SlowGuess/ACL_2020_OCR huggingface dataset:
Pengyu Cheng $^{1*}$ , Martin Renqiang Min $^{2}$ , Dinghan Shen $^{3}$ , Christopher Malon $^{2}$ , Yizhe Zhang $^{4}$ , Yitong Li $^{1}$ , Lawrence Carin $^{1}$
$^{1}$ Duke University  $^{2}$ NEC Labs America
<sup>3</sup>Microsoft Dynamics 365 AI <sup>4</sup>Microsoft Research
pengyu.cheng@duke.edu, {renqiang, malon}@nec-labs.com
{dishen, yizzhang}@microsoft.com, {yitong.li, lcarin}@duke.edu
Learning disentangled representations of natural language is essential for many NLP tasks, e.g., conditional text generation, style transfer, personalized dialogue systems, etc. Similar problems have been studied extensively for other forms of data, such as images and videos. However, the discrete nature of natural language makes the disentangling of textual representations more challenging (e.g., the manipulation over the data space cannot be easily achieved). Inspired by information theory, we propose a novel method that effectively manifests disentangled representations of text, without any supervision on semantics. A new mutual information upper bound is derived and leveraged to measure dependence between style and content. By minimizing this upper bound, the proposed method induces style and content embeddings into two independent low-dimensional spaces. Experiments on both conditional text generation and text-style transfer demonstrate the high quality of our disentangled representation in terms of content and style preservation.
Disentangled representation learning (DRL), which maps different aspects of data into distinct and independent low-dimensional latent vector spaces, has attracted considerable attention for making deep learning models more interpretable. Through a series of operations such as selecting, combining, and switching, the learned disentangled representations can be utilized for downstream tasks, such as domain adaptation (Liu et al., 2018), style transfer (Lee et al., 2018), conditional generation (Denton et al., 2017; Burgess et al., 2018), and few-shot learning (Kumar Verma et al., 2018). Although widely used in various domains, such
as images (Tran et al., 2017; Lee et al., 2018), videos (Yingzhen and Mandt, 2018; Hsieh et al., 2018), and speech (Chou et al., 2018; Zhou et al., 2019), many challenges in DRL have received limited exploration in natural language processing (John et al., 2019).
To disentangle various attributes of text, two distinct types of embeddings are typically considered: the style embedding and the content embedding (John et al., 2019). The content embedding is designed to encapsulate the semantic meaning of a sentence. In contrast, the style embedding should represent desired attributes, such as the sentiment of a review, or the personality associated with a post. Ideally, a disentangled-text-representation model should learn representative embeddings for both style and content.
To accomplish this, several strategies have been introduced. Shen et al. (2017) proposed to learn a semantically-meaningful content embedding space by matching the content embedding from two different style domains. However, their method requires predefined style domains, and thus cannot automatically infer style information from unlabeled text. Hu et al. (2017) and Lample et al. (2019) utilized one-hot vectors as style-related features (instead of inferring the style embeddings from the original data). These models are not applicable when new data comes from an unseen style class. John et al. (2019) proposed an encoder-decoder model in combination with an adversarial training objective to infer both style and content embeddings from the original data. However, their adversarial training framework requires manually-processed supervised information for content embeddings (e.g., reconstructing sentences with manually-chosen sentiment-related words removed). Further, there is no theoretical guarantee for the quality of disentanglement.
In this paper, we introduce a novel Information-
* This work was conducted while the first author was doing an internship at NEC Labs America.
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Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 7530-7541 July 5 - 10, 2020. ©2020 Association for Computational Linguistics
theoretic Disentangled Embedding Learning method (IDEL) for text, based on guidance from information theory. Inspired by Variation of Information (VI), we introduce a novel information-theoretic objective to measure how well the learned representations are disentangled. Specifically, our IDEL reduces the dependency between style and content embeddings by minimizing a sample-based mutual information upper bound. Furthermore, the mutual information between latent embeddings and the input data is also maximized to ensure the representativeness of the latent embeddings (i.e., style and content embeddings). The contributions of this paper are summarized as follows:
- A principled framework is introduced to learn disentangled representations of natural language. By minimizing a novel VI-based DRL objective, our model not only explicitly reduces the correlation between style and content embeddings, but also simultaneously preserves the sentence information in the latent spaces.
- A general sample-based mutual information upper bound is derived to facilitate the minimization of our VI-based objective. With this new upper bound, the dependency of style and content embeddings can be decreased effectively and stably.
