Li Sun

CV
h-index29
19papers
1,251citations
Novelty60%
AI Score40

19 Papers

17.7LGAug 30, 2022
A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning

Li Sun, Junda Ye, Hao Peng et al.

Representation learning on temporal graphs has drawn considerable research attention owing to its fundamental importance in a wide spectrum of real-world applications. Though a number of studies succeed in obtaining time-dependent representations, it still faces significant challenges. On the one hand, most of the existing methods restrict the embedding space with a certain curvature. However, the underlying geometry in fact shifts among the positive curvature hyperspherical, zero curvature Euclidean and negative curvature hyperbolic spaces in the evolvement over time. On the other hand, these methods usually require abundant labels to learn temporal representations, and thereby notably limit their wide use in the unlabeled graphs of the real applications. To bridge this gap, we make the first attempt to study the problem of self-supervised temporal graph representation learning in the general Riemannian space, supporting the time-varying curvature to shift among hyperspherical, Euclidean and hyperbolic spaces. In this paper, we present a novel self-supervised Riemannian graph neural network (SelfRGNN). Specifically, we design a curvature-varying Riemannian GNN with a theoretically grounded time encoding, and formulate a functional curvature over time to model the evolvement shifting among the positive, zero and negative curvature spaces. To enable the self-supervised learning, we propose a novel reweighting self-contrastive approach, exploring the Riemannian space itself without augmentation, and propose an edge-based self-supervised curvature learning with the Ricci curvature. Extensive experiments show the superiority of SelfRGNN, and moreover, the case study shows the time-varying curvature of temporal graph in reality.

13.4LGAug 23, 2024Code
Multivariate Time-Series Anomaly Detection based on Enhancing Graph Attention Networks with Topological Analysis

Zhe Liu, Xiang Huang, Jingyun Zhang et al.

Unsupervised anomaly detection in time series is essential in industrial applications, as it significantly reduces the need for manual intervention. Multivariate time series pose a complex challenge due to their feature and temporal dimensions. Traditional methods use Graph Neural Networks (GNNs) or Transformers to analyze spatial while RNNs to model temporal dependencies. These methods focus narrowly on one dimension or engage in coarse-grained feature extraction, which can be inadequate for large datasets characterized by intricate relationships and dynamic changes. This paper introduces a novel temporal model built on an enhanced Graph Attention Network (GAT) for multivariate time series anomaly detection called TopoGDN. Our model analyzes both time and feature dimensions from a fine-grained perspective. First, we introduce a multi-scale temporal convolution module to extract detailed temporal features. Additionally, we present an augmented GAT to manage complex inter-feature dependencies, which incorporates graph topology into node features across multiple scales, a versatile, plug-and-play enhancement that significantly boosts the performance of GAT. Our experimental results confirm that our approach surpasses the baseline models on four datasets, demonstrating its potential for widespread application in fields requiring robust anomaly detection. The code is available at https://github.com/ljj-cyber/TopoGDN.

4.8CVDec 30, 2022
DGFont++: Robust Deformable Generative Networks for Unsupervised Font Generation

Xinyuan Chen, Yangchen Xie, Li Sun et al.

Automatic font generation without human experts is a practical and significant problem, especially for some languages that consist of a large number of characters. Existing methods for font generation are often in supervised learning. They require a large number of paired data, which are labor-intensive and expensive to collect. In contrast, common unsupervised image-to-image translation methods are not applicable to font generation, as they often define style as the set of textures and colors. In this work, we propose a robust deformable generative network for unsupervised font generation (abbreviated as DGFont++). We introduce a feature deformation skip connection (FDSC) to learn local patterns and geometric transformations between fonts. The FDSC predicts pairs of displacement maps and employs the predicted maps to apply deformable convolution to the low-level content feature maps. The outputs of FDSC are fed into a mixer to generate final results. Moreover, we introduce contrastive self-supervised learning to learn a robust style representation for fonts by understanding the similarity and dissimilarities of fonts. To distinguish different styles, we train our model with a multi-task discriminator, which ensures that each style can be discriminated independently. In addition to adversarial loss, another two reconstruction losses are adopted to constrain the domain-invariant characteristics between generated images and content images. Taking advantage of FDSC and the adopted loss functions, our model is able to maintain spatial information and generates high-quality character images in an unsupervised manner. Experiments demonstrate that our model is able to generate character images of higher quality than state-of-the-art methods.

