Population synthesis is concerned with the generation of synthetic yet realistic representations of populations. It is a fundamental problem in the modeling of transport where the synthetic populations of micro-agents represent a key input to most agent-based models. In this paper, a new methodological framework for how to 'grow' pools of micro-agents is presented. The model framework adopts a deep generative modeling approach from machine learning based on a Variational Autoencoder (VAE). Compared to the previous population synthesis approaches, including Iterative Proportional Fitting (IPF), Gibbs sampling and traditional generative models such as Bayesian Networks or Hidden Markov Models, the proposed method allows fitting the full joint distribution for high dimensions. The proposed methodology is compared with a conventional Gibbs sampler and a Bayesian Network by using a large-scale Danish trip diary. It is shown that, while these two methods outperform the VAE in the low-dimensional case, they both suffer from scalability issues when the number of modeled attributes increases. It is also shown that the Gibbs sampler essentially replicates the agents from the original sample when the required conditional distributions are estimated as frequency tables. In contrast, the VAE allows addressing the problem of sampling zeros by generating agents that are virtually different from those in the original data but have similar statistical properties. The presented approach can support agent-based modeling at all levels by enabling richer synthetic populations with smaller zones and more detailed individual characteristics.
Agent-based transportation modelling has become the standard to simulate travel behaviour, mobility choices and activity preferences using disaggregate travel demand data for entire populations, data that are not typically readily available. Various methods have been proposed to synthesize population data for this purpose. We present a Composite Travel Generative Adversarial Network (CTGAN), a novel deep generative model to estimate the underlying joint distribution of a population, that is capable of reconstructing composite synthetic agents having tabular (e.g. age and sex) as well as sequen…
Generative adversarial networks (GANs) are an expressive class of neural generative models with tremendous success in modeling high-dimensional continuous measures. In this paper, we present a scalable method for unbalanced optimal transport (OT) based on the generative-adversarial framework. We formulate unbalanced OT as a problem of simultaneously learning a transport map and a scaling factor that push a source measure to a target measure in a cost-optimal manner. In addition, we propose an algorithm for solving this problem based on stochastic alternating gradient updates, similar in practi…
In this paper, we propose Generative Adversarial Network (GAN) architectures that use Capsule Networks for image-synthesis. Based on the principal of positional-equivariance of features, Capsule Network's ability to encode spatial relationships between the features of the image helps it become a more powerful critic in comparison to Convolutional Neural Networks (CNNs) used in current architectures for image synthesis. Our proposed GAN architectures learn the data manifold much faster and therefore, synthesize visually accurate images in significantly lesser number of training samples and trai…
Bayesian Generative Adversarial Networks via Gaussian Approximation for Tabular Data Synthesis
Department of Social Statistics, The University of Manchester（社会统计系，曼彻斯特大学）；Alliance Manchester Business School, The University of Manchester（曼彻斯特商业联盟学院，曼彻斯特大学）
University of New South Wales（新南威尔士大学）；Fudan University（复旦大学）；University of Technology, Sydney（悉尼科技大学）
We propose a probabilistic framework for modelling and exploring the latent structure of relational data. Given feature information for the nodes in a network, the scalable deep generative relational model (SDREM) builds a deep network architecture that can approximate potential nonlinear mappings between nodes' feature information and the nodes' latent representations. Our contribution is two-fold: (1) We incorporate high-order neighbourhood structure information to generate the latent representations at each node, which vary smoothly over the network. (2) Due to the Dirichlet random variable…
Yonsei University（延世大学）；Kakao Corp.（Kakao公司）；Linger Studio Corp.（Linger工作室公司）
Time series synthesis is an important research topic in the field of deep learning, which can be used for data augmentation. Time series data types can be broadly classified into regular or irregular. However, there are no existing generative models that show good performance for both types without any model changes. Therefore, we present a general purpose model capable of synthesizing regular and irregular time series data. To our knowledge, we are the first designing a general purpose time series synthesis model, which is one of the most challenging settings for time series synthesis. To thi…
Footsteps are among the most ubiquitous sound effects in multimedia applications. There is substantial research into understanding the acoustic features and developing synthesis models for footstep sound effects. In this paper, we present a first attempt at adopting neural synthesis for this task. We implemented two GAN-based architectures and compared the results with real recordings as well as six traditional sound synthesis methods. Our architectures reached realism scores as high as recorded samples, showing encouraging results for the task at hand.
