popular frameworks for dialogue modeling (Zhao et al. , 2017;
Revised: The variational autoencoder (VAE) (Kingma and Welling, 2014) is among the most popular frameworks for dialogue modeling (Zhao et al. , 2017;

Original: Shen et al. , 2018;
Revised: Shen et al. , 2018;

Original: Park et al. , 2018).
Revised: Park et al. , 2018).

Original: Serban et al.
Revised: Serban et al.

Original: (2017) propose VHRED, a hierarchical latent variable sequenceto-sequence model that explicitly models multiple levels of variability in the responses.
Revised: (2017) propose VHRED, a hierarchical latent variable sequenceto-sequence model that explicitly models multiple levels of variability in the responses.

Original: A main challenge for the VAE conversation models is the so-called “posterior collapse”.
Revised: A main challenge for the VAE conversation models is the so-called “posterior collapse”.

Original: To alleviate the problem, Zhao et al.
Revised: To alleviate the problem, Zhao et al.

Original: (2017) introduce an auxiliary bag-of-words loss to the decoder.
Revised: (2017) introduce an auxiliary bag-of-words loss to the decoder.

Original: They further incorporate extra dialogue information such as dialogue acts and speaker proﬁles.
Revised: They further incorporate extra dialogue information such as dialogue acts and speaker proﬁles.

Original: Shen et al.
Revised: Shen et al.

Original: (2018) propose a collaborative CVAE model which samples the latent variable by transforming a Gaussian noise using neural networks and matches the prior and posterior distributions of the Gaussian noise with KL divergence.
Revised: (2018) propose a collaborative CVAE model which samples the latent variable by transforming a Gaussian noise using neural networks and matches the prior and posterior distributions of the Gaussian noise with KL divergence.

Original: Park et al.
Revised: Park et al.

Original: (2018) propose a variational hierarchical conversation RNN (VHCR) which incorporates a hierarchical structure to latent variables.
Revised: (2018) propose a variational hierarchical conversation RNN (VHCR) which incorporates a hierarchical structure to latent variables.

Original: DialogWAE addresses the limitation of VAE conversation models by using a GAN architecture in the latent space.
Revised: DialogWAE addresses the limitation of VAE conversation models by using a GAN architecture in the latent space.

Original: GAN conversation models Although GAN/CGAN has shown great success in image generation, adapting it to natural dialog generators is a non-trivial task.
Revised: GAN conversation models Although GAN/CGAN has shown great success in image generation, adapting it to natural dialog generators is a non-trivial task.

Original: This is due to the non-differentiable nature of natural language tokens (Shen et al. , 2017; Xu et al. , 2017).
Revised: This is due to the non-differentiable nature of natural language tokens (Shen et al. , 2017; Xu et al. , 2017).

Original: Li et al.
Revised: Li et al.

Original: (2017a) address this problem by combining GAN with Reinforcement Learning (RL) where the discriminator predicts a reward to optimize the generator.
Revised: (2017a) address this problem by combining GAN with Reinforcement Learning (RL) where the discriminator predicts a reward to optimize the generator.

Original: However, training with REINFORCE can be unstable due to the high variance of the sampled gradient (Shen et al. , 2017).
Revised: However, training with REINFORCE can be unstable due to the high variance of the sampled gradient (Shen et al. , 2017).

Original: Xu et al.
Revised: Xu et al.

Original: (2017) make the sequenceto-sequence GAN differentiable by directly multiplying the word probabilities obtained from the decoder to the corresponding word vectors, yielding an approximately vectorized representation of the target sequence.
Revised: (2017) make the sequenceto-sequence GAN differentiable by directly multiplying the word probabilities obtained from the decoder to the corresponding word vectors, yielding an approximately vectorized representation of the target sequence.

Original: However, their approach injects diversity in the word level rather than the level of the whole responses.
Revised: However, their approach injects diversity in the word level rather than the level of the whole responses.

Original: DialogWAE differs from exiting GAN conversation models in that it shapes the distribution of responses in a high level latent space rather than direct tokens and does not rely on RL where the gradient variances are large.
Revised: DialogWAE differs from exiting GAN conversation models in that it shapes the distribution of responses in a high level latent space rather than direct tokens and does not rely on RL where the gradient variances are large.

Original:  P ROPOSED A PPROACH 3. P ROBLEM S TATEMENT
Revised:  P ROPOSED A PPROACH 3. P ROBLEM S TATEMENT

Original: Let d =[ u 1 , ..., u k ] denote a dialogue of k utterances where u i =[ w 1 , ..., w | u i | ] represents an utterance and w n denotes the n -th word in u i .
Revised: Let d =[ u 1 , ..., u k ] denote a dialogue of k utterances where u i =[ w 1 , ..., w | u i | ] represents an utterance and w n denotes the n -th word in u i .

Original: Let c
Revised: Let c

Original: =[
Revised: =[

Original: u 1 , ..., u k − 1 ] denote a dialogue context, the k - 1 historical utterances, and x = u
Revised: u 1 , ..., u k − 1 ] denote a dialogue context, the k - 1 historical utterances, and x = u

Original: k be a response which means the next utterance.
Revised: k be a response which means the next utterance.