- The proposed model is evaluated empirically relative to other disentangled representation learning methods. Our model exhibits competitive results in several real-world applications.
2.1 Mutual Information Variational Bounds
Mutual information (MI) is a key concept in information theory, for measuring the dependence between two random variables. Given two random variables  $x$  and  $y$ , their MI is defined as
$$
\operatorname {I} (\boldsymbol {x}; \boldsymbol {y}) = \mathbb {E} _ {p (\boldsymbol {x}, \boldsymbol {y})} [ \log \frac {p (\boldsymbol {x} , \boldsymbol {y})}{p (\boldsymbol {x}) p (\boldsymbol {y})} ], \tag {1}
$$
where  $p(\boldsymbol{x}, \boldsymbol{y})$  is the joint distribution of the random variables, with  $p(\boldsymbol{x})$  and  $p(\boldsymbol{y})$  representing the respective marginal distributions.
In disentangled representation learning, a common goal is to minimize the MI between different types of embeddings (Poole et al., 2019). However, the exact MI value is difficult to calculate in practice, because in most cases the integral in Eq. (1) is
Figure 1: The green and purple circles represent the entropy of  $\pmb{x}$  and  $\pmb{y}$ , respectively. The intersection (blue region) is the mutual information between  $\pmb{x}$  and  $\pmb{y}$ . The symmetric difference of the two circles (green and purple regions) is  $\mathrm{VI}(\pmb{x};\pmb{y})$ .
intractable. To address this problem, various MI estimation methods have been introduced (Chen et al., 2016; Belghazi et al., 2018; Poole et al., 2019). One of the commonly used estimation approaches is the Barber-Agakov lower bound (Barber and Agakov, 2003). By introducing a variational distribution  $q(\pmb{x}|\pmb{y})$ , one may derive
$$
\mathrm {I} (\boldsymbol {x}; \boldsymbol {y}) \geq \mathrm {H} (\boldsymbol {x}) + \mathbb {E} _ {p (\boldsymbol {x}, \boldsymbol {y})} [ \log q (\boldsymbol {x} | \boldsymbol {y}) ], \tag {2}
$$
where  $\mathbf{H}(\pmb {x}) = \mathbb{E}_{p(\pmb {x})}[-\log p(\pmb {x})]$  is the entropy of variable  $\pmb{x}$ .
2.2 Variation of Information
In information theory, Variation of Information (VI, also called Shared Information Distance) is a measure of independence between two random variables. The mathematical definition of VI between random variables  $\mathbf{x}$  and  $\mathbf{y}$  is
$$
\operatorname {V I} (\boldsymbol {x}; \boldsymbol {y}) = \mathrm {H} (\boldsymbol {x}) + \mathrm {H} (\boldsymbol {y}) - 2 \mathrm {I} (\boldsymbol {x}; \boldsymbol {y}), \tag {3}
$$
where  $\mathrm{H}(\pmb {x})$  and  $\mathrm{H}(\pmb {y})$  are entropies of  $\pmb{x}$  and  $\pmb{y}$ , respectively (shown in Figure 1). Kraskov et al. (2005) show that VI is a well-defined metric, which satisfies the triangle inequality:
$$
\operatorname {V I} (\boldsymbol {y}; \boldsymbol {x}) + \operatorname {V I} (\boldsymbol {x}; \boldsymbol {z}) \geq \operatorname {V I} (\boldsymbol {y}; \boldsymbol {z}), \tag {4}
$$
for any random variables  $\pmb{x}$ ,  $\pmb{y}$  and  $\pmb{z}$ . Additionally,  $\mathrm{VI}(\pmb{x};\pmb{y}) = 0$  indicates  $\pmb{x}$  and  $\pmb{y}$  are the same variable (Meilä, 2007). From Eq. (3), the VI distance has a close relation to mutual information: if the mutual information is a measure of "dependence" between two variables, then the VI distance is a measure of "independence" between them.
