Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive conditions that guarantee eventual stationarity of the generator when it is trained with gradient descent, conditions that must be satisfied by the divergence that is minimized by the GAN and the generator's architecture. We find that existing GAN variants satisfy some, but not all, of these conditions. Using tools from convex analysis, optimal transport, and reproducing kernels, we construct a GAN that fulfills these conditions simultaneously. In the process, we explain and clarify the need for various existing GAN stabilization techniques, including Lipschitz constraints, gradient penalties, and smooth activation functions.
Google Brain（谷歌大脑）；Georgia Institute of Technology（佐治亚理工学院）；University College London（伦敦大学学院）；University of Illinois at Urbana Champaign（伊利诺伊大学厄巴纳-香槟分校）
We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that avoids computation of the partition function. This technique also allows the development of a flexible sampling strategy that amortizes the cost of Monte-Carlo sampling in the inference stage. The resulting estimator can be easily generalized to kernel conditional exponential families. We establish a connection between kernel exponential family estimation and M…
The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to no cost of computational overhead added. In this article, we study a minibatch variant of SPP, namely M-SPP, for solving convex composite risk minimization problems. The core contribution is a set of novel excess risk bounds of M-SPP derived through the lens of algorithmic stability theory. Particularly under smoothness and quadratic growth conditions, we s…
The multiplicative structure of parameters and input data in the first layer of neural networks is explored to build connection between the landscape of the loss function with respect to parameters and the landscape of the model function with respect to input data. By this connection, it is shown that flat minima regularize the gradient of the model function, which explains the good generalization performance of flat minima. Then, we go beyond the flatness and consider high-order moments of the gradient noise, and show that Stochastic Gradient Descent (SGD) tends to impose constraints on these…
Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions on the boundedness of gradients, strong smoothness and convexity of loss functions. In this paper, we provide a fine-grained analysis of stability and generalization for SGD by substantially relaxing these assumptions. Firstly, we establish stability and generalization for SGD by removing the existing bounded gradient assumptions. The key idea is the introd…
Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems that are prone to the exploding gradient problem. Despite its widespread popularity, the convergence properties of the gradient clipping heuristic are poorly understood, especially for stochastic problems. This paper establishes both qualitative and quantitative convergence results of the clipped stochastic (sub)gradient method (SGD) for non-smooth convex f…
On the Interaction of Batch Noise, Adaptivity, and Compression, under $(L_0,L_1)$-Smoothness: An SDE Approach
University of Basel（巴塞尔大学）；University of Oslo（奥斯陆大学）；MBZUAI（马克斯·普朗克智能系统研究所）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；ELLIS Institute Tübingen（图宾根ELLIS研究所）；Tübingen AI Center（图宾根人工智能中心）
Despite the growing prominence of generative adversarial networks (GANs), optimization in GANs is still a poorly understood topic. In this paper, we analyze the "gradient descent" form of GAN optimization i.e., the natural setting where we simultaneously take small gradient steps in both generator and discriminator parameters. We show that even though GAN optimization does not correspond to a convex-concave game (even for simple parameterizations), under proper conditions, equilibrium points of this optimization procedure are still \emph{locally asymptotically stable} for the traditional GAN f…
The field of deep generative modeling is dominated by generative adversarial networks (GANs). However, the training of GANs often lacks stability, fails to converge, and suffers from model collapse. It takes an assortment of tricks to solve these problems, which may be difficult to understand for those seeking to apply generative modeling. Instead, we propose two novel generative autoencoders, AE-OTtrans and AE-OTgen, which rely on optimal transport instead of adversarial training. AE-OTtrans and AEOTgen, unlike VAE and WAE, preserve the manifold of the data; they do not force the latent distr…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Tencent AI Lab（腾讯人工智能实验室）；Shenzhen Research Institute of Big Data（深圳大数据研究院）
In adversarial machine learning, deep neural networks can fit the adversarial examples on the training dataset but have poor generalization ability on the test set. This phenomenon is called robust overfitting, and it can be observed when adversarially training neural nets on common datasets, including SVHN, CIFAR-10, CIFAR-100, and ImageNet. In this paper, we study the robust overfitting issue of adversarial training by using tools from uniform stability. One major challenge is that the outer function (as a maximization of the inner function) is nonsmooth, so the standard technique (e.g., har…