Original: Our goal is to estimate the conditional distribution p θ ( x | c ) .
Revised: Our goal is to estimate the conditional distribution p θ ( x | c ) .

Original: As x and c are sequences of discrete tokens, it is non-trivial to ﬁnd a direct coupling between them.
Revised: As x and c are sequences of discrete tokens, it is non-trivial to ﬁnd a direct coupling between them.

Original: Instead, we introduce a continuous latent variable z that represents the high-level representation of the response.
Revised: Instead, we introduce a continuous latent variable z that represents the high-level representation of the response.

Original: The response generation can be viewed as a two-step procedure, where a latent variable z is sampled from a distribution p θ ( z | c ) on a latent space Z , and then the response x is decoded from z with p θ ( x | z, c ) .
Revised: The response generation can be viewed as a two-step procedure, where a latent variable z is sampled from a distribution p θ ( z | c ) on a latent space Z , and then the response x is decoded from z with p θ ( x | z, c ) .

Original: Under this model, the likelihood of a response is
Revised: Under this model, the likelihood of a response is

Original: [Equation]
Revised: [Equation]

Original: The exact log-probability is difﬁcult to compute since it is intractable to marginalize out z .
Revised: The exact log-probability is difﬁcult to compute since it is intractable to marginalize out z .

Original: Therefore, we approximate the posterior distribution of z as q φ ( z | x, c ) which can be computed by a neural network named recognition network .
Revised: Therefore, we approximate the posterior distribution of z as q φ ( z | x, c ) which can be computed by a neural network named recognition network .

Original: Using this approximate posterior, we can instead compute the evidence lower bound (ELBO):
Revised: Using this approximate posterior, we can instead compute the evidence lower bound (ELBO):

Original: [Equation]
Revised: [Equation]

Original: where p ( z | c ) represents the prior distribution of z given c and can be modeled with a neural network named prior network .
Revised: where p ( z | c ) represents the prior distribution of z given c and can be modeled with a neural network named prior network .

Original: 3. C ONDITIONAL W ASSERSTEIN A UTO -E NCODERS FOR D IALOGUE M ODELING
Revised: 3. C ONDITIONAL W ASSERSTEIN A UTO -E NCODERS FOR D IALOGUE M ODELING

Original: The conventional VAE conversation models assume that the latent variable z follows a simple prior distribution such as the normal distribution.
Revised: The conventional VAE conversation models assume that the latent variable z follows a simple prior distribution such as the normal distribution.

Original: However, the latent space of real responses is more complicated and difﬁcult to be estimated with such a simple distribution.
Revised: However, the latent space of real responses is more complicated and difﬁcult to be estimated with such a simple distribution.

Original: This often leads to the posterior collapse problem (Shen et al. , 2018).
Revised: This often leads to the posterior collapse problem (Shen et al. , 2018).

Original: Inspired by GAN and the adversarial auto-encoder (AAE)
Revised: Inspired by GAN and the adversarial auto-encoder (AAE)

Original: (Makhzani et al. , 2015; Tolstikhin et al. , 2017), we model the distribution of z by training a GAN within the latent space.
Revised: (Makhzani et al. , 2015; Tolstikhin et al. , 2017; Zhao et al. , 2018), we model the distribution of z by training a GAN within the latent space.

Original: We sample from the prior and posterior over the latent variables by transforming random noise (cid:15) using neural networks.
Revised: We sample from the prior and posterior over the latent variables by transforming random noise (cid:15) using neural networks.

Original: Speciﬁcally, the prior sample ˜
Revised: Speciﬁcally, the prior sample ˜

Original: z ∼ p θ ( z | c ) is generated by a generator G from context-dependent random noise ˜ (cid:15) , while the approximate posterior sample z ∼ q φ ( z | c, x ) is generated by a generator Q from context-dependent random noise (cid:15) .
Revised: z ∼ p θ ( z | c ) is generated by a generator G from context-dependent random noise ˜ (cid:15) , while the approximate posterior sample z ∼ q φ ( z | c, x ) is generated by a generator Q from context-dependent random noise (cid:15) .

Original: Both ˜ (cid:15) and (cid:15) are drawn from a normal distribution whose mean and covariance matrix (assumed diagonal) are computed from c with feed-forward neural networks, prior network and recognition network , respectively:
Revised: Both ˜ (cid:15) and (cid:15) are drawn from a normal distribution whose mean and covariance matrix (assumed diagonal) are computed from c with feed-forward neural networks, prior network and recognition network , respectively:

Original: [Equation]
Revised: [Equation]

Original: [Equation]
Revised: [Equation]

Original: (4) where f θ ( · ) and g φ ( · ) are feed-forward neural networks.
Revised: (4) where f θ ( · ) and g φ ( · ) are feed-forward neural networks.

Original: Our goal is to minimize the divergence between p θ ( z | c ) and q φ ( z | x, c ) while maximizing the log-probability of a reconstructed response from z .
Revised: Our goal is to minimize the divergence between p θ ( z | c ) and q φ ( z | x, c ) while maximizing the log-probability of a reconstructed response from z .