Prior works about text-to-image synthesis typically concatenated the sentence embedding with the noise vector, while the sentence embedding and the noise vector are two different factors, which control the different aspects of the generation. Simply concatenating them will entangle the latent factors and encumber the generative model. In this paper, we attempt to decompose these two factors and propose Factor Decomposed Generative Adversarial Networks~(FDGAN). To achieve this, we firstly generate images from the noise vector and then apply the sentence embedding in the normalization layer for …
Samsung AI Center Moscow（三星莫斯科人工智能中心）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；National Research University Higher School of Economics（高等经济大学）
We propose a novel multi-texture synthesis model based on generative adversarial networks (GANs) with a user-controllable mechanism. The user control ability allows to explicitly specify the texture which should be generated by the model. This property follows from using an encoder part which learns a latent representation for each texture from the dataset. To ensure a dataset coverage, we use an adversarial loss function that penalizes for incorrect reproductions of a given texture. In experiments, we show that our model can learn descriptive texture manifolds for large datasets and from raw …
Future climate change scenarios are usually hypothesized using simulations from weather generators. However, there only a few works comparing and evaluating promising deep learning models for weather generation against classical approaches. This study shows preliminary results making such evaluations for the multisite precipitation synthesis task. We compared two open-source weather generators: IBMWeathergen (an extension of the Weathergen library) and RGeneratePrec, and two deep generative models: GAN and VAE, on a variety of metrics. Our preliminary results can serve as a guide for improving…
Generative Adversarial Networks (GAN) are known to produce synthetic data that are difficult to discern from real ones by humans. In this paper we present an approach to use GAN to produce realistically looking ECG signals. We utilize them to train and evaluate a denoising autoencoder that achieves state-of-the-art filtering quality for ECG signals. It is demonstrated that generated data improves the model performance compared to the model trained on real data only. We also investigate an effect of transfer learning by reusing trained discriminator network for denoising model.
Technion - Israel Institute of Technology（以色列理工学院）；Google Research（谷歌研究院）
Generating training examples for supervised tasks is a long sought after goal in AI. We study the problem of heart signal electrocardiogram (ECG) synthesis for improved heartbeat classification. ECG synthesis is challenging: the generation of training examples for such biological-physiological systems is not straightforward, due to their dynamic nature in which the various parts of the system interact in complex ways. However, an understanding of these dynamics has been developed for years in the form of mathematical process simulators. We study how to incorporate this knowledge into the gener…
Several recent work on speech synthesis have employed generative adversarial networks (GANs) to produce raw waveforms. Although such methods improve the sampling efficiency and memory usage, their sample quality has not yet reached that of autoregressive and flow-based generative models. In this work, we propose HiFi-GAN, which achieves both efficient and high-fidelity speech synthesis. As speech audio consists of sinusoidal signals with various periods, we demonstrate that modeling periodic patterns of an audio is crucial for enhancing sample quality. A subjective human evaluation (mean opini…
Massachusetts Institute of Technology（麻省理工学院）；Universiti Teknologi PETRONAS（马来西亚石油科技大学）
Modern machine learning techniques, such as deep neural networks, are transforming many disciplines ranging from image recognition to language understanding, by uncovering patterns in big data and making accurate predictions. They have also shown promising results for synthesizing new designs, which is crucial for creating products and enabling innovation. Generative models, including generative adversarial networks (GANs), have proven to be effective for design synthesis with applications ranging from product design to metamaterial design. These automated computational design methods can supp…
Skin cancer is by far the most common type of cancer. Early detection is the key to increase the chances for successful treatment significantly. Currently, Deep Neural Networks are the state-of-the-art results on automated skin cancer classification. To push the results further, we need to address the lack of annotated data, which is expensive and require much effort from specialists. To bypass this problem, we propose using Generative Adversarial Networks for generating realistic synthetic skin lesion images. To the best of our knowledge, our results are the first to show visually-appealing s…