We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimization. We derive stability bounds for both convex and non-convex optimization under standard Lipschitz and smoothness assumptions. Applying our results to the convex case, we provide new insights for why multiple epochs of stochastic gradient methods generalize well in practice. In…
École de Technologie Supérieure (ÉTS)（高等技术学院）；Université du Québec（魁北克大学）
In this paper we address the instability issue of generative adversarial network (GAN) by proposing a new similarity metric in unitary space of Schur decomposition for 2D representations of audio and speech signals. We show that encoding departure from normality computed in this vector space into the generator optimization formulation helps to craft more comprehensive spectrograms. We demonstrate the effectiveness of binding this metric for enhancing stability in training with less mode collapse compared to baseline GANs. Experimental results on subsets of UrbanSound8k and Mozilla common voice…
Generative Adversarial Networks (GANs) are one of the most popular tools for learning complex high dimensional distributions. However, generalization properties of GANs have not been well understood. In this paper, we analyze the generalization of GANs in practical settings. We show that discriminators trained on discrete datasets with the original GAN loss have poor generalization capability and do not approximate the theoretically optimal discriminator. We propose a zero-centered gradient penalty for improving the generalization of the discriminator by pushing it toward the optimal discrimin…
University of Birmingham（伯明翰大学）；State University of New York at Albany（纽约州立大学奥尔巴尼分校）；The University of Iowa（爱荷华大学）
Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the convergence behavior of their stochastic gradient-type algorithms. In contrast, there is relatively little work on their generalization, i.e., how the learning models built from training examples would behave on test examples. In this paper, we provide a comprehensive generalization analysis of stochastic gradient methods for minimax problems under both conve…
This paper studies the distribution estimation of contaminated data by the MoM-GAN method, which combines generative adversarial net (GAN) and median-of-mean (MoM) estimation. We use a deep neural network (DNN) with a ReLU activation function to model the generator and discriminator of the GAN. Theoretically, we derive a non-asymptotic error bound for the DNN-based MoM-GAN estimator measured by integral probability metrics with the $b$-smoothness Hölder class. The error bound decreases essentially as $n^{-b/p}\vee n^{-1/2}$, where $n$ and $p$ are the sample size and the dimension of input data…
We describe a new training methodology for generative adversarial networks. The key idea is to grow both the generator and discriminator progressively: starting from a low resolution, we add new layers that model increasingly fine details as training progresses. This both speeds the training up and greatly stabilizes it, allowing us to produce images of unprecedented quality, e.g., CelebA images at 1024^2. We also propose a simple way to increase the variation in generated images, and achieve a record inception score of 8.80 in unsupervised CIFAR10. Additionally, we describe several implementa…
Lipschitz continuity recently becomes popular in generative adversarial networks (GANs). It was observed that the Lipschitz regularized discriminator leads to improved training stability and sample quality. The mainstream implementations of Lipschitz continuity include gradient penalty and spectral normalization. In this paper, we demonstrate that gradient penalty introduces undesired bias, while spectral normalization might be over restrictive. We accordingly propose a new method which is efficient and unbiased. Our experiments verify our analysis and show that the proposed method is able to …
University of Copenhagen（哥本哈根大学）；IT University of Copenhagen（哥本哈根信息技术大学）
Generative Adversial Networks (GANs) have made a major impact in computer vision and machine learning as generative models. Wasserstein GANs (WGANs) brought Optimal Transport (OT) theory into GANs, by minimizing the $1$-Wasserstein distance between model and data distributions as their objective function. Since then, WGANs have gained considerable interest due to their stability and theoretical framework. We contribute to the WGAN literature by introducing the family of $(q,p)$-Wasserstein GANs, which allow the use of more general $p$-Wasserstein metrics for $p\geq 1$ in the GAN learning proce…
University of Maryland, College Park（马里兰大学帕克分校）；Stanford University（斯坦福大学）
Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. In this paper, we aim to provide an understanding of some of the basic issues surrounding GANs including their formulation, generalization and stability on a simple benchmark where the data has a high-dimensional Gaussian distribution. Even in this simple benchmark, the GAN problem has not been well-understood as we observe that existing state-of-the-art GAN architectures may fail to learn a proper generative distribution owing to (1) stability issues (i.e., convergence to bad local solu…