Consider data  $\{(x_i, y_i)\}_{i=1}^N$ , where each  $x_i$  is a sentence drawn from a distribution  $p(x)$ , and  $y_i$
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is the label indicating the style of  $\pmb{x}_i$ . The goal is to encode each sentence  $\pmb{x}_i$  into its corresponding style embedding  $\pmb{s}_i$  and content embedding  $\pmb{c}_i$  with an encoder  $q_{\theta}(\pmb{s}, \pmb{c}|\pmb{x})$ :
$$
\boldsymbol {s} _ {i}, \boldsymbol {c} _ {i} | \boldsymbol {x} _ {i} \sim q _ {\theta} (\boldsymbol {s}, \boldsymbol {c} | \boldsymbol {x} _ {i}). \tag {5}
$$
The collection of style embeddings  $\{s_i\}_{i = 1}^N$  can be regarded as samples drawn from a variable  $s$  in the style embedding space, while the collection of content embeddings  $\{c_{i}\}_{i = 1}^{N}$  are samples from a variable  $c$  in the content embedding space. In practice, the dimension of the content embedding is typically higher than that of the style embedding, considering that the content usually contains more information than the style (John et al., 2019).
We first give an intuitive introduction to our proposed VI-based objective, then in Section 3.1 we provide the theoretical justification for it. To disentangle the style and content embedding, we try to minimize the mutual information  $\mathrm{I}(s; c)$  between  $s$  and  $c$ . Meanwhile, we maximize  $\mathrm{I}(c; x)$  to ensure that the content embedding  $s$  sufficiently encapsulates information from the sentence  $x$ . The embedding  $s$  is expected to contain rich style information. Therefore, the mutual information  $\mathrm{I}(s; y)$  should be maximized. Thus, our overall disentangled representation learning objective is:  $\mathcal{L}_{\mathrm{Dis}} = \mathrm{I}(s; c) - \mathrm{I}(c; x) - \mathrm{I}(s; y)$ .
3.1 Theoretical Justification of the Objective
The objective  $\mathcal{L}_{\mathrm{Dis}}$  has a strong connection with the independence measurement in information theory. As described in Section 2.2, Variation of Information (VI) is a well-defined metric of independence between variables. Applying the triangle inequality from Eq. (4) to  $s$ ,  $c$  and  $x$ , we have  $\operatorname{VI}(s; x) + \operatorname{VI}(x; c) \geq \operatorname{VI}(s; c)$ . Equality occurs if and only if the information from variable  $x$  is totally separated into two independent variable  $s$  and  $c$ , which is an ideal scenario for disentangling sentence  $x$  into its corresponding style embedding  $s$  and content embedding  $c$ .
Therefore, the difference between  $\mathrm{VI}(s;x) + \mathrm{VI}(x;c)$  and  $\mathrm{VI}(s;c)$  represents the degree of disentanglement. Hence we introduce a measurement:
$$
D (\boldsymbol {x}; \boldsymbol {s}, \boldsymbol {c}) = \operatorname {V I} (\boldsymbol {s}; \boldsymbol {x}) + \operatorname {V I} (\boldsymbol {x}; \boldsymbol {c}) - \operatorname {V I} (\boldsymbol {c}; \boldsymbol {s}).
$$
From Eq. (4), we know that  $\mathbf{D}(\pmb{x};\pmb{y},\pmb{z})$  is always non-negative. By the definition of VI in Eq. (3),  $D(\pmb{x};\pmb{s},\pmb{c})$  can be simplified as:
$$
\begin{array}{l} \operatorname {V I} (\boldsymbol {c}; \boldsymbol {x}) + \operatorname {V I} (\boldsymbol {x}; \boldsymbol {s}) - \operatorname {V I} (\boldsymbol {s}; \boldsymbol {c}) \\ = 2 \mathrm {H} (\boldsymbol {x}) + 2 [ \mathrm {I} (\boldsymbol {s}; \boldsymbol {c}) - \mathrm {I} (\boldsymbol {x}; \boldsymbol {c}) - \mathrm {I} (\boldsymbol {x}; \boldsymbol {s}) ]. \\ \end{array}
$$
Since  $\mathrm{H}(\pmb {x})$  is a constant associated with the data, we only need to focus on  $\operatorname {I}(s;c) - \operatorname {I}(x;c) - \operatorname {I}(x;s)$
The measurement  $D(\pmb{x}; \pmb{s}, \pmb{c})$  is symmetric to style  $s$  and content  $c$ , giving rise to the problem that without any inductive bias in supervision, the disentangled representation could be meaningless (as observed by Locatello et al. (2019)). Therefore, we add inductive biases by utilizing the style label  $y$  as supervised information for style embedding  $s$ . Noting that  $s \rightarrow x \rightarrow y$  is a Markov Chain, we have  $\mathrm{I}(s; x) \geq \mathrm{I}(s; y)$  based on the MI data-processing inequality (Cover and Thomas, 2012). Then we convert the minimization of  $\mathrm{I}(s; c) - \mathrm{I}(x; c) - \mathrm{I}(x; s)$  into the minimization of the upper bound  $\mathrm{I}(s; c) - \mathrm{I}(x; c) - \mathrm{I}(y; s)$ , which further leads to our objective  $\mathcal{L}_{\mathrm{Dis}}$ .