Original: We thus solve the following problem:
Revised: We thus solve the following problem:

Original: [Equation]
Revised: [Equation]

Original: where p θ ( z | c ) and q φ ( z | x, c ) are neural networks implementing Equations 3 and 4, respectively.
Revised: where p θ ( z | c ) and q φ ( z | x, c ) are neural networks implementing Equations 3 and 4, respectively.

Original: p ψ ( x | z, c ) is a decoder.
Revised: p ψ ( x | z, c ) is a decoder.

Original: W( ·||· ) represents the Wasserstein distance between these two distributions (Arjovsky et al. , 2017).
Revised: W( ·||· ) represents the Wasserstein distance between these two distributions (Arjovsky et al. , 2017).

Original: Figure 1 illustrates an overview of our model.

Original: The utterance encoder (RNN) transforms each utterance (including the response x ) in the dialogue into a real-valued vector. For the i -th utterance
Revised: We choose the Wasserstein distance as the divergence since the WGAN has been shown to produce good results in text generation (Zhao et al. , 2018).

Original: Recognition Network ෤ ε
Revised: Recognition Network ෤ ε

Original: I like tennis
Revised: I like tennis

Original: Prior Network ε
Revised: Prior Network ε

Original: I like like tennis I 
 𝑧 ǁ𝑧 𝜇, 𝜎 𝜋 𝑖 ,𝜇 𝑖 , 𝜎 𝑖 𝒄 𝒙 0/ utterance encoder context encoder conversation floor response decoder
Revised: I like like tennis I 
 𝑧 ǁ𝑧 𝜇, 𝜎 𝜋 𝑖 ,𝜇 𝑖 , 𝜎 𝑖 𝒄 𝒙 0/ utterance encoder context encoder conversation floor response decoder

Original: Q
Revised: Q

Original: G
Revised: G

Original: D
Revised: D

Original: I like soccer how about you that is cool  in the context, the context encoder (RNN) takes as input the concatenation of its encoding vector and the conversation ﬂoor (1 if the utterance is from the speaker of the response, otherwise 0) and computes its hidden state h ctxi .
Revised: I like soccer how about you that is cool Figure 1 illustrates an overview of our model. The utterance encoder (RNN) transforms each utterance (including the response x ) in the dialogue into a real-valued vector. For the i -th utterance in the context, the context encoder (RNN) takes as input the concatenation of its encoding vector and the conversation ﬂoor (1 if the utterance is from the speaker of the response, otherwise 0) and computes its hidden state h ctxi .

Original: The ﬁnal hidden state of the context encoder is used as the context representation.
Revised: The ﬁnal hidden state of the context encoder is used as the context representation.

Original: At generation time, the model draws a random noise ˜ (cid:15) from the prior network (PriNet) which transforms c through a feed-forward network followed by two matrix multiplications which result in the mean and diagonal covariance, respectively.
Revised: At generation time, the model draws a random noise ˜ (cid:15) from the prior network (PriNet) which transforms c through a feed-forward network followed by two matrix multiplications which result in the mean and diagonal covariance, respectively.

Original: Then, the generator G generates a sample of latent variable ˜
Revised: Then, the generator G generates a sample of latent variable ˜

Original: z from the noise through a feed-forward network.
Revised: z from the noise through a feed-forward network.

Original: The decoder RNN decodes the generated ˜ z into a response.
Revised: The decoder RNN decodes the generated ˜ z into a response.

Original: At training time, the model infers the posterior distribution of the latent variable conditioned on the context c and the response x .
Revised: At training time, the model infers the posterior distribution of the latent variable conditioned on the context c and the response x .

Original: The recognition network (RecNet) takes as input the concatenation of both x and c and transforms them through a feed-forward network followed by two matrix multiplications which deﬁne the normal mean and diagonal covariance, respectively.
Revised: The recognition network (RecNet) takes as input the concatenation of both x and c and transforms them through a feed-forward network followed by two matrix multiplications which deﬁne the normal mean and diagonal covariance, respectively.

Original: A Gaussian noise (cid:15) is drawn from the recognition network with the re-parametrization trick.
Revised: A Gaussian noise (cid:15) is drawn from the recognition network with the re-parametrization trick.

Original: Then, the generator Q transforms the Gaussian noise (cid:15) into a sample of latent variable z through a feed-forward network.
Revised: Then, the generator Q transforms the Gaussian noise (cid:15) into a sample of latent variable z through a feed-forward network.

Original: The response decoder (RNN) computes the reconstruction loss:
Revised: The response decoder (RNN) computes the reconstruction loss:

Original: [Equation]

Original: [Equation]
Revised: [Equation]

Original: We match the approximate posterior with the prior distributions of z by introducing an adversarial discriminator D which tells apart the prior samples from posterior samples.
Revised: We match the approximate posterior with the prior distributions of z by introducing an adversarial discriminator D which tells apart the prior samples from posterior samples.

Original: D is implemented as a feed-forward neural network which takes as input the concatenation of z and c and outputs a real value.
Revised: D is implemented as a feed-forward neural network which takes as input the concatenation of z and c and outputs a real value.