2.3SIJul 23, 2024
Adaptive Differentially Private Structural Entropy Minimization for Unsupervised Social Event Detection

Zhiwei Yang, Yuecen Wei, Haoran Li et al.

Social event detection refers to extracting relevant message clusters from social media data streams to represent specific events in the real world. Social event detection is important in numerous areas, such as opinion analysis, social safety, and decision-making. Most current methods are supervised and require access to large amounts of data. These methods need prior knowledge of the events and carry a high risk of leaking sensitive information in the messages, making them less applicable in open-world settings. Therefore, conducting unsupervised detection while fully utilizing the rich information in the messages and protecting data privacy remains a significant challenge. To this end, we propose a novel social event detection framework, ADP-SEMEvent, an unsupervised social event detection method that prioritizes privacy. Specifically, ADP-SEMEvent is divided into two stages, i.e., the construction stage of the private message graph and the clustering stage of the private message graph. In the first stage, an adaptive differential privacy approach is used to construct a private message graph. In this process, our method can adaptively apply differential privacy based on the events occurring each day in an open environment to maximize the use of the privacy budget. In the second stage, to address the reduction in data utility caused by noise, a novel 2-dimensional structural entropy minimization algorithm based on optimal subgraphs is used to detect events in the message graph. The highlight of this process is unsupervised and does not compromise differential privacy. Extensive experiments on two public datasets demonstrate that ADP-SEMEvent can achieve detection performance comparable to state-of-the-art methods while maintaining reasonable privacy budget parameters.

22.7CVApr 7, 2021Code
DG-Font: Deformable Generative Networks for Unsupervised Font Generation

Yangchen Xie, Xinyuan Chen, Li Sun et al.

Font generation is a challenging problem especially for some writing systems that consist of a large number of characters and has attracted a lot of attention in recent years. However, existing methods for font generation are often in supervised learning. They require a large number of paired data, which is labor-intensive and expensive to collect. Besides, common image-to-image translation models often define style as the set of textures and colors, which cannot be directly applied to font generation. To address these problems, we propose novel deformable generative networks for unsupervised font generation (DGFont). We introduce a feature deformation skip connection (FDSC) which predicts pairs of displacement maps and employs the predicted maps to apply deformable convolution to the low-level feature maps from the content encoder. The outputs of FDSC are fed into a mixer to generate the final results. Taking advantage of FDSC, the mixer outputs a high-quality character with a complete structure. To further improve the quality of generated images, we use three deformable convolution layers in the content encoder to learn style-invariant feature representations. Experiments demonstrate that our model generates characters in higher quality than state-of-art methods. The source code is available at https://github.com/ecnuycxie/DG-Font.

35.0SIAug 19, 2020Code
Enhancing Graph Neural Network-based Fraud Detectors against Camouflaged Fraudsters

Yingtong Dou, Zhiwei Liu, Li Sun et al.

Graph Neural Networks (GNNs) have been widely applied to fraud detection problems in recent years, revealing the suspiciousness of nodes by aggregating their neighborhood information via different relations. However, few prior works have noticed the camouflage behavior of fraudsters, which could hamper the performance of GNN-based fraud detectors during the aggregation process. In this paper, we introduce two types of camouflages based on recent empirical studies, i.e., the feature camouflage and the relation camouflage. Existing GNNs have not addressed these two camouflages, which results in their poor performance in fraud detection problems. Alternatively, we propose a new model named CAmouflage-REsistant GNN (CARE-GNN), to enhance the GNN aggregation process with three unique modules against camouflages. Concretely, we first devise a label-aware similarity measure to find informative neighboring nodes. Then, we leverage reinforcement learning (RL) to find the optimal amounts of neighbors to be selected. Finally, the selected neighbors across different relations are aggregated together. Comprehensive experiments on two real-world fraud datasets demonstrate the effectiveness of the RL algorithm. The proposed CARE-GNN also outperforms state-of-the-art GNNs and GNN-based fraud detectors. We integrate all GNN-based fraud detectors as an opensource toolbox: https://github.com/safe-graph/DGFraud. The CARE-GNN code and datasets are available at https://github.com/YingtongDou/CARE-GNN.