Generative Adversarial Networks (GANs) are a powerful class of generative models. Despite their successes, the most appropriate choice of a GAN network architecture is still not well understood. GAN models for image synthesis have adopted a deep convolutional network architecture, which eliminates or minimizes the use of fully connected and pooling layers in favor of convolution layers in the generator and discriminator of GANs. In this paper, we demonstrate that a convolution network architecture utilizing deep fully connected layers and pooling layers can be more effective than the tradition…
Spectral normalization (SN) is a widely-used technique for improving the stability and sample quality of Generative Adversarial Networks (GANs). However, there is currently limited understanding of why SN is effective. In this work, we show that SN controls two important failure modes of GAN training: exploding and vanishing gradients. Our proofs illustrate a (perhaps unintentional) connection with the successful LeCun initialization. This connection helps to explain why the most popular implementation of SN for GANs requires no hyper-parameter tuning, whereas stricter implementations of SN ha…
Rutgers University（罗格斯大学）；University of Patras（帕特雷大学）
We are interested in the design of generative networks. The training of these mathematical structures is mostly performed with the help of adversarial (min-max) optimization problems. We propose a simple methodology for constructing such problems assuring, at the same time, consistency of the corresponding solution. We give characteristic examples developed by our method, some of which can be recognized from other applications, and some are introduced here for the first time. We present a new metric, the likelihood ratio, that can be employed online to examine the convergence and stability dur…
University of Utah（犹他大学）；Scientific Computing and Imaging Institute（科学计算与成像研究所）
Generative adversarial networks (GANs) have proven effective in modeling distributions of high-dimensional data. However, their training instability is a well-known hindrance to convergence, which results in practical challenges in their applications to novel data. Furthermore, even when convergence is reached, GANs can be affected by mode collapse, a phenomenon for which the generator learns to model only a small part of the target distribution, disregarding the vast majority of the data manifold or distribution. This paper addresses these challenges by introducing SetGAN, an adversarial arch…
Generative adversarial networks are used to generate images but still their convergence properties are not well understood. There have been a few studies who intended to investigate the stability properties of GANs as a dynamical system. This short writing can be seen in that direction. Among the proposed methods for stabilizing training of GANs, ß-GAN was the first who proposed a complete annealing strategy to change high-level conditions of the GAN objective. In this note, we show by a simple example how annealing strategy works in GANs. The theoretical analysis is supported by simple simula…
Dalian University of Technology（大连理工大学）；The University of Hong Kong（香港大学）
Though recent research has achieved remarkable progress in generating realistic images with generative adversarial networks (GANs), the lack of training stability is still a lingering concern of most GANs, especially on high-resolution inputs and complex datasets. Since the randomly generated distribution can hardly overlap with the real distribution, training GANs often suffers from the gradient vanishing problem. A number of approaches have been proposed to address this issue by constraining the discriminator's capabilities using empirical techniques, like weight clipping, gradient penalty, …
We propose studying GAN training dynamics as regret minimization, which is in contrast to the popular view that there is consistent minimization of a divergence between real and generated distributions. We analyze the convergence of GAN training from this new point of view to understand why mode collapse happens. We hypothesize the existence of undesirable local equilibria in this non-convex game to be responsible for mode collapse. We observe that these local equilibria often exhibit sharp gradients of the discriminator function around some real data points. We demonstrate that these degenera…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；ETH Zürich（苏黎世联邦理工学院）
Modern implicit generative models such as generative adversarial networks (GANs) are generally known to suffer from issues such as instability, uninterpretability, and difficulty in assessing their performance. If we see these implicit models as dynamical systems, some of these issues are caused by being unable to control their behavior in a meaningful way during the course of training. In this work, we propose a theoretically grounded method to guide the training trajectories of GANs by augmenting the GAN loss function with a kernel-based regularization term that controls local and global dis…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Tencent AI Lab（腾讯AI实验室）；Shenzhen Research Institute of Big Data（深圳大数据研究院）