In this paper, we propose a generative model which learns the relationship between language and human action in order to generate a human action sequence given a sentence describing human behavior. The proposed generative model is a generative adversarial network (GAN), which is based on the sequence to sequence (SEQ2SEQ) model. Using the proposed generative network, we can synthesize various actions for a robot or a virtual agent using a text encoder recurrent neural network (RNN) and an action decoder RNN. The proposed generative network is trained from 29,770 pairs of actions and sentence a…
Renmin University of China（中国人民大学）；Tsinghua University（清华大学）
The proliferation of big data has brought an urgent demand for privacy-preserving data publishing. Traditional solutions to this demand have limitations on effectively balancing the tradeoff between privacy and utility of the released data. Thus, the database community and machine learning community have recently studied a new problem of relational data synthesis using generative adversarial networks (GAN) and proposed various algorithms. However, these algorithms are not compared under the same framework and thus it is hard for practitioners to understand GAN's benefits and limitations. To br…
Department of Information Engineering, The Chinese University of Hong Kong（香港中文大学信息工程学系）
Despite the success of Generative Adversarial Networks (GANs) in image synthesis, there lacks enough understanding on what generative models have learned inside the deep generative representations and how photo-realistic images are able to be composed of the layer-wise stochasticity introduced in recent GANs. In this work, we show that highly-structured semantic hierarchy emerges as variation factors from synthesizing scenes from the generative representations in state-of-the-art GAN models, like StyleGAN and BigGAN. By probing the layer-wise representations with a broad set of semantics at di…
The impacts of new real estate developments are strongly associated to its population distribution (types and compositions of households, incomes, social demographics) conditioned on aspects such as dwelling typology, price, location, and floor level. This paper presents a Machine Learning based method to model the population distribution of upcoming developments of new buildings within larger neighborhood/condo settings. We use a real data set from Ecopark Township, a real estate development project in Hanoi, Vietnam, where we study two machine learning algorithms from the deep generative mod…
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；Shenzhen University（深圳大学）；Central South University（中南大学）；Harbin Engineering University（哈尔滨工程大学）
Fusing multi-modality medical images, such as MR and PET, can provide various anatomical or functional information about human body. But PET data is always unavailable due to different reasons such as cost, radiation, or other limitations. In this paper, we propose a 3D end-to-end synthesis network, called Bidirectional Mapping Generative Adversarial Networks (BMGAN), where image contexts and latent vector are effectively used and jointly optimized for brain MR-to-PET synthesis. Concretely, a bidirectional mapping mechanism is designed to embed the semantic information of PET images into the h…
Instituto de Telecomunicações（电信研究所）；Universidade da Beira Interior（贝拉内陆大学）；DeepNeuronic；NOVA LINCS（新里斯本大学计算机科学实验室）；C4-Cloud Computing Competence Center（C4云计算能力中心）
Synthesising the spatial and temporal dynamics of the human body skeleton remains a challenging task, not only in terms of the quality of the generated shapes, but also of their diversity, particularly to synthesise realistic body movements of a specific action (action conditioning). In this paper, we propose Kinetic-GAN, a novel architecture that leverages the benefits of Generative Adversarial Networks and Graph Convolutional Networks to synthesise the kinetics of the human body. The proposed adversarial architecture can condition up to 120 different actions over local and global body moveme…
Unlike human speakers, typical text-to-speech (TTS) systems are unable to produce multiple distinct renditions of a given sentence. This has previously been addressed by adding explicit external control. In contrast, generative models are able to capture a distribution over multiple renditions and thus produce varied renditions using sampling. Typical neural TTS models learn the average of the data because they minimise mean squared error. In the context of prosody, taking the average produces flatter, more boring speech: an "average prosody". A generative model that can synthesise multiple pr…
Sony Computer Science Laboratories（索尼计算机科学实验室）；National Institute of Applied Sciences, Lyon（里昂国立应用科学学院）