6.4LGJan 2, 2024
Contrastive Sequential Interaction Network Learning on Co-Evolving Riemannian Spaces

Li Sun, Junda Ye, Jiawei Zhang et al.

The sequential interaction network usually find itself in a variety of applications, e.g., recommender system. Herein, inferring future interaction is of fundamental importance, and previous efforts are mainly focused on the dynamics in the classic zero-curvature Euclidean space. Despite the promising results achieved by previous methods, a range of significant issues still largely remains open: On the bipartite nature, is it appropriate to place user and item nodes in one identical space regardless of their inherent difference? On the network dynamics, instead of a fixed curvature space, will the representation spaces evolve when new interactions arrive continuously? On the learning paradigm, can we get rid of the label information costly to acquire? To address the aforementioned issues, we propose a novel Contrastive model for Sequential Interaction Network learning on Co-Evolving RiEmannian spaces, CSINCERE. To the best of our knowledge, we are the first to introduce a couple of co-evolving representation spaces, rather than a single or static space, and propose a co-contrastive learning for the sequential interaction network. In CSINCERE, we formulate a Cross-Space Aggregation for message-passing across representation spaces of different Riemannian geometries, and design a Neural Curvature Estimator based on Ricci curvatures for modeling the space evolvement over time. Thereafter, we present a Reweighed Co-Contrast between the temporal views of the sequential network, so that the couple of Riemannian spaces interact with each other for the interaction prediction without labels. Empirical results on 5 public datasets show the superiority of CSINCERE over the state-of-the-art methods.

10.2CVMay 12, 2025
SparseMeXT Unlocking the Potential of Sparse Representations for HD Map Construction

Anqing Jiang, Jinhao Chai, Yu Gao et al.

Recent advancements in high-definition \emph{HD} map construction have demonstrated the effectiveness of dense representations, which heavily rely on computationally intensive bird's-eye view \emph{BEV} features. While sparse representations offer a more efficient alternative by avoiding dense BEV processing, existing methods often lag behind due to the lack of tailored designs. These limitations have hindered the competitiveness of sparse representations in online HD map construction. In this work, we systematically revisit and enhance sparse representation techniques, identifying key architectural and algorithmic improvements that bridge the gap with--and ultimately surpass--dense approaches. We introduce a dedicated network architecture optimized for sparse map feature extraction, a sparse-dense segmentation auxiliary task to better leverage geometric and semantic cues, and a denoising module guided by physical priors to refine predictions. Through these enhancements, our method achieves state-of-the-art performance on the nuScenes dataset, significantly advancing HD map construction and centerline detection. Specifically, SparseMeXt-Tiny reaches a mean average precision \emph{mAP} of 55.5% at 32 frames per second \emph{fps}, while SparseMeXt-Base attains 65.2% mAP. Scaling the backbone and decoder further, SparseMeXt-Large achieves an mAP of 68.9% at over 20 fps, establishing a new benchmark for sparse representations in HD map construction. These results underscore the untapped potential of sparse methods, challenging the conventional reliance on dense representations and redefining efficiency-performance trade-offs in the field.

7.1LGMay 20, 2025Code
Unsupervised Graph Clustering with Deep Structural Entropy

Jingyun Zhang, Hao Peng, Li Sun et al.

Research on Graph Structure Learning (GSL) provides key insights for graph-based clustering, yet current methods like Graph Neural Networks (GNNs), Graph Attention Networks (GATs), and contrastive learning often rely heavily on the original graph structure. Their performance deteriorates when the original graph's adjacency matrix is too sparse or contains noisy edges unrelated to clustering. Moreover, these methods depend on learning node embeddings and using traditional techniques like k-means to form clusters, which may not fully capture the underlying graph structure between nodes. To address these limitations, this paper introduces DeSE, a novel unsupervised graph clustering framework incorporating Deep Structural Entropy. It enhances the original graph with quantified structural information and deep neural networks to form clusters. Specifically, we first propose a method for calculating structural entropy with soft assignment, which quantifies structure in a differentiable form. Next, we design a Structural Learning layer (SLL) to generate an attributed graph from the original feature data, serving as a target to enhance and optimize the original structural graph, thereby mitigating the issue of sparse connections between graph nodes. Finally, our clustering assignment method (ASS), based on GNNs, learns node embeddings and a soft assignment matrix to cluster on the enhanced graph. The ASS layer can be stacked to meet downstream task requirements, minimizing structural entropy for stable clustering and maximizing node consistency with edge-based cross-entropy loss. Extensive comparative experiments are conducted on four benchmark datasets against eight representative unsupervised graph clustering baselines, demonstrating the superiority of the DeSE in both effectiveness and interpretability.

