Title: VARIATIONAL HETERO-ENCODER RANDOMIZED GANS FOR JOINT IMAGE-TEXT MODELING

Abstract: For bidirectional joint image-text modeling, we develop variational hetero-encoder (VHE) randomized generative adversarial network (GAN), a versatile deep generative model that integrates a probabilistic text decoder, probabilistic image encoder, and GAN into a coherent end-to-end multi-modality learning framework. VHE randomized GAN (VHE-GAN) encodes an image to decode its associated text, and feeds the variational posterior as the source of randomness into the GAN image generator. We plug three off-the-shelf modules, including a deep topic model, a ladder-structured image encoder, and StackGAN++, into VHE-GAN, which already achieves competitive performance. This further motivates the development of VHE-raster-scan-GAN that generates photo-realistic images in not only a multiscale low-to-high-resolution manner, but also a hierarchical-semantic coarse-to-fine fashion. By capturing and relating hierarchical semantic and visual concepts with end-to-end training, VHE-raster-scan-GAN achieves state-of-the-art performance in a wide variety of image-text multi-modality learning and generation tasks.

1. INTRODUCTION:

Images and texts commonly occur together in the real world. There exists a wide variety of deep neural network based unidirectional methods that model images (texts) given texts (images) (Gomez et al., 2017; Kiros & Szepesvari, 2012; Reed et al., 2016; Xu et al., 2018; Zhang et al., 2017a) . There also exist probabilistic graphic model based bidirectional methods (Srivastava & Salakhutdinov, 2012b; a; Wang et al., 2018) that capture the joint distribution of images and texts. These bidirectional methods, however, often make restrictive parametric assumptions that limit their image generation ability. Exploiting recent progress on deep probabilistic models and variational inference (Kingma & Welling, 2014; Zhou et al., 2016; Zhang et al., 2018a; Goodfellow et al., 2014; Zhang et al., 2017b) , we propose an end-to-end learning framework to construct multi-modality deep generative models that can not only generate vivid image-text pairs, but also achieve state-of-the-art results on various unidirectional tasks (Srivastava & Salakhutdinov, 2012b; a; Wang et al., 2018; Gomez et al., 2017; Xu et al., 2018; Zhang et al., 2017a; b; Verma et al., 2018; Zhang et al., 2018b) , such as generating photo-realistic images given texts and performing text-based zero-shot learning.

To extract and relate semantic and visual concepts, we first introduce variational hetero-encoder (VHE) that encodes an image to decode its textual description (e.g., tags, sentences, binary attributes, and long documents), where the probabilistic encoder and decoder are jointly optimized using variational inference (Blei et al., 2017; Hoffman et al., 2013; Kingma & Welling, 2014; Rezende et al., 2014) . The latent representation of VHE can be sampled from either the variational posterior provided by the image encoder given an image input, or the posterior of the text decoder via MCMC given a text input. VHE by construction has the ability to generate texts given images. To further enhance its text generation performance and allow synthesizing photo-realistic images given an image, text, or random noise, we feed the variational posterior of VHE in lieu of random noise as the source of randomness into the image generator of a generative adversarial network (GAN) (Goodfellow et al., 2014) . We refer to this new modeling framework as VHE randomized GAN (VHE-GAN).

Off-the-shelf text decoders, image encoders, and GANs can be directly plugged into the VHE-GAN framework for end-to-end multi-modality learning. To begin with, as shown in Figs. 1(a ) and 1(b), we construct VHE-StackGAN++ by using the Poisson gamma belief network (PGBN) (Zhou et al., 2016) as the VHE text decoder, using the Weibull upward-downward variational encoder (Zhang et al., 2018a) as the VHE image encoder, and feeding the concatenation of the multi-stochastic-layer latent representation of the VHE as the source of randomness into the image generator of StackGAN++ (Zhang et al., 2017b) . While VHE-StackGAN++ already achieves very attractive performance, we find that its performance can be clearly boosted by better exploiting the multi-stochastic-layer semantically meaningful hierarchical latent structure of the PGBN text decoder. To this end, as shown in Figs. 1(a ) and 1(c), we develop VHE-raster-scan-GAN to perform image generation in not only a multi-scale low-to-high-resolution manner in each layer, as done by StackGAN++, but also a hierarchical-semantic coarse-to-fine fashion across layers, a unique feature distinguishing it from existing methods. Consequently, not only can VHE-raster-scan-GAN generate vivid high-resolution images with better details, but also build interpretable hierarchical semantic-visual relationships between the generated images and texts.

Our main contributions include: 1) VHE-GAN that provides a plug-and-play framework to integrate off-the-shelf probabilistic decoders, variational encoders, and GANs for end-to-end bidirectional multi-modality learning; the shared latent space can be inferred either by image encoder q(z | x), if given images, or by Gibbs sampling from the conditional posterior of text decoder p(t | z), if given texts; 2) VHE-raster-scan-GAN that captures and relates hierarchical semantic and visual concepts to achieve state-of-the-art results in various unidirectional and bidirectional image-text modeling tasks.

2. VARIATIONAL HETERO-ENCODER RANDOMIZED GANS:

VAEs and GANs are two distinct types of deep generative models. Consisting of a generator (decoder) p(x | z), a prior p(z), and an inference network (encoder) q(z | x) that is used to approximate the posterior p(z | x), VAEs (Kingma & Welling, 2014; Rezende et al., 2014) are optimized by maximizing the evidence lower bound (ELBO) as

EQUATION

where p data (x) = N i=1

1 N δ xi represents the empirical data distribution. Distinct from VAEs that make parametric assumptions on data distribution and perform posterior inference, GANs in general use implicit data distribution and do not provide meaningful latent representations (Goodfellow et al., 2014) ; they learn both a generator G and a discriminator D by optimizing a mini-max objective as

EQUATION

where p(z) is a random noise distribution that acts as the source of randomness for data generation.

2.1. VHE-GAN OBJECTIVE FUNCTION FOR END-TO-END MULTI-MODALITY LEARNING:

Below we show how to construct VHE-GAN to jointly model images x and their associated texts t, capturing and relating hierarchical semantic and visual concepts. First, we modify the usual VAE into VHE, optimizing a lower bound of the text log-marginal-likelihood E t∼pdata(t) [ln p(t) ] as

EQUATION

where

p(t | z) is the text decoder, p(z) is the prior, p(t) = E z∼p(z) [p(t | z)], and L vhe (t, x) ≤ ln E z∼q(z | x) [ p(t | z)p(z) q(z | x) ] = ln p(t).

Second, the image encoder q(z | x), which encodes image x into its latent representation z, is used to approximate the posterior p(z | t) = p(t | z)p(z)/p(t). Third, variational posterior q(z | x) in lieu of random noise p(z) is fed as the source of randomness into the GAN image generator. Combing these three steps, with the parameters of the image encoder

EQUATION

:

(1) 1 

x 16  x 8  x 4  x x D D D D D (1)  (2)  (3)  t (1) g (2) g (3) g ( ) f x (3)  (2)  (1)  (c) (1)  (2)  h (3)  s  x D (d) (1)  (1) 1 h (2)  (2) 1 h (3)  (3) 1 h (3) 1 s (2) 1 s (1) 1 s 4  x 2  x x D D D (e)

D E pdata(t,x) [L(t, x)], L(t, x) := ln D(x) + KL [q(z | x)||p(z)] + E z∼q(z | x) ln(1 -D(G gan (z))) -ln p(t | z) . (4)

Note the objective function in (4) implies a data-triple-reuse training strategy, which uses the same data mini-batch in each stochastic gradient update iteration to jointly train the VHE, GAN discriminator, and GAN generator; see a related objective function, shown in (10) of Appendix A, that is resulted from naively combining the VHE and GAN training objectives. In VHE-GAN, the optimization of the encoder parameter E is related to not only the VHE's ELBO, but also the GAN mini-max objective function, forcing the variational posterior q(z | x) to serve as a bridge between VHE and GAN, allowing them to help each other. Although there are some models (Mescheder et al., 2017; Makhzani et al., 2015; Tolstikhin et al., 2018; Dumoulin et al., 2017; Donahue et al., 2017; Che et al., 2017; Srivastava et al., 2017; Grover et al., 2018; Larsen et al., 2016; Huang et al., 2018) combining VAEs and GANs in various ways, they focus on single-modality tasks while the VHE-GAN on two different modalities. In Appendix A, we analyze the properties of the VHE-GAN objective function and discuss related works. Below we develop two different VHE-GANs, one integrates off-the-shelf modules, while the other introduces new interpretable hierarchical latent structure.