Adversarial Training (AT) has been demonstrated as one of the most effective methods against adversarial examples. While most existing works focus on AT with a single type of perturbation e.g., the $\ell_\infty$ attacks), DNNs are facing threats from different types of adversarial examples. Therefore, adversarial training for multiple perturbations (ATMP) is proposed to generalize the adversarial robustness over different perturbation types (in $\ell_1$, $\ell_2$, and $\ell_\infty$ norm-bounded perturbations). However, the resulting model exhibits trade-off between different attacks. Meanwhile…
Massachusetts Institute of Technology（麻省理工学院）；IBM Research（IBM研究院）；The Chinese University of Hong Kong（香港中文大学）
Generative Adversarial Networks (GANs) have achieved impressive results for many real-world applications. As an active research topic, many GAN variants have emerged with improvements in sample quality and training stability. However, visualization and understanding of GANs is largely missing. How does a GAN represent our visual world internally? What causes the artifacts in GAN results? How do architectural choices affect GAN learning? Answering such questions could enable us to develop new insights and better models. In this work, we present an analytic framework to visualize and understand …
IBM Research（IBM研究院）；IBM T.J Watson Research Center（IBM托马斯·J·沃森研究中心）
We present an empirical investigation of a recent class of Generative Adversarial Networks (GANs) using Integral Probability Metrics (IPM) and their performance for semi-supervised learning. IPM-based GANs like Wasserstein GAN, Fisher GAN and Sobolev GAN have desirable properties in terms of theoretical understanding, training stability, and a meaningful loss. In this work we investigate how the design of the critic (or discriminator) influences the performance in semi-supervised learning. We distill three key take-aways which are important for good SSL performance: (1) the K+1 formulation, (2…
Université de Toulouse（图卢兹大学）；INP（国立理工学院）；IRIT（图卢兹计算机科学研究所）
Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibr…
MILA（蒙特利尔学习算法研究所）；University of Montréal（蒙特利尔大学）；IVADO（魁北克人工智能研究所）；MSR（微软研究院）；University of Waterloo（滑铁卢大学）；New York University（纽约大学）；CIFAR（加拿大高级研究所）
Generative adversarial networks (GANs) are a learning framework that rely on training a discriminator to estimate a measure of difference between a target and generated distributions. GANs, as normally formulated, rely on the generated samples being completely differentiable w.r.t. the generative parameters, and thus do not work for discrete data. We introduce a method for training GANs with discrete data that uses the estimated difference measure from the discriminator to compute importance weights for generated samples, thus providing a policy gradient for training the generator. The importa…
Modern implicit generative models such as generative adversarial networks (GANs) are generally known to suffer from issues such as instability, uninterpretability, and difficulty in assessing their performance. If we see these implicit models as dynamical systems, some of these issues are caused by being unable to control their behavior in a meaningful way during the course of training. In this work, we propose a theoretically grounded method to guide the training trajectories of GANs by augmenting the GAN loss function with a kernel-based regularization term that controls local and global dis…
City University of Hong Kong（香港城市大学）；The Education University of Hong Kong（香港教育大学）；Northwestern Polytechnical University（西北工业大学）；CodeHatch Corp.（CodeHatch公司）
Unsupervised learning with generative adversarial networks (GANs) has proven to be hugely successful. Regular GANs hypothesize the discriminator as a classifier with the sigmoid cross entropy loss function. However, we found that this loss function may lead to the vanishing gradients problem during the learning process. To overcome such a problem, we propose in this paper the Least Squares Generative Adversarial Networks (LSGANs) which adopt the least squares loss for both the discriminator and the generator. We show that minimizing the objective function of LSGAN yields minimizing the Pearson…
Generative adversarial networks (GANs) are capable of generating strikingly realistic samples but state-of-the-art GANs can be extremely computationally expensive to train. In this paper, we propose the fused propagation (FusedProp) algorithm which can be used to efficiently train the discriminator and the generator of common GANs simultaneously using only one forward and one backward propagation. We show that FusedProp achieves 1.49 times the training speed compared to the conventional training of GANs, although further studies are required to improve its stability. By reporting our prelimina…