2.3SIMar 4, 2024
RCoCo: Contrastive Collective Link Prediction across Multiplex Network in Riemannian Space

Li Sun, Mengjie Li, Yong Yang et al.

Link prediction typically studies the probability of future interconnection among nodes with the observation in a single social network. More often than not, real scenario is presented as a multiplex network with common (anchor) users active in multiple social networks. In the literature, most existing works study either the intra-link prediction in a single network or inter-link prediction among networks (a.k.a. network alignment), and consider two learning tasks are independent from each other, which is still away from the fact. On the representation space, the vast majority of existing methods are built upon the traditional Euclidean space, unaware of the inherent geometry of social networks. The third issue is on the scarce anchor users. Annotating anchor users is laborious and expensive, and thus it is impractical to work with quantities of anchor users. Herein, in light of the issues above, we propose to study a challenging yet practical problem of Geometry-aware Collective Link Prediction across Multiplex Network. To address this problem, we present a novel contrastive model, RCoCo, which collaborates intra- and inter-network behaviors in Riemannian spaces. In RCoCo, we design a curvature-aware graph attention network ($κ-$GAT), conducting attention mechanism in Riemannian manifold whose curvature is estimated by the Ricci curvatures over the network. Thereafter, we formulate intra- and inter-contrastive loss in the manifolds, in which we augment graphs by exploring the high-order structure of community and information transfer on anchor users. Finally, we conduct extensive experiments with 14 strong baselines on 8 real-world datasets, and show the effectiveness of RCoCo.

7.7LGMay 6, 2023
SINCERE: Sequential Interaction Networks representation learning on Co-Evolving RiEmannian manifolds

Junda Ye, Zhongbao Zhang, Li Sun et al.

Sequential interaction networks (SIN) have been commonly adopted in many applications such as recommendation systems, search engines and social networks to describe the mutual influence between users and items/products. Efforts on representing SIN are mainly focused on capturing the dynamics of networks in Euclidean space, and recently plenty of work has extended to hyperbolic geometry for implicit hierarchical learning. Previous approaches which learn the embedding trajectories of users and items achieve promising results. However, there are still a range of fundamental issues remaining open. For example, is it appropriate to place user and item nodes in one identical space regardless of their inherent discrepancy? Instead of residing in a single fixed curvature space, how will the representation spaces evolve when new interaction occurs? To explore these issues for sequential interaction networks, we propose SINCERE, a novel method representing Sequential Interaction Networks on Co-Evolving RiEmannian manifolds. SIN- CERE not only takes the user and item embedding trajectories in respective spaces into account, but also emphasizes on the space evolvement that how curvature changes over time. Specifically, we introduce a fresh cross-geometry aggregation which allows us to propagate information across different Riemannian manifolds without breaking conformal invariance, and a curvature estimator which is delicately designed to predict global curvatures effectively according to current local Ricci curvatures. Extensive experiments on several real-world datasets demonstrate the promising performance of SINCERE over the state-of-the-art sequential interaction prediction methods.

18.2LGDec 10, 2021
A Self-supervised Mixed-curvature Graph Neural Network

Li Sun, Zhongbao Zhang, Junda Ye et al.

Graph representation learning received increasing attentions in recent years. Most of existing methods ignore the complexity of the graph structures and restrict graphs in a single constant-curvature representation space, which is only suitable to particular kinds of graph structure indeed. Additionally, these methods follow the supervised or semi-supervised learning paradigm, and thereby notably limit their deployment on the unlabeled graphs in real applications. To address these aforementioned limitations, we take the first attempt to study the self-supervised graph representation learning in the mixed-curvature spaces. In this paper, we present a novel Self-supervised Mixed-curvature Graph Neural Network (SelfMGNN). Instead of working on one single constant-curvature space, we construct a mixed-curvature space via the Cartesian product of multiple Riemannian component spaces and design hierarchical attention mechanisms for learning and fusing the representations across these component spaces. To enable the self-supervisd learning, we propose a novel dual contrastive approach. The mixed-curvature Riemannian space actually provides multiple Riemannian views for the contrastive learning. We introduce a Riemannian projector to reveal these views, and utilize a well-designed Riemannian discriminator for the single-view and cross-view contrastive learning within and across the Riemannian views. Finally, extensive experiments show that SelfMGNN captures the complicated graph structures in reality and outperforms state-of-the-art baselines.