In contemporary popular music production, drum sound design is commonly performed by cumbersome browsing and processing of pre-recorded samples in sound libraries. One can also use specialized synthesis hardware, typically controlled through low-level, musically meaningless parameters. Today, the field of Deep Learning offers methods to control the synthesis process via learned high-level features and allows generating a wide variety of sounds. In this paper, we present DrumGAN VST, a plugin for synthesizing drum sounds using a Generative Adversarial Network. DrumGAN VST operates on 44.1 kHz s…
Computer Vision Center (CVC)（计算机视觉中心）；Universitat Autònoma de Barcelona（巴塞罗那自治大学）
Generative Adversarial Networks have long since revolutionized the world of computer vision and, tied to it, the world of art. Arduous efforts have gone into fully utilizing and stabilizing training so that outputs of the Generator network have the highest possible fidelity, but little has gone into using the Discriminator after training is complete. In this work, we propose to use the latter and show a way to use the features it has learned from the training dataset to both alter an image and generate one from scratch. We name this method Discriminator Dreaming, and the full code can be found…
A Review of Human Emotion Synthesis Based on Generative Technology
Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ)（广东省人工智能与数字经济实验室（深圳））；Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件学院）；MICS Thrust, The Hong Kong University of Science and Technology (GZ)（香港科技大学（广州）MICS学科）；School of Computer Science and Engineering, University of Electronic Science and Technology of China（电子科技大学计算机科学与工程学院）；Shenzhen Institute for Advanced Study, University of Electronic Science and Technology of China（电子科技大学深圳高等研究院）；School of Information Technology, Carleton University（卡尔顿大学信息技术学院）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present an empirical evaluation of fMRI data augmentation via synthesis. For synthesis we use generative mod-els trained on real neuroimaging data to produce novel task-dependent functional brain images. Analyzed generative mod-els include classic approaches such as the Gaussian mixture model (GMM), and modern implicit generative models such as the generative adversarial network (GAN) and the variational auto-encoder (VAE). In particular, the proposed GAN and VAE models utilize 3-dimensional convolutions, which enables modeling of high-dimensional brain image tensors with structured spatial…
Generative Semantic Communication for Text-to-Speech Synthesis
Shenzhen Future Network of Intelligence Institute（深圳未来网络智能研究院）；Guangdong Provincial Key Laboratory of Future Networks of Intelligence, The Chinese University of Hong Kong (Shenzhen)（广东省未来网络智能重点实验室，香港中文大学（深圳））；School of Automation, Central South University（中南大学自动化学院）
Deep learning is a popular and powerful tool in computed tomography (CT) image processing such as organ segmentation, but its requirement of large training datasets remains a challenge. Even though there is a large anatomical variability for children during their growth, the training datasets for pediatric CT scans are especially hard to obtain due to risks of radiation to children. In this paper, we propose a method to conditionally synthesize realistic pediatric CT images using a new auxiliary classifier generative adversarial network (ACGAN) architecture by taking age information into accou…
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Massachusetts Institute of Technology（麻省理工学院）；Univ. Lille（里尔大学）；Inserm（法国国家健康与医学研究院）；CHU Lille（里尔大学医院）
Image synthesis via Generative Adversarial Networks (GANs) of three-dimensional (3D) medical images has great potential that can be extended to many medical applications, such as, image enhancement and disease progression modeling. However, current GAN technologies for 3D medical image synthesis need to be significantly improved to be readily adapted to real-world medical problems. In this paper, we extend the state-of-the-art StyleGAN2 model, which natively works with two-dimensional images, to enable 3D image synthesis. In addition to the image synthesis, we investigate the controllability a…
Recent studies have shown that text-to-speech synthesis quality can be improved by using glottal vocoding. This refers to vocoders that parameterize speech into two parts, the glottal excitation and vocal tract, that occur in the human speech production apparatus. Current glottal vocoders generate the glottal excitation waveform by using deep neural networks (DNNs). However, the squared error-based training of the present glottal excitation models is limited to generating conditional average waveforms, which fails to capture the stochastic variation of the waveforms. As a result, shaped noise …
Sony CSL（索尼计算机科学实验室）；CentraleSupélec（巴黎中央理工-高等电力学院）