2.2. VHE-STACKGAN++ WITH OFF-THE-SHELF MODULES:

As shown in Figs. 1(a ) and 1(b), we first construct VHE-StackGAN++ by plugging into VHE-GAN three off-the-shelf modules, including a deep topic model (Zhou et al., 2016) , a ladder-structured encoder (Zhang et al., 2018a), and StackGAN++ (Zhang et al., 2017b) . For text analysis, both sequence models and topic models are widely used. Sequence models (Bengio et al., 2003) often represent each document as a sequence of word embedding vectors, capturing local dependency structures with some type of recurrent neural networks (RNNs), such as long short-term memory (LSTM) (Hochreiter & Schmidhuber, 1997) . Topic models such as latent Dirichlet allocation (LDA) (Blei et al., 2003) often represent each document as a bag of words (BoW), capturing global word cooccurrence patterns into latent topics. Suitable for capturing local dependency structure, existing sequence models often have difficulty in capturing long-range word dependencies and hence macrolevel information, such as global word cooccurrence patterns (i.e., topics), especially for long documents. By contrast, while topic models ignore word order, they are very effective in capturing latent topics, which are often directly related to macro-level visual information (Gomez et al., 2017; Dieng et al., 2017; Lau et al., 2017) . Moreover, topic models can be applied to not only sequential texts, such as few sentences (Wang et al., 2009; Jin et al., 2015) and long documents (Zhou et al., 2016) , but also non-sequential ones, such as textual tags (Srivastava & Salakhutdinov, 2012a; 2014; Wang et al., 2018) and binary attributes (Elhoseiny et al., 2017b; Zhu et al., 2018) . For this reason, for the VHE text decoder, we choose PGBN (Zhou et al., 2016) , a state-of-the-art topic model that can also be represented as a multi-stochastic-layer deep generalization of LDA (Cong et al., 2017) . We complete VHE-StackGAN++ by choosing the Weibull upward-downward variational encoder (Zhang et al., 2018a) as the VHE image encoder, and feeding the concatenation of all the hidden layers of PGBN as the source of randomness to the image generator of StackGAN++ (Zhang et al., 2017b) .

As in Fig. 1 , we use a VHE that encodes an image into a deterministic-upward-stochastic-downward ladder-structured latent representation, which is used to decode the corresponding text. Specifically, we represent each document as a BoW high-dimensional sparse count vector t n ∈ Z K0 , where Z = {0, 1, • • • } and K 0 is the vocabulary size. For the VHE text decoder, we choose to use PGBN to extract hierarchical latent representation from t n . PGBN consists of multiple gamma distributed stochastic hidden layers, generalizing the "shallow" Poisson factor analysis (Zhou et al., 2012; Zhou & Carin, 2015) into a deep setting. PGBN with L hidden layers, from top to bottom, is expressed as

EQUATION

where the hidden units θ (l) n ∈ R K l + of layer l are factorized under the gamma likelihood into the product of topics

Φ (l) ∈ R K l-1 ×K l +

and hidden units of the next layer, R + = {x, x ≥ 0}, s (l) n > 0, and K l is the number of topics of layer l. If the texts are represented as binary attribute vectors b n , we can add a Bernoulli-Poisson link layer as b n = 1(t n ≥ 1) (Zhou, 2015; Zhou et al., 2016) . We place a Dirichlet prior on each column of Φ (l) . The topics can be organized into a directed acyclic graph (DAG), whose node k at layer l can be visualized with the top words of

l-1 t=1 Φ (t) φ (l)

k ; the topics tend to be very general in the top layer and become increasingly more specific when moving downwards. This semantically meaningful latent hierarchy provides unique opportunities to build a better image generator by coupling the semantic hierarchical structures with visual ones.

Let us denote Φ = {Φ (1) , . . . , Φ (L) , r} as the set of global parameters of PGBN shown in (5). Given Φ, we adopt the inference in Zhang et al. (2018a) to build an Weibull upward-downward variational image encoder as

N n=1 L l=1 q(θ (l) n | x n , Φ (l+1) , θ (l+1) n

), where Φ (L+1) := r, θ (L+1) n := ∅, and

EQUATION

The Weibull distribution is used to approximate the gamma distributed conditional posterior, and its parameters k (l) n , λ (l) n ∈ R K l are deterministically transformed from the convolutional neural network (CNN) image features f (x n ) (Szegedy et al., 2016) , as shown in Fig. 1 (a) and described in Appendix D.1. We denote Ω as the set of encoder parameters. We refer to Zhang et al. (2018a) for more details about this deterministic-upward-stochastic-downward ladder-structured inference network, which is distinct from a usual inference network that has a pure bottom-up structure and only interacts with the generative model via the ELBO (Kingma & Welling, 2014; Gulrajani et al., 2017) .

The multi-stochastic-layer latent representation z = {θ (l) } L l=1 is the bridge between two modalities. As shown in Fig. 1 (b), VHE-StackGAN++ simply randomizes the image generator of StackGAN++ (Zhang et al., 2017b) with the concatenated vector θ = θ (1) , • • • , θ (L) . We provide the overall objective function in (15) of Appendix D.2. Note that existing neural-network-based models (Gomez et al., 2017; Xu et al., 2018; Zhang et al., 2017a; b; Verma et al., 2018; Zhang et al., 2018b) are often able to perform unidirectional but not bidirectional transforms between images x and texts t. However, bidirectional transforms are straightforward for the proposed model, as z can be either drawn from the image encoder q(z | x) in (6), or drawn with an upward-downward Gibbs sampler (Zhou et al., 2016) from the conditional posteriors p(z | t) of the PGBN text decoder p(t | z) in (5).

2.3. VHE-RASTER-SCAN-GAN WITH A HIERARCHICAL-SEMANTIC MULTI-RESOLUTION IMAGE GENERATOR:

While we find that VHE-StackGAN++ has already achieved impressive results, its simple concatenation of θ (l) does not fully exploit the semantically-meaningful hierarchical latent representation of the PGBN-based text decoder. For three DAG subnets inferred from three different datasets, as shown in Figs. 21 -23 of Appendix C.7, the higher-layer PGBN topics match general visual concepts, such as those on shapes, colors, and backgrounds, while the lower-layer ones provide finer details. This motivates us to develop an image generator to exploit the semantic structure, which matches coarse-to-fine visual concepts, to gradually refine its generation. To this end, as shown in Fig. 1 (c), we develop "raster-scan" GAN that performs generation not only in a multi-scale low-to-high-resolution manner in each layer, but also a hierarchical-semantic coarse-to-fine fashion across layers.

Suppose we are building a three-layer raster-scan GAN to generate an image of size 256 2 . We randomly select an image x n and then sample {θ (l) n } 3 l=1 from the variational posterior semantic information, is transformed to hidden features h

(3) i for the i th branch:

EQUATION

where

EQUATION

2 , and s

(3) 3 are of 16 2 , 32 2 , and 64 2 , respectively. Third, s

(3) 3 is down-sampled to ŝ(3) 3 of size 32 2 and combined with the information from θ (2) to provide the hidden features at layer two:

EQUATION

where C denotes concatenation along the channel. Fourth, the generators synthesize image samples {s

EQUATION

2 , and s

(2)

3 are of 32 2 , 64 2 , and 128 2 , respectively. The same process is then replicated at layer one to generate {s

EQUATION

2 , and s

(1) 3

are of size 64 2 , 128 2 , and 256 2 , respectively, and s

(1)

3 becomes a desired high-resolution synthesized image with fine details. The detailed structure of raster-scan-GAN is described in Fig. 26 of Appendix D.3. PyTorch code is provided to aid the understanding and help reproduce the results.

Different from many existing methods (Gomez et al., 2017; Reed et al., 2016; Xu et al., 2018; Zhang et al., 2017b) whose textual feature extraction is separated from the end task, VHE-raster-scan-GAN performs joint optimization. As detailedly described in the Algorithm in Appendix E, at each minibatch based iteration, after updating Φ by the topic-layer-adaptive stochastic gradient Riemannian (TLASGR) MCMC of Cong et al. (2017) , a Weibull distribution based reparameterization gradient (Zhang et al., 2018a) is used to end-to-end optimize the following objective:

EQUATION

where {x

(l) n,i } 3,3 i=1,l=1 denote different resolutions of x n , corresponding to {s (l) n,i } 3,3 i=1,l=1 .