11.1CVNov 25, 2021Code
Attribute-specific Control Units in StyleGAN for Fine-grained Image Manipulation

Rui Wang, Jian Chen, Gang Yu et al.

Image manipulation with StyleGAN has been an increasing concern in recent years.Recent works have achieved tremendous success in analyzing several semantic latent spaces to edit the attributes of the generated images.However, due to the limited semantic and spatial manipulation precision in these latent spaces, the existing endeavors are defeated in fine-grained StyleGAN image manipulation, i.e., local attribute translation.To address this issue, we discover attribute-specific control units, which consist of multiple channels of feature maps and modulation styles. Specifically, we collaboratively manipulate the modulation style channels and feature maps in control units rather than individual ones to obtain the semantic and spatial disentangled controls. Furthermore, we propose a simple yet effective method to detect the attribute-specific control units. We move the modulation style along a specific sparse direction vector and replace the filter-wise styles used to compute the feature maps to manipulate these control units. We evaluate our proposed method in various face attribute manipulation tasks. Extensive qualitative and quantitative results demonstrate that our proposed method performs favorably against the state-of-the-art methods. The manipulation results of real images further show the effectiveness of our method.

2.6CVOct 11, 2021Code
Bridging the Gap between Label- and Reference-based Synthesis in Multi-attribute Image-to-Image Translation

Qiusheng Huang, Zhilin Zheng, Xueqi Hu et al.

The image-to-image translation (I2IT) model takes a target label or a reference image as the input, and changes a source into the specified target domain. The two types of synthesis, either label- or reference-based, have substantial differences. Particularly, the label-based synthesis reflects the common characteristics of the target domain, and the reference-based shows the specific style similar to the reference. This paper intends to bridge the gap between them in the task of multi-attribute I2IT. We design the label- and reference-based encoding modules (LEM and REM) to compare the domain differences. They first transfer the source image and target label (or reference) into a common embedding space, by providing the opposite directions through the attribute difference vector. Then the two embeddings are simply fused together to form the latent code S_rand (or S_ref), reflecting the domain style differences, which is injected into each layer of the generator by SPADE. To link LEM and REM, so that two types of results benefit each other, we encourage the two latent codes to be close, and set up the cycle consistency between the forward and backward translations on them. Moreover, the interpolation between the S_rand and S_ref is also used to synthesize an extra image. Experiments show that label- and reference-based synthesis are indeed mutually promoted, so that we can have the diverse results from LEM, and high quality results with the similar style of the reference.

13.5CVSep 1, 2021
EventPoint: Self-Supervised Interest Point Detection and Description for Event-based Camera

Ze Huang, Li Sun, Cheng Zhao et al.

This paper proposes a self-supervised learned local detector and descriptor, called EventPoint, for event stream/camera tracking and registration. Event-based cameras have grown in popularity because of their biological inspiration and low power consumption. Despite this, applying local features directly to the event stream is difficult due to its peculiar data structure. We propose a new time-surface-like event stream representation method called Tencode. The event stream data processed by Tencode can obtain the pixel-level positioning of interest points while also simultaneously extracting descriptors through a neural network. Instead of using costly and unreliable manual annotation, our network leverages the prior knowledge of local feature extraction on color images and conducts self-supervised learning via homographic and spatio-temporal adaptation. To the best of our knowledge, our proposed method is the first research on event-based local features learning using a deep neural network. We provide comprehensive experiments of feature point detection and matching, and three public datasets are used for evaluation (i.e. DSEC, N-Caltech101, and HVGA ATIS Corner Dataset). The experimental findings demonstrate that our method outperforms SOTA in terms of feature point detection and description.