Original: We train D by minimizing the discriminator loss:
Revised: We train D by minimizing the discriminator loss:

Original: [Equation]
Revised: [Equation]

Original: 3. M ULTIMODAL R ESPONSE G ENERATION WITH A G AUSSIAN M IXTURE P RIOR N ETWORK
Revised: 3. M ULTIMODAL R ESPONSE G ENERATION WITH A G AUSSIAN M IXTURE P RIOR N ETWORK

Original: It is a usual practice for the prior distribution in the AAE architecture to be a normal distribution.
Revised: It is a usual practice for the prior distribution in the AAE architecture to be a normal distribution.

Original: However, responses often have a multimodal nature reﬂecting many equally possible situations (Sato et al. , 2017), topics and sentiments.
Revised: However, responses often have a multimodal nature reﬂecting many equally possible situations (Sato et al. , 2017), topics and sentiments.

Original: A random noise with normal distribution could restrict the generator to output a latent space with a single dominant mode due to the single-modal nature of Gaussian distribution.
Revised: A random noise with normal distribution could restrict the generator to output a latent space with a single dominant mode due to the unimodal nature of Gaussian distribution.

Original: Consequently, the generated responses could follow simple prototypes.
Revised: Consequently, the generated responses could follow simple prototypes.

Original: To capture multiple modes in the probability distribution over the latent variable, we further propose to use a distribution that explicitly deﬁnes more than one mode.
Revised: To capture multiple modes in the probability distribution over the latent variable, we further propose to use a distribution that explicitly deﬁnes more than one mode.

Original: Each time, the noise to generate the latent variable is selected from one of the modes.
Revised: Each time, the noise to generate the latent variable is selected from one of the modes.

Original: To achieve so, we make the prior network to capture a mixture of Gaussian distributions, namely, GMM( { π k , µ k , σ 2 k I } Kk =1 ) , where π k , µ k and σ k are parameters of the k -th component.
Revised: To achieve so, we make the prior network to capture a mixture of Gaussian distributions, namely, GMM( { π k , µ k , σ 2 k I } Kk =1 ) , where π k , µ k and σ k are parameters of the k -th component.

Original: This allows it to learn a multimodal manifold in the latent variable space in a two-step generation process – ﬁrst choosing a component k with π k , and then sampling Gaussian noise within the selected component:
Revised: This allows it to learn a multimodal manifold in the latent variable space in a two-step generation process – ﬁrst choosing a component k with π k , and then sampling Gaussian noise within the selected component:

Original: [Equation]
Revised: [Equation]

Original: where v k ∈ ∆ K − 1 is a component indicator with class probabilities

Original: π 1 , · · · , π K ; π k is the mixture coefﬁcient of the k -th component of the GMM. They are computed as π k = [Equation] e k )
Revised: σ

Original: [Equation]
Revised: [Equation]

Original: Ki [Equation] exp( e i ) , where [Equation]
Revised: k I ) , (8)

Original: = critic
Revised: = critic

Original: In: a dialog corpus D = { ( c i , x i ) } |D| i =1 , the number of prior modes K , discriminator iterations n critic 1 Initialize { θ UEnc , θ CEnc , θ PriNet , θ RecNet , θ Q , θ G , θ D , θ Dec }  not convergence do
Revised: In: a dialog corpus D = { ( c i , x i ) } |D| i =1 , the number of prior modes K , discriminator iterations n critic 1 Initialize { θ UEnc , θ CEnc , θ PriNet , θ RecNet , θ Q , θ G , θ D , θ Dec } 2 while not convergence do

Original: Initialize  has unsampled batches do
Revised: Initialize D while D has unsampled batches do

Original: UEnc
Revised: Sample a N { ( x n , c n ) } Nn 1 from D

Original:  Equation
Revised: Get the representations of context and response x n =UEnc( x n ), c n = CEnc( c n ) Sample from RecNet( n c n ) according to Equation PriNet according to Equation

Original: Instead of exact sampling we use Gumbel-Softmax re-parametrization (Kusner and Hern ´ andezLobato, 2016) to sample an instance of v :
Revised: end where v k ∈ ∆ K − 1 is a component indicator with class probabilities π 1 , · · · , π K ; π k is the mixture coefﬁcient of the k -th component of the GMM. They are computed as

Original: [Equation]
Revised: [Equation]

Original: where g i is a Gumbel noise computed as g i = − log
Revised: e i ) , where

Original: [Equation]
Revised: [Equation]

Original: − log
Revised: Instead of exact sampling, we use Gumbel-Softmax re-parametrization (Kusner and Hern ´ andezLobato, 2016) to sample an instance of v :

Original: [Equation]
Revised: [Equation]

Original: u i )) , u i ∼ U
Revised: where g i is a Gumbel noise computed as

Original: [Equation]
Revised: [Equation]

Original: 1) and τ ∈ [0,1] is the softmax temperature which is set to 0.1 in all experiments.
Revised: [Equation] and τ ∈ [0,1] is the softmax temperature which is set to 0.1 in all experiments.