In this paper, we propose a novel score-base generative model for unconditional raw audio synthesis. Our proposal builds upon the latest developments on diffusion process modeling with stochastic differential equations, which already demonstrated promising results on image generation. We motivate novel heuristics for the choice of the diffusion processes better suited for audio generation, and consider the use of a conditional U-Net to approximate the score function. While previous approaches on diffusion models on audio were mainly designed as speech vocoders in medium resolution, our method …
Universitat de Barcelona（巴塞罗那大学）；University of Arkansas for Medical Sciences（阿肯色医科大学）
Synthetic data generated by generative models can enhance the performance and capabilities of data-hungry deep learning models in medical imaging. However, there is (1) limited availability of (synthetic) datasets and (2) generative models are complex to train, which hinders their adoption in research and clinical applications. To reduce this entry barrier, we propose medigan, a one-stop shop for pretrained generative models implemented as an open-source framework-agnostic Python library. medigan allows researchers and developers to create, increase, and domain-adapt their training data in jus…
Friedrich-Alexander Universität Erlangen-Nürnberg（弗里德里希-亚历山大大学埃尔兰根-纽伦堡分校）；Technical University of Applied Sciences Amberg-Weiden（安贝格-魏登应用技术大学）；Siemens Healthcare GmbH（西门子医疗有限公司）
A Magnetic Resonance Imaging (MRI) exam typically consists of the acquisition of multiple MR pulse sequences, which are required for a reliable diagnosis. Each sequence can be parameterized through multiple acquisition parameters affecting MR image contrast, signal-to-noise ratio, resolution, or scan time. With the rise of generative deep learning models, approaches for the synthesis of MR images are developed to either synthesize additional MR contrasts, generate synthetic data, or augment existing data for AI training. However, current generative approaches for the synthesis of MR images are…
Significant strides have been made toward designing better generative models in recent years. Despite this progress, however, state-of-the-art approaches are still largely unable to capture complex global structure in data. For example, images of buildings typically contain spatial patterns such as windows repeating at regular intervals; state-of-the-art generative methods can't easily reproduce these structures. We propose to address this problem by incorporating programs representing global structure into the generative model---e.g., a 2D for-loop may represent a configuration of windows. Fu…
Machine learning approaches now achieve impressive generation capabilities in numerous domains such as image, audio or video. However, most training \& evaluation frameworks revolve around the idea of strictly modelling the original data distribution rather than trying to extrapolate from it. This precludes the ability of such models to diverge from the original distribution and, hence, exhibit some creative traits. In this paper, we propose various perspectives on how this complicated goal could ever be achieved, and provide preliminary results on our novel training objective called \textit{B…
We propose a framework for synthesis of geological images based on an exemplar image. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum mean discrepancy. To enable fast synthesis, we train a generative neural network in an offline phase to sample realizations efficiently during deployment, while also providing a parametrization of the synthesis process. We assess the framework on a classical binary image represent…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；OpenAI
A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation an…
Scalability in terms of object density in a scene is a primary challenge in unsupervised sequential object-oriented representation learning. Most of the previous models have been shown to work only on scenes with a few objects. In this paper, we propose SCALOR, a probabilistic generative world model for learning SCALable Object-oriented Representation of a video. With the proposed spatially-parallel attention and proposal-rejection mechanisms, SCALOR can deal with orders of magnitude larger numbers of objects compared to the previous state-of-the-art models. Additionally, we introduce a backgr…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are structurally similar to real networks. An important research problem is to identify the generative model that best fits to a target network. In this paper, we investigate this problem and our goal is to select the model that is able to generate graphs similar to a given network instance. By the means of generating synthetic networks with seven outstanding generativ…
Harvard Data Science Initiative（哈佛数据科学倡议）；Harvard University（哈佛大学）