21.0LGApr 6, 2021
Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs

Li Sun, Zhongbao Zhang, Jiawei Zhang et al.

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling uncertainty. To bridge this gap, we propose to learn dynamic graph representation in hyperbolic space, for the first time, which aims to infer stochastic node representations. Working with hyperbolic space, we present a novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TGNN) based on a theoretically grounded time encoding approach. To model the uncertainty, we devise a hyperbolic graph variational autoencoder built upon the proposed TGNN to generate stochastic node representations of hyperbolic normal distributions. Furthermore, we introduce a reparameterisable sampling algorithm for the hyperbolic normal distribution to enable the gradient-based learning of HVGNN. Extensive experiments show that HVGNN outperforms state-of-the-art baselines on real-world datasets.

3.7CVMar 3, 2021Code
ID-Unet: Iterative Soft and Hard Deformation for View Synthesis

Mingyu Yin, Li Sun, Qingli Li

View synthesis is usually done by an autoencoder, in which the encoder maps a source view image into a latent content code, and the decoder transforms it into a target view image according to the condition. However, the source contents are often not well kept in this setting, which leads to unnecessary changes during the view translation. Although adding skipped connections, like Unet, alleviates the problem, but it often causes the failure on the view conformity. This paper proposes a new architecture by performing the source-to-target deformation in an iterative way. Instead of simply incorporating the features from multiple layers of the encoder, we design soft and hard deformation modules, which warp the encoder features to the target view at different resolutions, and give results to the decoder to complement the details. Particularly, the current warping flow is not only used to align the feature of the same resolution, but also as an approximation to coarsely deform the high resolution feature. Then the residual flow is estimated and applied in the high resolution, so that the deformation is built up in the coarse-to-fine fashion. To better constrain the model, we synthesize a rough target view image based on the intermediate flows and their warped features. The extensive ablation studies and the final results on two different data sets show the effectiveness of the proposed model.

6.5CVOct 29, 2019
Disentangling the Spatial Structure and Style in Conditional VAE

Ziye Zhang, Li Sun, Zhilin Zheng et al.

This paper aims to disentangle the latent space in cVAE into the spatial structure and the style code, which are complementary to each other, with one of them $z_s$ being label relevant and the other $z_u$ irrelevant. The generator is built by a connected encoder-decoder and a label condition mapping network. Depending on whether the label is related with the spatial structure, the output $z_s$ from the condition mapping network is used either as a style code or a spatial structure code. The encoder provides the label irrelevant posterior from which $z_u$ is sampled. The decoder employs $z_s$ and $z_u$ in each layer by adaptive normalization like SPADE or AdaIN. Extensive experiments on two datasets with different types of labels show the effectiveness of our method.

16.7CVDec 22, 2018
Disentangling Latent Space for VAE by Label Relevant/Irrelevant Dimensions

Zhilin Zheng, Li Sun

VAE requires the standard Gaussian distribution as a prior in the latent space. Since all codes tend to follow the same prior, it often suffers the so-called "posterior collapse". To avoid this, this paper introduces the class specific distribution for the latent code. But different from CVAE, we present a method for disentangling the latent space into the label relevant and irrelevant dimensions, $\bm{\mathrm{z}}_s$ and $\bm{\mathrm{z}}_u$, for a single input. We apply two separated encoders to map the input into $\bm{\mathrm{z}}_s$ and $\bm{\mathrm{z}}_u$ respectively, and then give the concatenated code to the decoder to reconstruct the input. The label irrelevant code $\bm{\mathrm{z}}_u$ represent the common characteristics of all inputs, hence they are constrained by the standard Gaussian, and their encoder is trained in amortized variational inference way, like VAE. While $\bm{\mathrm{z}}_s$ is assumed to follow the Gaussian mixture distribution in which each component corresponds to a particular class. The parameters for the Gaussian components in $\bm{\mathrm{z}}_s$ encoder are optimized by the label supervision in a global stochastic way. In theory, we show that our method is actually equivalent to adding a KL divergence term on the joint distribution of $\bm{\mathrm{z}}_s$ and the class label $c$, and it can directly increase the mutual information between $\bm{\mathrm{z}}_s$ and the label $c$. Our model can also be extended to GAN by adding a discriminator in the pixel domain so that it produces high quality and diverse images.