2.4 RELATED WORK ON JOINT IMAGE-TEXT LEARNING Gomez et al. (2017) develop a CNN to learn a transformation from images to textual features preextracted by LDA. GANs have been exploited to generate images given pre-learned textual features extracted by RNNs (Denton et al., 2015; Reed et al., 2016; Zhang et al., 2017a; Xu et al., 2018; Zhang et al., 2018b; Li et al., 2019) . All these works need a pre-trained linguistic model based on large-scale extra text data and the transformations between images and texts are only unidirectional. The recently proposed Obj-GAN (Li et al., 2019) needs even more side information such as the locations and labels of objects inside images, which could be difficult and costly to acquire in practice. On the other hand, probabilistic graphical model based methods (Srivastava & Salakhutdinov, 2012b; a; Wang et al., 2018) are proposed to learn a joint latent space for images and texts to realize bidirectional transformations, but their image generators are often limited to generating low-level image features. By contrast, VHE-raster-scan-GAN performs bidirectional end-to-end learning to capture and relate hierarchical visual and semantic concepts across multiple stochastic layers, capable of a wide variety of joint image-text learning and generation tasks, as described below.

3. EXPERIMENTAL RESULTS:

For joint image-text learning, following previous work, we evaluate the proposed VHE-StackGAN++ and VHE-raster-scan-GAN on three datasets: CUB (Wah et al., 2011) , Flower (Nilsback & Zisserman, 2008) , and COCO (Lin et al., 2014) , as described in Appendix F. Besides the usual text-to-image generation task, due to the distinct bidirectional inference capability of the proposed models, we can perform a rich set of additional tasks such as image-to-text, image-to-image, and noise-to-image-textpair generations. Due to space constraint, we present below some representative results, and defer additional ones to the Appendix. We provide the details of our experimental settings in Appendix F. PyTorch code is provided at https://github.com/BoChenGroup/VHE-GAN.

Table 1 : Inception score (IS, larger is better) and Frechet inception distance (FID, smaller is better) of StackGAN++ (Zhang et al., 2017b) , HDGAN (Zhang et al., 2018b) , AttGAN (Xu et al., 2018) , Obj-GAN (Li et al., 2019) , and the proposed VHE-raster-scan-GAN; the values labeled with * are calculated by the provided well-trained models and the others are quoted from the original publications; see Tab. 5 in Appendix C.1 for the error bars of IS. Note that while the FID of Obj-GAN is the lowest, it does not necessarily imply it produces high-quality images, as shown in Figs. 13 and 27; this is because FID only measures the similarity on the image feature space, but ignores the shapes of objects and diversity of generated images. More discussions can be found in Section 3.1 and Appendix G. A wooden desk topped with a laptop computer.

A very dark city street with cars and buildings.

AttnGAN Text-to-image generation: In Tab. 1, with inception score (IS) (Salimans et al., 2016) and Frechet inception distance (FID) (Heusel et al., 2017) , we compare our models with three state-of-the-art GANs in text-to-image generation. For visualization, we show in the top row of Fig. 2 different test textual descriptions and the real images associated with them, and in the other rows random images generated conditioning on these textual descriptions by different algorithms. Higher-resolution images are shown in Appendix C.2. We also provide example results on COCO, a much more challenging dataset, in Fig. 13 of Appendix C.3.

N/A

It is clear from Fig. 2 that although both StackGAN++ (Zhang et al., 2017b) and HDGAN (Zhang et al., 2018b) generate photo-realistic images nicely matched to the given texts, they often misrepresent or ignore some key textual information, such as "black crown" for the 2nd test text, "yellow pistil" for 5th, "yellow stamen" for 6th, and "computer" for 7th. These observations also apply to AttnGAN (Xu et al., 2018) . By contrast, both the proposed VHE-StackGAN++ and VHE-raster-scan-GAN do a better job in capturing and faithfully representing these key textual information into their generated images. Fig. 13 for COCO further shows the advantages of VHE-raster-scan-GAN in better representing the given textual information in its generated images. Note Obj-GAN, which learns a bounding box generator that restricts object locations, obtains the lowest FID on COCO. However, it appears that this type of restriction significantly improves FID at the expense of sacrificing the diversity of generated images given text, as shown in Fig. 27 of Appendix G. From the results in Fig. 13 , it also appears that Obj-GAN overly emphasizes correctly arranging the spatial locations of different visual features, which is important to achieve low FID, but does not do well in generating correct object shapes, which is important to visual effect. Besides, the training of Obj-GAN requires more side information including the locations and labels of objects in the images, which are often not provided in practice (e.g., neither CUB nor Flower comes with this type of side information). While the proposed VHE-GAN models do not need these additional side information, they could be further improved by following Obj-GAN to take them into consideration.

As discussed in Section 2.2, compared with sequence models, topic models can be applied to more diverse textual descriptions, including textual attributes and long documents. For illustration, we show in Figs. 3(a ) and 3(b) example images generated conditioning on a set of textual attributes and an encyclopedia document, respectively. These synthesized images are photo-realistic and their visual contents well match the semantics of the given texts. Trained on CelebA (Liu et al., 2015) , we provide in Fig. 9 examples of facial image generation given attributes; see Appendix B for details.

Ablation studies: We also consider several ablation studies for text-to-image generation, as shown in Tab. 2. First, we modify StackGAN++ (Zhang et al., 2017b) , using the text features extracted by PGBN to replace the original ones by RNN, referred to as PGBN+StackGAN++. It is clear that PGBN+StackGAN++ outperforms the original StackGAN++, but underperforms VHE-StackGAN++, which can be explained by that 1) the PGBN deep topic model is more effective in extracting macro-level textual information, such as key words, than RNNs; and 2) jointly end-to-end training the textual feature extractor and image encoder, discriminator, and generator helps better capture and relate the visual and semantical concepts. Second, note that VHE-StackGAN++ has the same structured image generator as both StackGAN++ and HDGAN do, but performs better than them. We attribute its performance gain to 1) its PGBN deep topic model helps better capture key semantic information from the textual descriptions; and 2) it performs end-to-end joint image-text learning via the VHE-GAN framework, rather than separating the extraction of textual features from text-toimage generation. Third, VHE-vanilla-GAN underperforms VHE-StackGAN++, suggesting that the stacking structure is helpful for generating high resolution images, as previously verified in Zhang et al. (2017a) . VHE-simple-raster-scan-GAN outperforms VHE-StackGAN++ but underperforms VHE-raster-scan-GAN, confirming the benefits of combining the stacking and raster-scan structures. More visual results for ablation studies can be found in Appendix C.2. Below we focus on illustrating the outstanding performance of VHE-raster-scan-GAN.

Latent space interpolation: In order to understand the jointly learned image and text manifolds, given texts t 1 and t 2 , we draw θ 1 and θ 2 and use the interpolated variables between them to generate both images via the GAN's image generator and texts via the PGBN text decoder. As in Fig. 3(c ), the first row shows the true texts t 1 and images generated with θ 1 , the last row shows t 2 and images generated with θ 2 , and the second to fourth rows show the generated texts and images with the interpolations from θ 1 to θ 2 . The strong correspondences between the generated images and texts, with smooth changes in colors, object positions, and backgrounds between adjacent rows, suggest that the latent space of VHE-raster-scan-GAN is both visually and semantically meaningful. Additional more fine-gridded latent space interpolation results are shown in Figs. 15-18 of Appendix C.4.

Visualization of captured semantic and visual concepts: Zhou et al. (2016) show that the semantic concepts extracted by PGBN and their hierarchical relationships can be represented as a DAG, only a subnet of which will be activated given a specific text input. In each subplot of Fig. 4 , we visualize example topic nodes of the DAG subnet activated by the given text input, and show the corresponding images generated at different hidden layers. There is a good match at each layer between the visual contents of the generated images and semantics of the top activated topics, which are mainly about general shapes, colors, or backgrounds at the top layer, and become more and more fine-grained when moving downward. In Fig. 5 , for the DAG learned on COCO, we show a representative subnet that is rooted at a top-layer node about "rooms and objects at home," and provide both semantic and visual representations for each node. Being able to capture and relate hierarchical semantic and visual concepts helps explain the state-of-the-art performance of VHE-raster-scan-GAN.