Original: We refer to this framework as DialogWAE-GMP.
Revised: We refer to this framework as DialogWAE-GMP.

Original: A comparison of performance with different numbers of prior components will be shown in Section 5.1.
Revised: A comparison of performance with different numbers of prior components will be shown in Section 5.1.

Original: 3. T RAINING
Revised: 3. T RAINING

Original: Our model is trained epochwise until a convergence is reached.
Revised: Our model is trained epochwise until a convergence is reached.

Original: In each epoch, we train the model iteratively by alternating two phases − an AE phase during which the reconstruction loss of decoded responses is minimized, and a GAN phaseduring which  the  approximate posterior distribution of the latent variable is matched to the conditional prior distribution.
Revised: In each epoch, we train the model iteratively by alternating two phases − an AE phase during which the reconstruction loss of decoded responses is minimized, and a GAN phase which minimizes the Wasserstein distance between the prior and approximate posterior distributions over the latent variables.

Original: The detailed procedures are presented in Algorithm
Revised: The detailed procedures are presented in Algorithm

Original:  E XPERIMENTAL S ETUP
Revised:  E XPERIMENTAL S ETUP

Original: Datasets We evaluate our model on two dialogue datasets, Dailydialog (Li et al. , 2017b) and
Revised: Datasets We evaluate our model on two dialogue datasets, Dailydialog (Li et al. , 2017b) and

Original: Switchboard (Godfrey and Holliman, 1997), which have been widely used in recent studies (Shen et al. , 2018; Zhao et al. , 2017).
Revised: Switchboard (Godfrey and Holliman, 1997), which have been widely used in recent studies (Shen et al. , 2018; Zhao et al. , 2017).

Original: Dailydialog has 13,118 daily conversations for a English learner in a daily life.
Revised: Dailydialog has 13,118 daily conversations for a English learner in a daily life.

Original: Switchboard contains 2,400 two-way telephone conversations under 70 speciﬁed topics.
Revised: Switchboard contains 2,400 two-way telephone conversations under 70 speciﬁed topics.

Original: The datasets are separated into training, validation, and test sets with the same ratios as in the baseline papers, that is, 2316:60:62 for Switchboard (Zhao et al. , 2017) and 10:1:1 for Dailydialog
Revised: The datasets are separated into training, validation, and test sets with the same ratios as in the baseline papers, that is, 2316:60:62 for Switchboard (Zhao et al. , 2017) and 10:1:1 for Dailydialog

Original: (Shen et al. , 2018), respectively.
Revised: (Shen et al. , 2018), respectively.

Original: Metrics To measure the performance of DialogWAE, we adopted several standard metrics widely used in existing studies: BLEU (Papineni et al. , 2002),
Revised: Metrics To measure the performance of DialogWAE, we adopted several standard metrics widely used in existing studies: BLEU (Papineni et al. , 2002),

Original: BOW Embedding (Liu et al. , 2016) and distinct (Li et al. , 2015).
Revised: BOW Embedding (Liu et al. , 2016) and distinct (Li et al. , 2015).

Original: In particular, BLEU measures how much a generated response contains n -gram overlaps with the reference.
Revised: In particular, BLEU measures how much a generated response contains n -gram overlaps with the reference.

Original: We compute BLEU scores for n < 4 using smoothing techniques (smoothing 7) 2 (Chen and Cherry, 2014).
Revised: We compute BLEU scores for n < 4 using smoothing techniques (smoothing 7) 2 (Chen and Cherry, 2014).

Original: For each test context, we sample 10 responses from the models and compute their BLEU scores.
Revised: For each test context, we sample 10 responses from the models and compute their BLEU scores.

Original: We deﬁne n -gram precision and n -gram recall as the average and the maximum score respectively.
Revised: We deﬁne n -gram precision and n -gram recall as the average and the maximum score respectively.

Original: BOW embedding metric is the cosine similarity of bag-of-words embeddings between the hypothesis and the reference.
Revised: BOW embedding metric is the cosine similarity of bag-of-words embeddings between the hypothesis and the reference.

Original: We use three metrics to compute the word embedding similarity: 1.
Revised: We use three metrics to compute the word embedding similarity: 1.

Original: Greedy : greedily matching words in two utterances based on the cosine similarities between their embeddings, and to average the obtained scores (Rus and Lintean, 2012).
Revised: Greedy : greedily matching words in two utterances based on the cosine similarities between their embeddings, and to average the obtained scores (Rus and Lintean, 2012).

Original: Average : cosine similarity between the averaged word embeddings in the two utterances (Mitchell and Lapata, 2008).
Revised: Average : cosine similarity between the averaged word embeddings in the two utterances (Mitchell and Lapata, 2008).

Original: Extrema : cosine similarity between the largest extreme values among the word embeddings in the two utterances (Forgues et al. , 2014).
Revised: Extrema : cosine similarity between the largest extreme values among the word embeddings in the two utterances (Forgues et al. , 2014).

Original: We use Glove vectors (Pennington et al. , 2014) as the embeddings which will be discussed later in this section.
Revised: We use Glove vectors (Pennington et al. , 2014) as the embeddings which will be discussed later in this section.