Uncertainty quantification has been a core of the statistical machine learning, but its computational bottleneck has been a serious challenge for both Bayesians and frequentists. We propose a model-based framework in quantifying uncertainty, called predictive-matching Generative Parameter Sampler (GPS). This procedure considers an Uncertainty Quantification (UQ) distribution on the targeted parameter, which matches the corresponding predictive distribution to the observed data. This framework adopts a hierarchical modeling perspective such that each observation is modeled by an individual para…
Generative adversarial networks (GANs) are a recent approach to train generative models of data, which have been shown to work particularly well on image data. In the current paper we introduce a new model for texture synthesis based on GAN learning. By extending the input noise distribution space from a single vector to a whole spatial tensor, we create an architecture with properties well suited to the task of texture synthesis, which we call spatial GAN (SGAN). To our knowledge, this is the first successful completely data-driven texture synthesis method based on GANs. Our method has the fo…
Sound modelling is the process of developing algorithms that generate sound under parametric control. There are a few distinct approaches that have been developed historically including modelling the physics of sound production and propagation, assembling signal generating and processing elements to capture acoustic features, and manipulating collections of recorded audio samples. While each of these approaches has been able to achieve high-quality synthesis and interaction for specific applications, they are all labour-intensive and each comes with its own challenges for designing arbitrary c…
In this paper we propose WaveGlow: a flow-based network capable of generating high quality speech from mel-spectrograms. WaveGlow combines insights from Glow and WaveNet in order to provide fast, efficient and high-quality audio synthesis, without the need for auto-regression. WaveGlow is implemented using only a single network, trained using only a single cost function: maximizing the likelihood of the training data, which makes the training procedure simple and stable. Our PyTorch implementation produces audio samples at a rate of more than 500 kHz on an NVIDIA V100 GPU. Mean Opinion Scores …
Aalto University（阿尔托大学）；National Institute of Informatics（国立信息学研究所）；NTT Communication Science Laboratories, NTT Corporation（NTT公司NTT通信科学实验室）
This paper proposes a method for generating speech from filterbank mel frequency cepstral coefficients (MFCC), which are widely used in speech applications, such as ASR, but are generally considered unusable for speech synthesis. First, we predict fundamental frequency and voicing information from MFCCs with an autoregressive recurrent neural net. Second, the spectral envelope information contained in MFCCs is converted to all-pole filters, and a pitch-synchronous excitation model matched to these filters is trained. Finally, we introduce a generative adversarial network -based noise model to …
Rutgers University（罗格斯大学）；Lehigh University（理海大学）；The Chinese University of Hong Kong（香港中文大学）；University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）
Although Generative Adversarial Networks (GANs) have shown remarkable success in various tasks, they still face challenges in generating high quality images. In this paper, we propose Stacked Generative Adversarial Networks (StackGAN) aiming at generating high-resolution photo-realistic images. First, we propose a two-stage generative adversarial network architecture, StackGAN-v1, for text-to-image synthesis. The Stage-I GAN sketches the primitive shape and colors of the object based on given text description, yielding low-resolution images. The Stage-II GAN takes Stage-I results and text desc…
Aalto University（阿尔托大学）；National Institute of Informatics（国立信息学研究所）；University of Edinburgh（爱丁堡大学）
The state-of-the-art in text-to-speech synthesis has recently improved considerably due to novel neural waveform generation methods, such as WaveNet. However, these methods suffer from their slow sequential inference process, while their parallel versions are difficult to train and even more expensive computationally. Meanwhile, generative adversarial networks (GANs) have achieved impressive results in image generation and are making their way into audio applications; parallel inference is among their lucrative properties. By adopting recent advances in GAN training techniques, this investigat…
We provide a bridge between generative modeling in the Machine Learning community and simulated physical processes in High Energy Particle Physics by applying a novel Generative Adversarial Network (GAN) architecture to the production of jet images -- 2D representations of energy depositions from particles interacting with a calorimeter. We propose a simple architecture, the Location-Aware Generative Adversarial Network, that learns to produce realistic radiation patterns from simulated high energy particle collisions. The pixel intensities of GAN-generated images faithfully span over many ord…