3.2. IMAGE-TO-TEXT LEARNING:

VHE-raster-scan-GAN can perform a wide variety of extra tasks, such as image-to-text generation, text-based zero-shot learning (ZSL), and image retrieval given a text query. In particular, given image x n , we draw tn as tn

| θ n ∼ p(t | Φ, θ n ), θ n | x n ∼ q Ω (θ | Φ,

x n ) and use it for downstream tasks.

Image-to-text generation: Given an image, we may generate some key words, as shown in Fig. 6(a) , where the true and generated ones are displayed on the left and right of the input image, respectively. It is clear that VHE-raster-scan-GAN successfully captures the object colors, shapes, locations, and backgrounds to predict relevant key words.

Text-based ZSL: Text-based ZSL is a specific task that learns a relationship between images and texts on the seen classes and transfer it to the unseen ones (Fu et al., 2018) . We follow the the same settings on CUB and Flower as existing text-based ZSL methods summarized in Tab. 3. There are two default splits for CUB-the hard (CUB-H) and easy one (CUB-E)-and one split setting for Flower, as described in Appendix F. Note that except for our models that infer a shared semantically meaningful latent space between two modalities, none of the other methods have generative models for both modalities, regardless of whether they learn a classifier or a distance metric in a latent space for ZSL. Tab. 3 shows that VHE-raster-scan-GAN clearly outperforms the state of the art in terms of the Top-1 accuracy on both the CUB-H and Flower, and is comparable to the second best on CUB-E (it is the best among all methods that have reported their Top-5 accuracies on CUB-E). Note for CUB-E, every unseen class has some corresponding seen classes under the same super-category, which makes the classification of surface or distance metric learned on the seen classes easier to generalize to the unseen ones. We also note that both GAZSL and ZSLPP rely on visual part detection to extract image features, making their performance sensitive to the quality of the visual part detector that often has to be elaborately tuned for different classes and hence limiting their generalization ability, for example, the visual part detector for birds is not suitable for flowers. Tab. 3 also includes the results of ZSL using VHE, which show that given the same structured text decoder and image encoder, VHE consistently underperforms both VHE-StackGAN++ and VHE-raster-scan-GAN. This suggests 1) the advantage of a joint generation of two modalities, and 2) the ability of GAN in helping VHE achieve better data representation. The results in Tab. 3 also show that the ZSL performance of VHE-raster-scan-GAN has a clear trend of improvement as PGBN becomes deeper, suggesting the advantage of having a multi-stochastic-hidden-layer deep topic model for text generation. We also collect the ZSL results of the last 1000 mini-batch based stochastic gradient update iterations to calculate the error bars. For existing methods, since there are no error bars provided in published paper, we only provide the text error bars of the methods that have publicly accessible code.

3.3. IMAGE/TEXT RETRIEVAL:

As discussed in Section 2.4, the proposed models are able to infer the shared latent space given either an image or text. We test both VHE-StackGAN++ and VHE-raster-scan-GAN on the same image/text The picture shows a view of village having blue fine sky, low house, grey road and green trees. retrieval tasks as in TA-GAN (Nam et al., 2018) , where we use the cosine distance between the inferred latent space given images (q(θ | x), image encoder) and these given texts (p(θ | t), Gibbs sampling) to compute the similarity scores. Similar with TA-GAN, the top-1 image-to-text retrieval accuracy (Top-1 Acc) and the percentage of matching images in top-50 text-to-image retrieval results (AP@50) on CUB-E dataset are used to measure the performance. As shown in Table 4 , VHE-rasterscan-GAN clearly outperforms AttnGAN (Xu et al., 2018) and is comparable with TA-GAN. Note TA-GAN needs to extract its text features based on the fastText model (Bojanowski et al., 2017) pre-trained on a large corpus, while VHE-raster-scan-GAN learns everything directly from the current dataset in an end-to-end manner. Also, VHE-raster-scan-GAN outperforms VHE-StackGAN++, which further confirms the benefits of combining both the stacking and raster scan structures.

3.4. GENERATION OF RANDOM TEXT-IMAGE PAIRS:

Below we show how to generate data samples that contain both modalities. After training a threestochastic-hidden-layer VHE-raster-scan-GAN, following the data generation process of the PGBN text decoder, given {Φ (l) } 3 l=1 and r, we first generate θ (3) ∼ Gam r, 1/s (4) and then downward propagate it through the PGBN as in (5) to calculate the Poisson rates for all words using Φ (1) θ (1) . Given a random draw, {θ (l) } 3 l=1 is fed into the raster-scan-GAN image generator to generate a corresponding image. Shown in Fig. 6(b ) are six random draws, for each of which we show its top seven words and generated image, whose relationships are clearly interpretable, suggesting that VHE-raster-scan-GAN is able to recode the key information of both modalities and the relationships between them. In addition to the tasks shown above, VHE-raster-scan-GAN can also be used to perform image retrieval given a text query, and image regeneration; see Appendices C.5 and C.6 for example results on these additional tasks.

4. CONCLUSION:

We develop variational hetero-encoder randomized generative adversarial network (VHE-GAN) to provide a plug-and-play joint image-text modeling framework. VHE-GAN is a versatile deep generative model that integrates off-the-shelf image encoders, text decoders, and GAN image discriminators and generators into a coherent end-to-end learning objective. It couples its VHE and GAN components by feeding the VHE variational posterior in lieu of noise as the source of randomness of the GAN generator. We show VHE-StackGAN++ that combines the Poisson gamma belief network, a deep topic model, and StackGAN++ achieves competitive performance, and VHE-raster-scan-GAN, which further improves VHE-StackGAN++ by exploiting the semantically-meaningful hierarchical structure of the deep topic model, generates photo-realistic images not only in a multi-scale low-to-high-resolution manner, but also in a hierarchical-semantic coarse-to-fine fashion, achieving outstanding results in many challenging image-to-text, text-to-image, and joint text-image learning and generation tasks.

A MODEL PROPERTY OF VHE-GAN AND RELATED WORK:

Let us denote q(z) = E x∼pdata(x) [q(z | x)] = 1 N N n=1 q(z | x n )

as the aggregated posterior (Hoffman & Johnson, 2016; Makhzani et al., 2015) . Removing the triple-data-reuse training strategy, we can re-express the VHE-GAN objective in (4) as

EQUATION

which corresponds to a naive combination of the VHE and GAN training objectives, where the data samples used to train the VHE, GAN generator, and GAN discriminator in each gradient update iteration are not imposed to be the same. While the naive objective function in (10) differs from the true one in (4) that is used to train VHE-GAN, it simplifies the analysis of its theoretical property, as described below.

Let us denote q(z, x, t) := q(z | x)p data (x, t) as the joint distribution of (x, t) and z under the VHE variational posterior q(z | x), I q (x, z) := E q(z,x) ln q(z,x) q(z)p data (x) as the mutual information between x ∼ p data (x) and z ∼ q(z), and JDS(p

1 ||p 2 ) := 1 2 KL[p 1 ||(p 1 + p 2 )/2] + 1 2 KL[p 2 ||(p 1 + p 2 )/2]

as the Jensen-Shannon divergence between distributions p 1 and p 2 . Similar to the analysis in Hoffman & Johnson (2016), the VHE's ELBO can be rewritten as

ELBO vhe = E q(z,x,t) [log p(t | z)] -I q (x, z) -KL[q(z)||p(z)],

where the mutual information term can also be expressed as

I q (x, z) = E x∼p data (x) KL[q(z | x)||q(z)].

Thus maximizing the ELBO encourages the mutual information term I q (x, z) to be minimized, which means while the data reconstruction term E q(z,x,t) [log p(t | z)] needs to be maximized, part of the VHE optimization objective penalizes a z from carrying the information of the x that it is encoded from. This mechanism helps provide necessary regularization to prevent overfitting. As in Goodfellow et al. (2014) , with an optimal discriminator D * G for generator G, we have min

L GAN (D * G , G) = ln 4 + 2JSD(p data (x)||p Gz (x))

, where p Gz(x) denotes the distribution of the generated data G(z) that use z ∼ q(z) as the random source fed into the GAN generator. The JSD term is minimized when p Gz (x) = p data (x).