Original: For each test context, we report the maximum BOW embedding score among the 10 sampled responses.
Revised: For each test context, we report the maximum BOW embedding score among the 10 sampled responses.

Original: Distinct computes the diversity of the generated responses.
Revised: Distinct computes the diversity of the generated responses.

Original: dist- n is deﬁned as the ratio of unique n -grams (n=1 , 2) over all n -grams in the generated responses.
Revised: dist- n is deﬁned as the ratio of unique n -grams (n=1 , 2) over all n -grams in the generated responses.

Original: As we sample multiple responses for each test context, we evaluate diversities for both within and among the sampled responses.
Revised: As we sample multiple responses for each test context, we evaluate diversities for both within and among the sampled responses.

Original: We deﬁne intra-dist as the average of distinct values within each sampled response and inter-dist as the distinct value among all sampled responses.
Revised: We deﬁne intra-dist as the average of distinct values within each sampled response and inter-dist as the distinct value among all sampled responses.

Original: Baselines We compare the performance of DialogWAE with seven recently-proposed baselines for dialogue modeling: (i) HRED: a generalized sequence-to-sequence model with hierarchical RNN encoder (Serban et al. , 2016), (ii) SeqGAN: a GAN based model for sequence generation (Li et al. , 
Revised: Baselines We compare the performance of DialogWAE with seven recently-proposed baselines for dialogue modeling: (i) HRED: a generalized sequence-to-sequence model with hierarchical RNN encoder (Serban et al. , 2016), (ii) SeqGAN: a GAN based model for sequence generation (Li et al. , 2017a), (iii) CVAE: a conditional VAE model with KL-annealing (Zhao et al. , 2017), (iv) CVAEBOW: a conditional VAE model with a BOW loss (Zhao et al. , 2017), (v) CVAE-CO: a collaborative conditional VAE model (Shen et al. , 2018), (vi) VHRED: a hierarchical VAE model (Serban et al. , 2017), and (vii) VHCR: a hierarchical VAE model with conversation modeling (Park et al. , 2018).

Original: Training and Evaluation Details We use the gated recurrent units (GRU) (Cho et al. , 2014) for the RNN encoders and decoders.
Revised: Training and Evaluation Details We use the gated recurrent units (GRU) (Cho et al. , 2014) for the RNN encoders and decoders.

Original: The utterance encoder is a bidirectional GRU with 300 hidden units in each direction.
Revised: The utterance encoder is a bidirectional GRU with 300 hidden units in each direction.

Original: The context encoder and decoder are both GRUs with 300 hidden units.
Revised: The context encoder and decoder are both GRUs with 300 hidden units.

Original: The prior and the recognition networks are both 2-layer feed-forward networks of size 200 with tanh non-linearity.
Revised: The prior and the recognition networks are both 2-layer feed-forward networks of size 200 with tanh non-linearity.

Original: The generators Q and G as well as the discriminator D are 3-layer feed-forward networks with ReLU non-linearity (Nair and Hinton, 2010) and hidden sizes of 200, 200 and 400, respectively.
Revised: The generators Q and G as well as the discriminator D are 3-layer feed-forward networks with ReLU non-linearity (Nair and Hinton, 2010) and hidden sizes of 200, 200 and 400, respectively.

Original: The dimension of a latent variable z is set to 200.
Revised: The dimension of a latent variable z is set to 200.

Original: The initial weights for all fully connected layers are sampled from a uniform distribution [-0.02, 0.02].
Revised: The initial weights for all fully connected layers are sampled from a uniform distribution [-0.02, 0.02].

Original: The gradient penalty is used when training D (Gulrajani et al. , 2017) and its hyper-parameter λ is set to 10.
Revised: The gradient penalty is used when training D (Gulrajani et al. , 2017) and its hyper-parameter λ is set to 10.

Original: We set the vocabulary size to 10,000 and deﬁne all the out-of-vocabulary words to a special token < unk > .
Revised: We set the vocabulary size to 10,000 and deﬁne all the out-of-vocabulary words to a special token < unk > .

Original: The word embedding size is 200 and initialized with Glove vectors pre-trained on Twitter (Pennington et al. , 2014).
Revised: The word embedding size is 200 and initialized with Glove vectors pre-trained on Twitter (Pennington et al. , 2014).

Original: The size of context window is set to 10 with a maximum utterance length of 40.
Revised: The size of context window is set to 10 with a maximum utterance length of 40.

Original: We sample responses with greedy decoding so that the randomness entirely come from the latent variables.
Revised: We sample responses with greedy decoding so that the randomness entirely come from the latent variables.

Original: The baselines were implemented with the same set of hyper-parameters.
Revised: The baselines were implemented with the same set of hyper-parameters.

Original: All the models are implemented with Pytorch 0.4.0 3 .
Revised: All the models are implemented with Pytorch 0.4.0 3 .

Original: The models are trained with mini-batches containing 32 examples each in an end-to-end manner.
Revised: The models are trained with mini-batches containing 32 examples each in an end-to-end manner.