To improve the stability of GAN training we need to understand why they can produce realistic samples. Presently, this is attributed to properties of the divergence obtained under an optimal discriminator. This argument has a fundamental flaw: If we do not impose regularity of the discriminator, it can exploit visually imperceptible errors of the generator to always achieve the maximal generator loss. In practice, gradient penalties are used to regularize the discriminator. However, this needs a metric on the space of images that captures visual similarity. Such a metric is not known, which ex…
Generative adversarial networks (GANs) are one of the most popular approaches when it comes to training generative models, among which variants of Wasserstein GANs are considered superior to the standard GAN formulation in terms of learning stability and sample quality. However, Wasserstein GANs require the critic to be 1-Lipschitz, which is often enforced implicitly by penalizing the norm of its gradient, or by globally restricting its Lipschitz constant via weight normalization techniques. Training with a regularization term penalizing the violation of the Lipschitz constraint explicitly, in…
Ecole Polytechnique Federale of Lausanne（洛桑联邦理工学院）
Generative adversarial networks (GANs) are pairs of artificial neural networks that are trained one against each other. The outputs from a generator are mixed with the real-world inputs to the discriminator and both networks are trained until an equilibrium is reached, where the discriminator cannot distinguish generated inputs from real ones. Since their introduction, GANs have allowed for the generation of impressive imitations of real-life films, images and texts, whose fakeness is barely noticeable to humans. Despite their impressive performance, training GANs remains to this day more of a…
One of the issues faced in training Generative Adversarial Nets (GANs) and their variants is the problem of mode collapse, wherein the training stability in terms of the generative loss increases as more training data is used. In this paper, we propose an alternative architecture via the Low-Complexity Neural Network (LCNN), which attempts to learn models with low complexity. The motivation is that controlling model complexity leads to models that do not overfit the training data. We incorporate the LCNN loss function for GANs, Deep Convolutional GANs (DCGANs) and Spectral Normalized GANs (SNG…
Generative Adversarial Networks are notoriously challenging to train. The underlying minmax optimization is highly susceptible to the variance of the stochastic gradient and the rotational component of the associated game vector field. To tackle these challenges, we propose the Lookahead algorithm for minmax optimization, originally developed for single objective minimization only. The backtracking step of our Lookahead-minmax naturally handles the rotational game dynamics, a property which was identified to be key for enabling gradient ascent descent methods to converge on challenging example…
International School of Information Science & Engineering, DUT（大连理工大学国际信息与软件学院）
In past years, the minimax type single-level optimization formulation and its variations have been widely utilized to address Generative Adversarial Networks (GANs). Unfortunately, it has been proved that these alternating learning strategies cannot exactly reveal the intrinsic relationship between the generator and discriminator, thus easily result in a series of issues, including mode collapse, vanishing gradients and oscillations in the training phase, etc. In this work, by investigating the fundamental mechanism of GANs from the perspective of hierarchical optimization, we propose Best-Res…
In this paper we address the problem of fine-tuned text generation with a limited computational budget. For that, we use a well-performing text generative adversarial network (GAN) architecture - Diversity-Promoting GAN (DPGAN), and attempted a drop-in replacement of the LSTM layer with a self-attention-based Transformer layer in order to leverage their efficiency. The resulting Self-Attention DPGAN (SADPGAN) was evaluated for performance, quality and diversity of generated text and stability. Computational experiments suggested that a transformer architecture is unable to drop-in replace the …
University of California, Los Angeles（加州大学洛杉矶分校）；University of South Carolina（南卡罗来纳大学）；Max Planck Institute for Mathematics in Sciences（马克斯·普朗克数学科学研究所）
We introduce a new method for training generative adversarial networks by applying the Wasserstein-2 metric proximal on the generators. The approach is based on Wasserstein information geometry. It defines a parametrization invariant natural gradient by pulling back optimal transport structures from probability space to parameter space. We obtain easy-to-implement iterative regularizers for the parameter updates of implicit deep generative models. Our experiments demonstrate that this method improves the speed and stability of training in terms of wall-clock time and Fréchet Inception Distance…