With these analyses, given an optimal GAN discriminator, the naive VHE-GAN objective function in (10) reduces to min E,Ggan,Gvae

-E q(z,x,t) [log p(t | z)] + KL[q(z)||p(z)] + I q (x, z) + 2JSD(p data (x)||p Gz (x)). (11)

From the VHEs' point of view, examining (11) shows that it alleviates the inherent conflict in VHE of maximizing the ELBO and maximizing the mutual information I q (x, z). This is because while the VHE part of VHE-GAN still relies on minimizing I q (x, z) to regularize the learning, the GAN part tries to transform q(z) through the GAN generator to match the true data distribution p data (x). In other words, while its VHE part penalizes a z from carrying the information about the x that it is encoded from, its GAN part encourages a z to carry information about the true data distribution p data (x), but not necessarily the observed x that it is encoded from.

From the GANs' point of view, examining (11) shows that it provides GAN with a meaningful latent space, necessary for performing inference and data reconstruction (with the aid of the data-triple-use training strategy). More specifically, this latent representation is also used by the VHE to maximize the data log-likelihood, a training procedure that tries to cover all modes of the empirical data distribution rather than dropping modes. For VHE-GAN (4), the source distribution is q(z | x), not only allowing GANs to participate in posterior inference and data reconstruction, but also helping GANs resist mode collapse. In the following, we discuss some related works on combining VAEs and GANs.

A.1 RELATED WORK ON COMBINING VAES AND GANS:

Examples in improving VAEs with adversarial learning include Mescheder et al. (2017) , which allows the VAEs to take implicit encoder distribution, and adversarial auto-encoder (Makhzani et al., 2015) and Wasserstein auto-encoder (Tolstikhin et al., 2018) , which drop the mutual information term from the ELBO and use adversarial learning to match the aggregated posterior and prior. Examples in allowing GANs to perform inference include Dumoulin et al. (2017) and Donahue et al. (2017) , which use GANs to match the joint distribution q(z | x)p data (x) defined by the encoder and the one p(x | z)p(z) defined by the generator. However, they often do not provide good data reconstruction. Examples in using VAEs or maximum likelihood to help GANs resist mode collapse include Che et al. (2017); Srivastava et al. (2017) ; Grover et al. (2018) . Another example is VAEGAN (Larsen et al., 2016) that combines unit-wise likelihood at hidden layer and adversarial loss at original space, but its update of the encoder is separated from the GAN mini-max objective. On the contrary, IntroVAE (Huang et al., 2018) retains the pixel-wise likelihood with an adversarial regularization on the latent space. Sharing network between the VAE decoder and GAN generator in VAEGAN and IntroVAE, however, limit them to model a single modality.

B MORE DISCUSSION ON SEQUENCE MODELS AND TOPIC MODELS IN TEXT ANALYSIS.:

In Section 3.1, we have discussed two models to represent the text: sequence models and topic models. Considering the versatility of topic models (Wang et al., 2009; Jin et al., 2015; Zhou et al., 2016; Srivastava & Salakhutdinov, 2012a; 2014; Wang et al., 2018; Elhoseiny et al., 2017b; Zhu et al., 2018) in dealing with different types of textual information, and its effectiveness in capturing latent topics that are often directly related to macro-level visual information (Gomez et al., 2017; Dieng et al., 2017; Lau et al., 2017) , we choose a state-of-the-art deep topic model, PGBN, to model the textual descriptions in VHE. Due to space constraint, we only provide simple illustrations in Figs. 3(a ) and 3(b). In this section, more insights and discussions are provided. As discussed before, topic models are able to model non-sequential texts such as binary attributes.

Red body:

The CUB dataset provides 312 binary attributes (Wah et al., 2011) for each images, such as whether "crown color is blue" and whether "tail shape is solid" to define the color or shape of different body parts of a bird. We first transform these binary attributes for the nth image to a 312-dimensional binary vector t n , whose ith element is 1 or 0 depending on whether the bird in this image owns the ith attribute or not. The binary attribute vectors t n are used together with the corresponding bird images x n to train VHE-raster-scan-GAN. As shown in Fig. 7 , we generate images given five binary attributes, which are formed into a 312-dimensional binary vector t (with five non-zero elements at these five attributes) that becomes the input to the PGBN text decoder. Clearly, these generated images are photo-realistic and faithfully represent the five provided attributes.

The proposed VHE-GANs can also well model long documents. In text-based ZSL discussed in Section 3.2, each class (not each image) is represented as a long encyclopedia document, whose global semantic structure is hard to captured by existing sequence models. Besides a good ZSL performance achieved by VHE-raster-scan-GAN, illustrating its advantages of text generation given images, we show Fig. 8 example results of image generation conditioning on long encyclopedia documents on the unseen classes of CUB-E (Qiao et al., 2016; Akata et al., 2015) and Flower (Elhoseiny et al., 2017a) .

It is a seabird, nesting in seabird colonies, with a large orange/brown bill.

Plumage is dark on top and paler below, in offshore and inshore water. Sometimes it swim in the water and sometimes it stand on the strong.

Brownish-olive upperparts, darker on the wings and tail, yellowish underparts.

Have small bill short tail, on a perch low or in the middle of a tree. Its eyes are dark and round with radiating vigor, like looking for food or insects. For text-to-image generation tasks, we use the official pre-defined training/testing split (illustrated in Appendix F) to train and test all the models. Following the definition of error bar of IS in StackGAN++ (Zhang et al., 2017b) , HDGAN (Zhang et al., 2018b) , and AttnGAN (Xu et al., 2018) , we provide the IS results with error bars for various methods in Table 5 , where the results of the StackGAN++ , HDGAN, and AttnGAN are quoted from the published papers. The FID error bar is not included as it has not been clearly defined. Due to space constraint, we provide relative small-size images in Fig. 2 . Below we show the corresponding images with larger sizes.

Brown duck playing on the lake making a poodle. 

StackGAN++:



C.3 MORE TEXT-TO-IMAGE GENERATION RESULTS ON COCO:

COCO is a more challenging dataset than CUB and Flower, as it contains very diverse objects and scenes. We show in Fig. 13 more samples conditioned on different textural descriptions.

A living room filled with lots of furniture.

A white tall cathedral towering under the sky.

A child with black clothes is standing on top of a snow covered hill.

People playing with kites outside under the blue sky.

A beach on a cloudy day with a bunch of people on it.

The baseball player with white clothes is ready for the game.

StackGAN++ HDGAN VHE-raster-scan-GAN AttnGAN Obj-GAN 

C.5 IMAGE RETRIEVAL GIVEN A TEXT QUERY:

For image x n , we draw its BoW textual description tn as tn

| θ n ∼ p(t | Φ, θ n ), θ n | x n ∼ q Ω (θ | Φ, x n ).

Given the BoW textual description t as a text query, we retrieve the top five images ranked by the cosine distances between t and tn 's. Shown in Fig. 19 are three example image retrieval results, which suggest that the retrieved images are semantically related to their text queries in colors, shapes, and locations. 

C.7 LEARNED HIERARCHICAL TOPICS IN VHE:

The inferred topics at different layers and the inferred sparse connection weights between the topics of adjacent layers are found to be highly interpretable. In particular, we can understand the meaning of each topic by projecting it back to the original data space via

l-1 t=1 Φ (t) φ (l)

k and understand the relationship between the topics by arranging them into a directed acyclic graph (DAG) and choose its subnets to visualize. We show in Figs. 21, 22, and 23 example subnets taken from the DAGs inferred by the three-layer VHE-raster-scan-GAN of size 256-128-64 on Flower, CUB, and COCO, respectively. The semantic meaning of each topic and the connection weights between the topics of adjacent layers are highly interpretable. For example, in Figs. 21, the topics describe very specific flower characteristics, such as special textures, shapes, and parts, at the bottom layer, and become increasingly more general when moving upwards. G ADDITIONAL DISCUSSION ON OBJ-GAN Focusing on the COCO dataset, the recently proposed Obj-GAN (Li et al., 2019) exploits more side information, including the bounding boxes and labels of objects existing in the images, to perform text-to-image generation. More specifically, Obj-GAN first trains an attentive sequence to sequence model to infer the bounding boxes given a text t:

EQUATION

where, e are the pre-trained bi-LSTM word vectors of t, B t = (l t , b t ) consists of the class label of the tth object and its bounding box b = (x, y, w, h) ∈ R 4 . Given the bounding boxes B 1:T , Obj-GAN learn a shape generator to predict the shape of each object in its bounding box:

EQUATION

)

where z t ∼ N (0, 1) is a random noise vector. Having obtained B 1:T and M1:T , Obj-GAN trains an attentive multi-stage image generator to generate the images conditioned on B 1:T , M1:T , and e.