Original: In the AE phase, the models are trained by SGD with an initial learning rate of 1.0 and gradient clipping at 1 (Pascanu et al. , 2013).
Revised: In the AE phase, the models are trained by SGD with an initial learning rate of 1.0 and gradient clipping at 1 (Pascanu et al. , 2013).

Original: We decay the learning rate by 40% every 10th epoch.
Revised: We decay the learning rate by 40% every 10th epoch.

Original: In the GAN phase, the models are updated using RMSprop (Tieleman and Hinton) with ﬁxed learning rates of 5 × e −and 1 × e − 5 for the generator and the discriminator, respectively.
Revised: In the GAN phase, the models are updated using RMSprop (Tieleman and Hinton) with ﬁxed learning rates of 5 × e −and 1 × e − 5 for the generator and the discriminator, respectively.

Original: We tune the hyper-parameters on the validation set and measure the performance on the test set. 
Revised: We tune the hyper-parameters on the validation set and measure the performance on the test set. [Table] [Table]

Original:  E XPERIMENTAL R ESULTS 5. Q UANTITATIVE A NALYSIS
Revised:  E XPERIMENTAL R ESULTS 5. Q UANTITATIVE A NALYSIS

Original: Tables 1 and 2 show the performance of DialogWAE and baselines on the two datasets.
Revised: Tables 1 and 2 show the performance of DialogWAE and baselines on the two datasets.

Original: DialogWAE outperforms the baselines in the majority of the experiments.
Revised: DialogWAE outperforms the baselines in the majority of the experiments.

Original: In terms of BLEU scores, Dialog- [Table] [Table] WAE (with a Gaussian mixture prior network) generates more relevant responses, with the average recall of 42.0% and 37.2% on both of the datasets.
Revised: In terms of BLEU scores, DialogWAE (with a Gaussian mixture prior network) generates more relevant responses, with the average recall of 42.0% and 37.2% on both of the datasets.

Original: These are signiﬁcantly higher than those of the
Revised: These are signiﬁcantly higher than those of the

Original: CVAE baselines (29.9% and 26.5%).
Revised: CVAE baselines (29.9% and 26.5%).

Original: We observe a similar trend to the BOW embedding metrics.
Revised: We observe a similar trend to the BOW embedding metrics.

Original: DialogWAE generates more diverse responses than the baselines do.
Revised: DialogWAE generates more diverse responses than the baselines do.

Original: The inter-dist scores are significantly higher than those of the baseline models.
Revised: The inter-dist scores are significantly higher than those of the baseline models.

Original: This indicates the sampled responses contain more distinct n -grams.
Revised: This indicates the sampled responses contain more distinct n -grams.

Original: DialogWAE does not show better intra-distinct scores.
Revised: DialogWAE does not show better intra-distinct scores.

Original: We conjecture that this is due to the relatively long responses generated by the DialogWAE as shown in the last columns of both tables.
Revised: We conjecture that this is due to the relatively long responses generated by the DialogWAE as shown in the last columns of both tables.

Original: It is highly unlikely for there to be many repeated n -grams in a short response.
Revised: It is highly unlikely for there to be many repeated n -grams in a short response.

Original: We further investigate the effects of the number of prior components ( K ).
Revised: We further investigate the effects of the number of prior components ( K ).

Original: Figure 2 shows the performance of DialogWAE-GMP with respect to the number of prior components K .
Revised: Figure 2 shows the performance of DialogWAE-GMP with respect to the number of prior components K .

Original: We vary K from 1 to 9.
Revised: We vary K from 1 to 9.

Original: As shown in the results, in most cases, the performance increases with K and decreases once K reaches a certain threshold, for example, three.
Revised: As shown in the results, in most cases, the performance increases with K and decreases once K reaches a certain threshold, for example, three.

Original: The optimal K on both of the datasets was around 3.
Revised: The optimal K on both of the datasets was around 3.

Original: We attribute this degradation to training difﬁculty of a mixture density network and the lack of appropriate regularization, which is left for future investigation.
Revised: We attribute this degradation to training difﬁculty of a mixture density network and the lack of appropriate regularization, which is left for future investigation.

Original: 5. Q UALITATIVE A NALYSIS
Revised: 5. Q UALITATIVE A NALYSIS

Original: Table 3 presents examples of responses generated by the models on the DailyDialog dataset.
Revised: Table 3 presents examples of responses generated by the models on the DailyDialog dataset.

Original: Due to the space limitation, we report the results of CVAE-CO and DialogWAE-GMP, which are the representative models among the baselines and the proposed models.
Revised: Due to the space limitation, we report the results of CVAE-CO and DialogWAE-GMP, which are the representative models among the baselines and the proposed models.

Original: For each context in the test set, we show three samples of generated responses from each model.
Revised: For each context in the test set, we show three samples of generated responses from each model.

Original: As we expected, DialogWAE generates more coherent and diverse responses that cover multiple plausible aspects.
Revised: As we expected, DialogWAE generates more coherent and diverse responses that cover multiple plausible aspects.