However, minimizing the exact value of mutual information in the objective  $\mathcal{L}_{\mathrm{Dis}}$  causes numerical instabilities, especially when the dimension of the latent embeddings is large (Chen et al., 2016). Therefore, we provide several MI estimations to the objective terms  $\operatorname {I}(s;c)$ $\operatorname {I}(\pmb {x};\pmb {c})$  and  $\operatorname {I}(s;y)$  in the following two sections.
3.2 MI Variational Lower Bound
To maximize  $\operatorname {I}(\pmb {x};\pmb {c})$  and  $\mathrm{I}(s;y)$  , we derive two variational lower bounds. For  $\mathrm{I}(\pmb {x};\pmb {c})$  , we introduce a variational decoder  $q_{\phi}(\pmb {x}|\pmb {c})$  to reconstruct the sentence  $\pmb{x}$  by the content embedding  $\pmb{c}$  . Leveraging the MI variational lower bound from Eq. (2), we have  $\mathrm{I}(\pmb {x};\pmb {c})\geq \mathrm{H}(\pmb {x}) + \mathbb{E}_{p(\pmb {x};\pmb {c})}[\log q_{\phi}(\pmb {x}|\pmb {c})]$  Similarly, for  $\mathrm{I}(s;y)$  , another variational lower bound can be obtained as:  $\mathrm{I}(s;y)\geq \mathrm{H}(y) +$ $\mathbb{E}_{p(y,s)}[\log q_{\psi}(y|s)]$  , where  $q_{\psi}(y|s)$  is a classifier mapping the style embedding  $\pmb{s}$  to its corresponding style label  $y$  . Based on these two lower bounds,  $\mathcal{L}_{\mathrm{Dis}}$  has an upper bound:
$$
\begin{array}{l} \mathcal {L} _ {\mathrm {D i s}} \leq \mathrm {I} (\boldsymbol {s}; \boldsymbol {c}) - [ \mathrm {H} (\boldsymbol {x}) + \mathbb {E} _ {p (\boldsymbol {x}, \boldsymbol {c})} [ \log q _ {\phi} (\boldsymbol {x} | \boldsymbol {c}) ] ] \\ - \left[ \mathrm {H} (y) + \mathbb {E} _ {p (y, s)} [ \log q _ {\psi} (y | s) ] \right]. \tag {6} \\ \end{array}
$$
Noting that both  $\mathrm{H}(\pmb {x})$  and  $\mathrm{H}(y)$  are constants from the data, we only need to minimize:
$$
\begin{array}{l} \bar {\mathcal {L}} _ {\mathrm {D i s}} = \operatorname {I} (\boldsymbol {s}; \boldsymbol {c}) - \mathbb {E} _ {p (\boldsymbol {x}, \boldsymbol {c})} [ \log q _ {\phi} (\boldsymbol {x} | \boldsymbol {c}) ] \\ - \mathbb {E} _ {p (y, s)} [ \log q _ {\psi} (y | s) ]. \qquad (7) \\ \end{array}
$$
As an intuitive explanation of  $\bar{\mathcal{L}}_{\mathrm{Dis}}$ , the style embedding  $s$  and content embedding  $c$  are expected to be independent by minimizing mutual information  $\operatorname{I}(s; c)$ , while they also need to be representative: the style embedding  $s$  is encouraged to give
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a better prediction of style label  $y$  by maximizing  $\mathbb{E}_{p(y,s)}[\log q_{\psi}(y|s)]$ ; the content embedding should maximize the log-likelihood  $\mathbb{E}_{p(\boldsymbol{x},\boldsymbol{c})}[\log q_{\phi}(\boldsymbol{x}|\boldsymbol{c})]$  to contain sufficient information from sentence  $\boldsymbol{x}$ .
3.3 MI Sample-based Upper Bound
To estimate  $\mathrm{I}(\pmb {s};\pmb {c})$  , we propose a novel samplebased upper bound. Assume we have  $M$  latent embedding pairs  $\{(s_j,c_j)\}_{j = 1}^M$  drawn from  $p(s,c)$  As shown in Theorem 3.1, we derive an upper bound of mutual information based on the samples. A detailed proof is provided in the Supplementary Material.