Although Obj-GAN achieves a better FID on COCO, it has two major limitations in practice. First, it is not always possible to obtain accurate bounding boxes and labels of objects in the image; even they can be acquired by manual labeling, it is often time and labor consuming, especially on large datasets. Second, each word is associated with one fixed bounding box; in other words, given one sentence, the locations of the objects in the generated images are fixed, which clearly hurts the diversity of the Obj-GAN generated images, as shown in Fig. 27 .

People playing with kites outside under the blue sky. 

Obj-GAN VHE-raster-scan-GAN:



:

l=1 q(θ (l) n | x n , Φ (l+1) , θ (l+1) n ).First, the top-layer latent variable θ (3) , often capturing general

Figures and Tables:

Figure 1: Illustration of (a) VHE, (b) StackGAN++, (c) raster-scan-GAN, (d) vanilla-GAN, and (e) simpleraster-scan-GAN. VHE-raster-scan-GAN consists of (a) and (c). x ↓d is down-sampled from x with scaling factor d. VHE-StackGAN++, consisting of (a) and (b), VHE-vanilla-GAN, consisting of (a) and (d), and VHE-simple-raster-scan-GAN, consisting of (a) and (e), are all used for ablation studies. q(z | x), text decoder p(t | z), and GAN generator denoted by E, G vae , and G gan , respectively, we express the objective function of VHE-GAN for joint image-text end-to-end learning as min E,Gvae,Ggan

max

Figure 2: Comparison on image generation given texts from CUB, Flower, and COCO. Shown in the top row are the textual descriptions and their associated real images; see Appendix C.2 for higher-resolution images. Note AttnGAN did not perform experiments on Flower and hence its results on Flower are not shown, and since Obj-GAN only performed experiment on COCO, we defer its visual results to Appendix C.3.3.1 TEXT-TO-IMAGE LEARNINGAlthough the proposed VHE-GANs do not have a text encoder to directly project a document to the shared latent space, given a document and a set of topics inferred during training, we use the upwarddownward Gibbs sampler ofZhou et al. (2016) to draw {θ (l) } L l=1 from its conditional posterior under PGBN, which are then fed into the GAN image generator to synthesize random images.

Figure 3: Example results of VHE-raster-scan-GAN on three different tasks: (a) image generation given five textual attributes; (b) image generation given a long class-specific document (showing three representative sentences for brevity) from CUB; and (c) latent space interpolation for joint image-text generation on CUB (left column) and Flower (right column), where the texts in the first and last row are given.

This bright colored red flower on the green leaves has petals that surround the ovary in a ruffled wavy manner.

Figure 4: Visualization of example semantic and visual concepts captured by a three-stochastic-hidden-layer VHE-raster-scan-GAN from (a) Flower, (b) Bird, and (c) COCO. In each subplot, given the real text tn shown at the bottom, we draw {θ (l) n } 3 l=1 via Gibbs sampling; we show the three most active topics in Φ (l) (ranked by the weights of θ (l) n ) at layer l = 3, 2, 1, where each topic is visualized by its top three words; and we feed {θ

scan-GAN to generate three random images (one per layer, coarse to fine from layers 3 to 1).

Figure 5: An example topic hierarchy learned on COCO and its visual representation. We sample θ (1:3) n ∼ q(θ (1:3) n | Φ, xn) for all n; for topic node k of layer l, we show both its top words and the top two images ranked by their activations θ (l) nk .

Figure 6: Example results of using VHE-raster-scan-GAN for (a) image-to-textual-tags generation, where the generated tags highlighted in red are included in the original ones; (b) image-text-pair generations (columns from left to right are based on Flower, CUB, and COCO, respectively).

Figure 7: Generated random images by VHE-raster-scan-GAN conditioning on five binary attributes.

Figure 8: Image generation conditioning on long encyclopedia documents using VHE-raster-scan-GAN trained on (a) CUB-E and (b) Flower. Shown in the top part of each subplot are representative sentences taken from the long document that describes an unseen class; for the three rows of images shown in the bottom part, the first row includes three real images from the corresponding unseen class, and the other two rows include a total of six randomly generated images conditioning on the long encyclopedia document of the corresponding unseen class.Analogous to how the Bird images are generated in Fig.7, we also perform facial image generation given a set of textual attributes. On CelebA dataset, given attributes, we train VHE-stackGAN++ and

Figure 10: The images above the blue line are the larger-size replots of CUB Bird images in Figure 2, while the images below the blue line are results for ablation study.

Figure 13: Example text-to-image generation results on COCO.

Figure 14: Example of latent space interpolation on CUB.

Figure 15: Example of latent space interpolation on CUB.

Figure 16: Example of latent space interpolation on CUB.

Figure 17: Example of latent space interpolation on Flower.

Figure 18: Example of latent space interpolation on Flower. 25

Figure 19: Top-5 retrieved images given a text query. Rows 1 to 3 are for Flower, CUB, and COCO, respectively.

Figure 23: Analogous plot to Fig. 21 on COCO.

Figure 25: The structure of Stack-GAN++ in VHE-StackGAN++, where JCU is a type of discriminator proposed in Zhang et al. (2017b).

Figure 27: The generated random images of Obj-GAN given text lack diversity.

Ablation

Table content: <table><tr><td>Criterion</td><td>IS</td><td>FID</td><td>IS</td><td>FID</td><td>IS</td><td>FID</td><td>IS</td><td>FID</td></tr><tr><td>Flower</td><td>3.29</td><td>41.04</td><td>3.01</td><td>52.15</td><td>3.56</td><td>38.66</td><td>3.62</td><td>36.18</td></tr><tr><td>CUB</td><td>3.92</td><td>13.79</td><td>3.52</td><td>21.24</td><td>4.20</td><td>12.93</td><td>4.31</td><td>12.35</td></tr><tr><td>COCO</td><td>10.63</td><td>79.65</td><td>6.36</td><td>97.15</td><td>12.63</td><td>78.02</td><td>20.13</td><td>77.18</td></tr><tr><td/><td>Brown duck</td><td/><td/><td/><td/><td/><td/><td/></tr><tr><td/><td>playing on the</td><td/><td/><td/><td/><td/><td/><td/></tr><tr><td/><td>lake making a</td><td/><td/><td/><td/><td/><td/><td/></tr><tr><td/><td>poodle.</td><td/><td/><td/><td/><td/><td/><td/></tr></table>



Table content: <table/>

is a seabird, nesting in seabird colonies, with a large orange/brown bill. Plumage is dark on top and paler below, in offshore and inshore water. Sometimes it swim in the water and sometimes it stand on the strong.

Table content: <table><tr><td>red body red body</td><td>colorful body</td><td>red grey red grey</td><td>red pink red pink</td></tr><tr><td>red head red head</td><td>blue head</td><td>brown dark brown dark</td><td>large petal large petal</td></tr><tr><td>black wings black wings</td><td>green back</td><td>long large long large</td><td>stamen light stamen light</td></tr><tr><td>long bill long bill</td><td>solid tail</td><td/><td/></tr><tr><td>black belly black belly</td><td>yellow belly</td><td>red brown red brown</td><td>red pink red pink</td></tr><tr><td/><td/><td>gray dark gray dark</td><td>stamen petal stamen petal</td></tr><tr><td/><td/><td>large black large black</td><td>long yellow long yellow</td></tr><tr><td/><td/><td>orange black orange black</td><td>red yellow red yellow</td></tr><tr><td/><td/><td>brown dark brown dark</td><td>long petal long petal</td></tr><tr><td/><td/><td>yellow head yellow head</td><td>brown thin brown thin</td></tr><tr><td/><td/><td>yellow black yellow black</td><td>yellow long yellow long</td></tr><tr><td/><td/><td>dark head dark head</td><td>red thin red thin</td></tr><tr><td/><td/><td>body blue body blue</td><td>petal green petal green</td></tr><tr><td/><td/><td>yellow blue yellow blue</td><td>yellow long yellow long</td></tr><tr><td/><td/><td>black body black body</td><td>green stamen green stamen</td></tr><tr><td/><td/><td>long colored long colored</td><td>petal dark petal dark</td></tr><tr><td>(a)</td><td/><td/><td/></tr></table>

is a seabird, nesting in seabird colonies, with a large orange/brown bill. Plumage is dark on top and paler below, in offshore and inshore water. Sometimes it swim in the water and sometimes it stand on the strong.