Original: Furthermore, we notice that the generated response is long and exhibits informative content.
Revised: Furthermore, we notice that the generated response is long and exhibits informative content.

Original: By contrast, the responses generated by the baseline model exhibit relatively limited variations.
Revised: By contrast, the responses generated by the baseline model exhibit relatively limited variations.

Original: Although the responses show some variants in contents, most of them share a similar preﬁx such as “how much” . 
Revised: Although the responses show some variants in contents, most of them share a similar preﬁx such as “how much” . [Figure] [Table]

Revised: thank your for calling

Revised: Eg

Revised: [Table]

Original: To validate the previous results, we further conduct a human evaluation with Amazon Mechanical
Revised: : i’m afraid i can’t ﬁnd it [Table] [Table] i’d like to make a reservation for you, please world airline.

Revised: what can

Revised: [Table]

Revised: what’s the matter?

Revised: [Table]

Revised: I do for you?

Revised: eou

Revised: [Table]

Revised: how much is the rent?

Revised: [Table]

Revised: the

Revised: [Table]

Revised: is

Revised: [Table]

Revised: the

Revised: [Table]

Revised: $1500 per month.

Revised: [Table]

Revised: guess who i saw just now

Revised: [Table]

Revised: he is

Revised: [Table]

Revised: able

Revised: [Table]

Revised: john smith

Revised: [Table]

Revised: that

Revised: [Table]

Revised: get married

Revised: [Table]

Revised: had no idea

Revised: [Table]

Revised: get

Revised: [Table]

Revised: bad egg who took the low

Revised: [Table]

Revised: is not

Revised: [Table]

Revised: not

Revised: [Table]

Revised: bad

Revised: [Table]

Revised: road since he was a boy.

Revised: it’s just a little bit, but it’s not too bad.

Revised: We further investigate the interpretability of Gaussian components in the prior network, that is, what each Gaussian model has captured before generation.

Revised: We pick a dialogue context “I’d like to invite you to dinner tonight, do you have time?”

Revised: which is also used in (Shen et al. , 2018) for analysis and generate ﬁve responses for each Gaussian component.

Revised: As shown in Table 4, different

Revised: [Table]

Revised: Gaussian models generate different types of responses: component 1 expresses a strong will, while component 2 expresses some uncertainty

Revised: [Table]

Revised: and component 3 generates strong negative responses.

Revised: The overlap between components is marginal (around 1/5).

Revised: The results indicate that the Gaussian mixture prior network can successfully capture the multimodal distribution of the responses.

Revised: To validate the previous results

Revised: [Table]

Revised: we further conduct a human evaluation with Amazon Mechanical

Original: Turk.
Revised: Turk.

Original: We randomly selected 50 dialogues from the test set of DailyDialog.
Revised: We randomly selected 50 dialogues from the test set of DailyDialog.

Original: For each dialogue context, we generated 10 responses from each of the four models.
Revised: For each dialogue context, we generated 10 responses from each of the four models.

Original: Responses for each context were inspected by 5 participants who were asked to choose the model which performs the best in regarding[Figure] [Table] to coherence, diversity and informative while being blind to the underlying algorithms.
Revised: Responses for each context were inspected by 5 participants who were asked to choose the model which performs the best in regarding to coherence, diversity and informative while being blind to the underlying algorithms.

Original: The average percentages that each model was selected as the best to a speciﬁc criterion are shown in Table 4:
Revised: The average percentages that each model was selected as the best to a speciﬁc criterion are shown in Table 5.

Original: [Table]
Revised: [Table]

Original: The proposed approach clearly outperforms the current state of the art, CVAE-CO and VHCR, by a large margin in terms of all three metrics.
Revised: The proposed approach clearly outperforms the current state of the art, CVAE-CO and VHCR, by a large margin in terms of all three metrics.

Original: This improvement is especially clear when the Gaussian mixture prior was used.
Revised: This improvement is especially clear when the Gaussian mixture prior was used.

Original:  C ONCLUSION
Revised:  C ONCLUSION

Original: In this paper, we introduced a new approach, named DialogWAE, for dialogue modeling.
Revised: In this paper, we introduced a new approach, named DialogWAE, for dialogue modeling.

Original: Different from existing VAE models which impose a simple prior distribution over the latent variables,
Revised: Different from existing VAE models which impose a simple prior distribution over the latent variables,

Original: DialogWAE samples the prior and posterior samples of latent variables by transforming contextdependent Gaussian noise using neural networks, and minimizes the Wasserstein distance between the prior and posterior distributions.
Revised: DialogWAE samples the prior and posterior samples of latent variables by transforming contextdependent Gaussian noise using neural networks, and minimizes the Wasserstein distance between the prior and posterior distributions.

Original: Furthermore, we enhance the model with a Gaussian mixture prior network to enrich the latent space.
Revised: Furthermore, we enhance the model with a Gaussian mixture prior network to enrich the latent space.

Original: Experiments on two widely used datasets show that our model outperforms state-of-the-art VAE models and generates more coherent, informative and diverse responses.
Revised: Experiments on two widely used datasets show that our model outperforms state-of-the-art VAE models and generates more coherent, informative and diverse responses.