Theorem 3.1. If  $\{(s_j, c_j)\}_{j=1}^M \sim p(s, c)$ , then
$$
\operatorname {I} (\boldsymbol {s}; \boldsymbol {c}) \leq \mathbb {E} \left[ \frac {1}{M} \sum_ {j = 1} ^ {M} R _ {j} \right] =: \hat {\mathrm {I}} (\boldsymbol {s}; \boldsymbol {c}), \tag {8}
$$
where  $R_{j} = \log p(\pmb{s}_{j}|\pmb{c}_{j}) - \frac{1}{M}\sum_{k = 1}^{M}\log p(\pmb{s}_{j}|\pmb{c}_{k})$
Based on Theorem 3.1, given embedding samples  $\{s_j,c_j\}_{j = 1}^M$  , we can minimize  $\frac{1}{M}\sum_{j = 1}^{M}R_{j}$  as an unbiased estimation of the upper bound  $\hat{\mathbf{I}} (s;c)$  The calculation of  $R_{j}$  requires the conditional distribution  $p(s|c)$  , whose closed form is unknown. Therefore, we use a variational network  $p_{\sigma}(s|c)$  to approximate  $p(s|c)$  with embedding samples.
To implement the upper bound in Eq. (8), we first feed  $M$  sentences  $\{\pmb{x}_j\}$  into encoder  $q_{\theta}(\pmb{s},\pmb{c}|\pmb{x})$  to obtain embedding pairs  $\{(s_j,c_j)\}$ . Then, we train the variational distribution  $p_{\sigma}(\pmb{c}|\pmb{x})$  by maximizing the log-likelihood  $\mathcal{L}(\sigma) = \frac{1}{M}\sum_{j=1}^{M}\log p_{\sigma}(s_j|c_j)$ . After the training of  $p_{\sigma}(\pmb{s}|\pmb{c})$  is finished, we calculate  $R_j$  for each embedding pair  $(s_j,c_j)$ . Finally, the gradient for  $\frac{1}{M}\sum_{j=1}^{M}R_j$  is calculated and backpropagated to encoder  $q_{\theta}(\pmb{s},\pmb{c}|\pmb{x})$ . We apply the reparameterization trick (Kingma and Welling, 2013) to ensure the gradient back-propagates through the sampled embeddings  $(s_j,c_j)$ . When the encoder weights are updated, the distribution  $q_{\theta}(\pmb{s},\pmb{c}|\pmb{x})$
changes, which leads to the changing of conditional distribution  $p(s|c)$ . Therefore, we need to update the approximation network  $p_{\sigma}(s|c)$  again. Consequently, the encoder network  $q_{\theta}(s,c|x)$  and the approximation network  $p_{\sigma}(s|c)$  are updated alternately during training.
In each training step, the above algorithm requires  $M$  pairs of embedding samples  $\{s_j, c_j\}_{j=1}^M$  and the calculation of all conditional distributions  $p_{\sigma}(s_j | c_k)$ . This leads to  $\mathcal{O}(M^2)$  computational complexity. To accelerate the training, we further approximate term  $\frac{1}{M} \sum_{k=1}^{M} \log p(s_j | c_k)$  in  $R_j$  by  $\log p(s_j | c_{k'})$ , where  $k'$  is selected uniformly from indices  $\{1, 2, \dots, M\}$ . This stochastic sampling not only leads to an unbiased estimation  $\hat{R}_j$  to  $R_j$ , but also improves the model robustness (as shown in Algorithm 1).
Symmetrically, we can also derive an MI upper bound based on the conditional distribution  $p(c|s)$ . However, the dimension of  $c$  is much higher than the dimension of  $s$ , which indicates that the neural approximation to  $p(c|s)$  would have worse performance compared with the approximation to  $p(s|c)$ . Alternatively, the lower-dimensional distribution  $p(s|c)$  used in our model is relatively easy to approximate with neural networks.
3.4 Encoder-Decoder Framework
One important downstream task for disentangled representation learning (DRL) is conditional generation. Our MI-based text DRL method can be also embedded into an Encoder-Decoder generative model and trained end-to-end.