Table content: <table><tr><td>red body</td><td>colorful body</td><td>red grey</td><td>red pink</td></tr><tr><td>red head</td><td>blue head</td><td>brown dark</td><td>large petal</td></tr><tr><td>black wings</td><td>green back</td><td>long large</td><td>stamen light</td></tr><tr><td>long bill</td><td>solid tail</td><td/><td/></tr><tr><td>black belly</td><td>yellow belly</td><td>red brown</td><td>red pink</td></tr><tr><td/><td/><td>gray dark</td><td>stamen petal</td></tr><tr><td/><td/><td>large black</td><td>long yellow</td></tr><tr><td/><td/><td>orange black</td><td>red yellow</td></tr><tr><td/><td/><td>brown dark</td><td>long petal</td></tr><tr><td/><td/><td>yellow head</td><td>brown thin</td></tr><tr><td/><td/><td>yellow black</td><td>yellow long</td></tr><tr><td/><td/><td>dark head</td><td>red thin</td></tr><tr><td/><td/><td>body blue</td><td>petal green</td></tr><tr><td/><td/><td>yellow blue</td><td>yellow long</td></tr><tr><td/><td/><td>black body</td><td>green stamen</td></tr><tr><td/><td/><td>long colored</td><td>petal dark</td></tr><tr><td/><td>(b)</td><td/><td/></tr></table>

is a seabird, nesting in seabird colonies, with a large orange/brown bill. Plumage is dark on top and paler below, in offshore and inshore water. Sometimes it swim in the water and sometimes it stand on the strong.

Table content: <table><tr><td>colorful body</td></tr><tr><td>blue head</td></tr><tr><td>green back</td></tr><tr><td>solid tail</td></tr><tr><td>yellow belly</td></tr><tr><td>(c)</td></tr></table>

Accuracy (%) of ZSL on CUB and Flower. Note that some of them are attribute-based methods but applicable in our setting by replacing attribute vectors with text features (labeled by * ), as discussed in(Elhoseiny  et al., 2017b).

Table content: <table><tr><td>Text-ZSL dataset</td><td>CUB-H</td><td>CUB-E</td><td/><td>Flower</td></tr><tr><td>Accuracy criterion</td><td>top-1</td><td>top-1</td><td>top-5</td><td>top-1</td></tr><tr><td>WAC-Kernel (Elhoseiny et al., 2017a)</td><td colspan="3">7.7 ± 0.28 33.5 ± 0.22 64.3 ± 0.20</td><td>9.1 ± 2.77</td></tr><tr><td>ZSLNS (Qiao et al., 2016)</td><td colspan="3">7.3 ± 0.36 29.1 ± 0.28 61.8 ± 0.22</td><td>8.7 ± 2.46</td></tr><tr><td colspan="4">ESZSL  *  (Romeraparedes &amp; Torr, 2015) 7.4 ± 0.31 28.5 ± 0.26 59.9 ± 0.20</td><td>8.6 ± 2.53</td></tr><tr><td>SynC  *  (Changpinyo et al., 2016)</td><td>8.6</td><td>28.0</td><td>61.3</td><td>8.2</td></tr><tr><td>ZSLPP (Elhoseiny et al., 2017b)</td><td>9.7</td><td>37.2</td><td>-</td><td>-</td></tr><tr><td>GAZSL (Zhu et al., 2018)</td><td colspan="3">10.3 ± 0.26 43.7 ± 0.28 67.61 ± 0.24</td><td>-</td></tr><tr><td>VHE-L3</td><td colspan="3">14.0 ± 0.24 34.6 ± 0.25 64.6 ± 0.20</td><td>8.9 ± 1.57</td></tr><tr><td>VHE-StackGAN++-L3</td><td>16.1</td><td>38.5</td><td>68.2</td><td>10.6</td></tr><tr><td>VHE-raster-scan-GAN-L1</td><td colspan="3">11.7 ± 0.31 32.1 ± 0.32 62.6 ± 0.33</td><td>9.4 ± 1.68</td></tr><tr><td>VHE-raster-scan-GAN-L2</td><td colspan="4">14.9 ± 0.26 37.1 ± 0.24 64.6 ± 0.25 11.0 ± 1.54</td></tr><tr><td>VHE-raster-scan-GAN-L3</td><td colspan="4">16.7 ± 0.24 39.6 ± 0.20 70.3 ± 0.18 12.1 ± 1.47</td></tr></table>

Comparison

Table content: <table><tr><td>Method</td><td>CNN-LSTM</td><td>AttnGAN</td><td>TA-GAN</td><td colspan="2">VHE-StackGAN++ VHE-raster-scan-GAN</td></tr><tr><td/><td colspan="3">(Li et al., 2017) (Xu et al., 2018) (Nam et al., 2018)</td><td/><td/></tr><tr><td>Top1-ACC(%)</td><td>61.5</td><td>55.1</td><td>61.3</td><td>60.2</td><td>61.7</td></tr><tr><td>AP@50(%)</td><td>57.6</td><td>51.0</td><td>62.8</td><td>61.3</td><td>62.6</td></tr></table>

Inception score (IS) results in Table 1 with error bars.

Table content: <table><tr><td colspan="2">Method StackGAN++</td><td>HDGAN</td><td>AttnGAN</td><td>Obj-GAN</td><td>VHE-raster-scan-GAN</td></tr><tr><td>Flower</td><td>3.26 ± .01</td><td>3.45 ± .07</td><td>-</td><td>-</td><td>3.72 ± .01</td></tr><tr><td>CUB</td><td>3.84 ± .06</td><td>4.15 ± .05</td><td>4.36 ± .03</td><td>-</td><td>4.41 ± .03</td></tr><tr><td>COCO</td><td>8.30 ± .10</td><td colspan="3">11.86 ± .18 25.89 ± .47 26.68 ± .52</td><td>27.16 ± .23</td></tr></table>

Inception score (IS) results in Table 2 with error bars.

Table content: <table><tr><td colspan="5">Method PGBN+StackGAN++ VHE-vanilla-GAN VHE-StackGAN++ VHE-simple-raster-scan-GAN</td></tr><tr><td>Flower</td><td>3.29 ± .02</td><td>3.01 ± .06</td><td>3.56 ± .03</td><td>3.62 ± .02</td></tr><tr><td>CUB</td><td>3.92 ± .06</td><td>3.52 ± .08</td><td>4.20 ± .04</td><td>4.31 ± .06</td></tr><tr><td>COCO</td><td>10.63 ± .10</td><td>6.36 ± .20</td><td>12.63 ± .15</td><td>20.13 ± 22</td></tr></table>

Figure 21: An example topic hierarchy taken from the directed acyclic graph learned by a three-layer VHEraster-scan-GAN of size 256-128-64 on Flower.Figure 22: Analogous plot to Fig. 21 on CUB.

Table content: <table><tr><td/><td/><td/><td colspan="3">11 green pedicel color purple</td><td/><td/><td colspan="3">60 red green color stamen</td></tr><tr><td/><td/><td/><td colspan="3">large ruffled wavy long</td><td/><td/><td colspan="3">ruffled edges long bright</td></tr><tr><td/><td/><td/><td colspan="3">shaped edges stem</td><td/><td/><td colspan="3">pedicel large dark sepal</td></tr><tr><td colspan="2">68</td><td/><td/><td/><td>7</td><td/><td>9</td><td/><td/><td>97</td></tr><tr><td colspan="5">ruffled large wavy brown</td><td colspan="2">red green long color</td><td colspan="4">red color bright stamen</td><td>center yellow bright</td></tr><tr><td colspan="5">green rounded wide wrinkled</td><td colspan="2">pedicel pointed pink</td><td colspan="4">green dark stigma pedicel</td><td>petal stamen color</td></tr><tr><td colspan="4">pedicels curled pistil</td><td/><td colspan="2">sepals stamen looking</td><td colspan="3">pistil deep shown</td><td>clustered large round</td></tr><tr><td>12</td><td/><td>72</td><td/><td>55</td><td>50</td><td>62</td><td>11</td><td>23</td><td/><td>1</td><td>66</td><td>77</td></tr><tr><td colspan="2">brown brown</td><td>stalks stalks</td><td/><td>ruffled ruffled</td><td>pedicel pedicel</td><td>red red</td><td>striations striations</td><td colspan="2">soft soft</td><td>sepals sepals</td><td>yellow yellow</td><td>clustered clustered</td></tr><tr><td colspan="2">flowers flowers</td><td>pistil pistil</td><td/><td>rounded rounded</td><td>sepals sepals</td><td>stamen stamen</td><td>striped striped</td><td colspan="2">Smooth Smooth</td><td>pedicel pedicel</td><td>golden golden</td><td>round round</td></tr><tr><td>fushia fushia</td><td/><td colspan="2">pedicels pedicels</td><td>wavy wavy</td><td>color color</td><td>pink pink</td><td>creases creases</td><td colspan="2">waxy waxy</td><td>shown shown</td><td>bright bright</td><td>bunch bunch</td></tr><tr><td>green green</td><td/><td>ovary ovary</td><td/><td>large large</td><td>long long</td><td>bright bright</td><td>ridges ridges</td><td colspan="2">bunch bunch</td><td>petal petal</td><td>center center</td><td>filament filament</td></tr><tr><td>black black</td><td/><td>stem stem</td><td/><td>wrinkled wrinkled</td><td>leaves leaves</td><td>dark dark</td><td>striated striated</td><td colspan="2">deep deep</td><td>stigma stigma</td><td>color color</td><td>sticking sticking</td></tr><tr><td>stalks stalks</td><td/><td>buds buds</td><td/><td>curled curled</td><td>pointed pointed</td><td>green green</td><td>clustered clustered</td><td colspan="2">tight tight</td><td>pistil pistil</td><td>round round</td><td>large large</td></tr><tr><td/><td/><td colspan="4">15 black white orange beak</td><td/><td/><td>36</td><td colspan="2">yellow green grey</td></tr><tr><td/><td/><td/><td colspan="3">long crown wings head</td><td/><td/><td colspan="3">small belly gray white</td></tr><tr><td/><td/><td/><td colspan="3">feet large body</td><td/><td/><td colspan="3">beak eye crown head</td></tr><tr><td>87</td><td/><td/><td/><td/><td>37</td><td/><td>40</td><td/><td/><td>22</td></tr><tr><td colspan="5">brown belly breast white</td><td colspan="2">white black beak long</td><td colspan="3">black orange feet</td><td>yellow grey wings</td></tr><tr><td colspan="5">beak throat long wings</td><td colspan="2">head eye body pointy</td><td colspan="3">white red crown webbed</td><td>head belly body beak</td></tr><tr><td/><td colspan="4">crown light small</td><td colspan="2">color rings rest</td><td colspan="3">beak long head tarsus</td><td>small brown wingbars</td></tr><tr><td>47 brown brown</td><td colspan="2">66 white white</td><td colspan="2">96 tarsus tarsus</td><td>79 black black</td><td>67 beak beak</td><td>23 feet feet</td><td colspan="2">45 webbed webbed</td><td>36 black black</td><td>97 yellow yellow</td><td>15 beak beak</td></tr><tr><td>light light</td><td colspan="2">belly belly</td><td colspan="2">black black</td><td>eye eye</td><td>long long</td><td>webbed webbed</td><td colspan="2">footed footed</td><td>tail tail</td><td>belly belly</td><td>body body</td></tr><tr><td>wings wings</td><td colspan="2">breast breast</td><td colspan="2">feet feet</td><td>beak beak</td><td>pointy pointy</td><td>large large</td><td>shore shore</td><td/><td>wings wings</td><td>brown brown</td><td>pointed pointed</td></tr><tr><td>dark dark</td><td colspan="2">wings wings</td><td colspan="2">gray gray</td><td>rings rings</td><td>sharp sharp</td><td>tarsus tarsus</td><td>snowy snowy</td><td/><td>feather feather</td><td>short short</td><td>feathers feathers</td></tr><tr><td>tan tan</td><td colspan="2">head head</td><td colspan="2">throat throat</td><td>yellow yellow</td><td>breast breast</td><td>body body</td><td colspan="2">waterbird waterbird</td><td>body body</td><td>wingbars wingbars</td><td>tiny tiny</td></tr><tr><td>tail tail</td><td colspan="2">chest chest</td><td colspan="2">nape nape</td><td>unique unique</td><td>feather feather</td><td>dark dark</td><td colspan="2">standing standing</td><td>petite petite</td><td>greenish greenish</td><td>flat flat</td></tr><tr><td>sharp sharp</td><td colspan="2">head head</td><td colspan="2">abdomen abdomen</td><td>crest crest</td><td>blends blends</td><td>wide wide</td><td>rock rock</td><td/><td>retrices retrices</td><td>secondary secondary</td><td>multicolored multicolored</td></tr><tr><td/><td/><td colspan="4">26 bear teddy stuffed bears</td><td/><td/><td colspan="3">37 room living table couch</td></tr><tr><td/><td/><td colspan="4">sitting animals brown toy</td><td/><td/><td/><td colspan="2">television tv chair sitting</td></tr><tr><td/><td/><td/><td colspan="3">white holding animal</td><td/><td/><td/><td colspan="2">furniture chairs kitchen</td></tr><tr><td>24</td><td/><td/><td/><td/><td>70</td><td/><td>2</td><td/><td/><td>37</td></tr><tr><td colspan="5">bed room bedroom white</td><td colspan="2">luggage floor suitcase</td><td colspan="4">chair desk table sitting</td><td>kitchen refrigerator</td></tr><tr><td colspan="5">window beds hotel sitting</td><td colspan="2">sitting bag suitcases</td><td colspan="4">laptop room window bed</td><td>white stove cabinets</td></tr><tr><td colspan="4">large small pillows</td><td/><td colspan="2">old bags red airport</td><td colspan="4">wooden chairs old</td><td>sink table room open</td></tr><tr><td>85 room room</td><td colspan="2">86 television television</td><td colspan="2">8 white white</td><td>52 pink pink</td><td>97 keyboard keyboard</td><td>16 old old</td><td colspan="2">9 window window</td><td>39 table table</td><td>50 refrigerator refrigerator</td><td>67 clock clock</td></tr><tr><td>living living</td><td>tv tv</td><td/><td colspan="2">black black</td><td>purple purple</td><td>mouse mouse</td><td>sitting sitting</td><td colspan="2">looking looking</td><td>chairs chairs</td><td>open open</td><td>wall wall</td></tr><tr><td>furniture furniture</td><td colspan="2">screen screen</td><td colspan="2">photo photo</td><td>colorful colorful</td><td>desk desk</td><td>fashioned fashioned</td><td colspan="2">outside outside</td><td>room room</td><td>fridge fridge</td><td>large large</td></tr><tr><td>fireplace fireplace</td><td>flat flat</td><td/><td colspan="2">picture picture</td><td>bright bright</td><td>sitting sitting</td><td>vintage vintage</td><td>sill sill</td><td/><td>dining dining</td><td>door door</td><td>time time</td></tr><tr><td>large large</td><td colspan="2">room room</td><td colspan="2">dark dark</td><td>flower flower</td><td>monitor monitor</td><td>antique antique</td><td colspan="2">glass glass</td><td>wooden wooden</td><td>food food</td><td>mounted mounted</td></tr><tr><td>chairs chairs</td><td>wall wall</td><td/><td colspan="2">image image</td><td>rests rests</td><td>white white</td><td>style style</td><td colspan="2">door door</td><td>kitchen kitchen</td><td>kitchen kitchen</td><td>gold gold</td></tr><tr><td>windows windows</td><td colspan="2">sitting sitting</td><td colspan="2">backgraph backgraph</td><td>cute cute</td><td>desktop desktop</td><td>display display</td><td colspan="2">open open</td><td>area area</td><td>white white</td><td>ornate ornate</td></tr></table>

Peer review (iclr2020):
Summary: The authors design a new model for bidirectional joint image-text modeling using a variational hetero-encoder (VHE) randomized generative adversarial network (GAN) that integrates a probabilistic text decoder, probabilistic image encoder, and GAN into an end-to-end multimodal model. Their proposed VHE-GAN model encodes an image to decode its associated text and feeds the variational posterior as the source of randomness into the GAN image generator. The authors also incorporate a deep topic model, a ladder-structured image encoder, and StackGAN++ into their framework for improved photo-realistic images. Strengths: - The authors have proposed a nice multimodal model that allows inference of latent variables given only text or image, and also allows realistic synthesis of images from images, text, or noise. - The paper is quite dense but generally well written. Weaknesses: - The experimental comparison only included old baselines and the authors should compare to some more recent work such as TA-GAN (NIPS18), and Object-GAN (CVPR19). - It would help if the paper contained more ablation studies across different modules that the framework uses. ### Post rebuttal ### Thank you for your detailed answers to my questions.