Since the proposed DRL encoder  $q_{\theta}(s, c|x)$  is a stochastic neural network, a natural extension is to add a decoder to build a variational autoencoder (VAE) (Kingma and Welling, 2013). Therefore, we introduce another decoder network  $p_{\gamma}(x|s, c)$  that generates a new sentence based on the given style  $s$  and content  $c$ . A prior distribution  $p(s, c) = p(s)p(c)$ , as the product of two multivariate unit-variance Gaussians, is used to regularize the posterior distribution  $q_{\theta}(s, c|x)$  by KL-divergence minimization. Meanwhile, the log-likelihood term for text reconstruction should be maximized. The objective for VAE is:
$$
\begin{array}{l} \mathcal {L} _ {\mathrm {V A E}} = \mathrm {K L} \left(q _ {\theta} (\boldsymbol {s}, \boldsymbol {c} | \boldsymbol {x}) \| p (\boldsymbol {s}, \boldsymbol {c})\right) \\ - \mathbb {E} _ {q _ {\theta} (\pmb {s}, \pmb {c} | \pmb {x})} [ \log p _ {\gamma} (\pmb {x} | \pmb {s}, \pmb {c}) ]. \\ \end{array}
$$
We combine the VAE objective and our MI-based disentanglement term to form an end-to-end learning framework (as shown in Figure 2). The total
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Figure 2: Proposed framework: Each sentence  $\pmb{x}$  is encoded into style embedding  $s$  and content embedding  $c$ . The style embedding  $s$  goes through a classifier  $q_{\psi}(y|s)$  to predict the style label  $y$ ; the content embedding  $c$  is used to reconstruct  $x$ . An auxiliary network  $p_{\sigma}(s|c)$  helps disentangle the style and content embeddings. The decoder  $p_{\gamma}(x|s,c)$  generates sentences based on the combination of  $s$  and  $c$ .
loss function is  $\mathcal{L}_{\mathrm{total}} = \beta \mathcal{L}_{\mathrm{Dis}}^{*} + \mathcal{L}_{\mathrm{VAE}}$  where  $\mathcal{L}_{\mathrm{Dis}}^{*}$  replaces  $\operatorname {I}(s;c)$  in  $\bar{\mathcal{L}}_{\mathrm{Dis}}$  (Eq. (7)) with our MI upper bound  $\hat{\mathbf{l}} (s;c)$  from Eq. (8);  $\beta >0$  is a hyperparameter re-weighting DRL and VAE terms. We call this final framework Information-theoretic Disentangled text Embedding Learning (IDEL).
4.1 Disentangled Representation Learning
Disentangled representation learning (DRL) can be classified into two categories: unsupervised disentangling and supervised disentangling. Unsupervised disentangling methods focus on adding constraints on the embedding space to enforce that each dimension of the space be as independent as possible (Burgess et al., 2018; Chen et al., 2018). However, Locatello et al. (2019) challenge the effectiveness of unsupervised disentangling without any induced bias from data or supervision. For supervised disentangling, supervision is always provided on different parts of disentangled representations. However, for text representation learning, supervised information can typically be provided only for the style embeddings (e.g. sentiment or personality labels), making the task much more challenging. John et al. (2019) tried to alleviate this issue by manually removing sentiment-related words from a sentence. In contrast, our model is trained in an end-to-end manner without manually adding any supervision on the content embeddings.
4.2 Mutual Information Estimation
Mutual information (MI) is a fundamental measurement of the dependence between two random variables. MI has been applied to a wide range of tasks in machine learning, including generative modeling (Chen et al., 2016), the information bottleneck (Tishby et al., 2000), and domain adaptation (Gholami et al., 2020). In our proposed method, we utilize MI to measure the dependence between content and style embedding. By minimizing the MI, the learned content and style representations are explicitly disentangled.
However, the exact value of MI is hard to calculate, especially for high-dimensional embedding vectors (Poole et al., 2019). To approximate MI, most previous work focuses on lower-bound estimations (Chen et al., 2016; Belghazi et al., 2018; Poole et al., 2019), which are not applicable to MI minimization tasks. Poole et al. (2019) propose a leave-one-out upper bound of MI; however it is not numerically stable in practice. Inspired by these observations, we introduce a novel MI upper bound for disentangled representation learning, which stably minimizes the correlation between content and style embedding in a principled manner.
We conduct experiments to evaluate our models on the following real-world datasets:
Yelp Reviews: The Yelp dataset contains online service reviews with associated rating scores. We follow the pre-processing from Shen et al. (2017) for a fair comparison. The resulting dataset includes 250,000 positive review sentences and 350,000 negative review sentences.