In this paper, we propose a novel technique for generating images in the 3D domain from images with high degree of geometrical transformations. By coalescing two popular concurrent methods that have seen rapid ascension to the machine learning zeitgeist in recent years: GANs (Goodfellow et. al.) and Capsule networks (Sabour, Hinton et. al.) - we present: \textbf{CapsGAN}. We show that CapsGAN performs better than or equal to traditional CNN based GANs in generating images with high geometric transformations using rotated MNIST. In the process, we also show the efficacy of using capsules archit…
Brown University（布朗大学）；NVIDIA（英伟达）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Julia Computing（朱莉娅计算公司）；Pacific Northwest National Lab（太平洋西北国家实验室）；Massachusetts Institute of Technology（麻省理工学院）
Uncertainty quantification for forward and inverse problems is a central challenge across physical and biomedical disciplines. We address this challenge for the problem of modeling subsurface flow at the Hanford Site by combining stochastic computational models with observational data using physics-informed GAN models. The geographic extent, spatial heterogeneity, and multiple correlation length scales of the Hanford Site require training a computationally intensive GAN model to thousands of dimensions. We develop a hierarchical scheme for exploiting domain parallelism, map discriminators and …
For the integration of renewable energy sources, power grid operators need realistic information about the effects of energy production and consumption to assess grid stability. Recently, research in scenario planning benefits from utilizing generative adversarial networks (GANs) as generative models for operational scenario planning. In these scenarios, operators examine temporal as well as spatial influences of different energy sources on the grid. The analysis of how renewable energy resources affect the grid enables the operators to evaluate the stability and to identify potential weak poi…
Class-conditional extensions of generative adversarial networks (GANs), such as auxiliary classifier GAN (AC-GAN) and conditional GAN (cGAN), have garnered attention owing to their ability to decompose representations into class labels and other factors and to boost the training stability. However, a limitation is that they assume that each class is separable and ignore the relationship between classes even though class overlapping frequently occurs in a real-world scenario when data are collected on the basis of diverse or ambiguous criteria. To overcome this limitation, we address a novel pr…
Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences（中国科学院深圳先进技术研究院）；School of Information and Electronics, Beijing Institute of Technology（北京理工大学信息与电子学院）
One-class novelty detection is to identify anomalous instances that do not conform to the expected normal instances. In this paper, the Generative Adversarial Networks (GANs) based on encoder-decoder-encoder pipeline are used for detection and achieve state-of-the-art performance. However, deep neural networks are too over-parameterized to deploy on resource-limited devices. Therefore, Progressive Knowledge Distillation with GANs (PKDGAN) is proposed to learn compact and fast novelty detection networks. The P-KDGAN is a novel attempt to connect two standard GANs by the designed distillation lo…
Stability and Generalization of lp-Regularized Stochastic Learning for GCN
University of Electronic Science and Technology of China（电子科技大学）；Northwestern Polytechnical University（西北工业大学）；Nanjing Audit University（南京审计大学）；Zhejiang Normal University（浙江师范大学）
The training of Generative Adversarial Networks is a difficult task mainly due to the nature of the networks. One such issue is when the generator and discriminator start oscillating, rather than converging to a fixed point. Another case can be when one agent becomes more adept than the other which results in the decrease of the other agent's ability to learn, reducing the learning capacity of the system as a whole. Additionally, there exists the problem of Mode Collapse which involves the generators output collapsing to a single sample or a small set of similar samples. To train GANs a carefu…
NASA Langley Research Center（美国国家航空航天局兰利研究中心）；University of Puerto Rico (Mayagüez)（波多黎各大学（马亚圭斯））
While standard generative adversarial networks (GANs) rely solely on training data to learn unknown probability distributions, physics-informed GANs (PI-GANs) encode physical laws in the form of stochastic partial differential equations (PDEs) using auto differentiation. By relating observed data to unobserved quantities of interest through PDEs, PI-GANs allow for the estimation of underlying probability distributions without their direct measurement (i.e. inverse problems). The scalable nature of GANs allows high-dimensional, spatially-dependent probability distributions (i.e., random fields)…
Generative Adversarial Networks (GANs) are well-known tools for data generation and semi-supervised classification. GANs, with less labeled data, outperform Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) in classification across various tasks, this shows promise for developing GANs capable of trespassing into the domain of semi-supervised regression. However, developing GANs for regression introduce two major challenges: (1) inherent instability in the GAN formulation and (2) performing regression and achieving stability simultaneously. This paper introduces techniques th…
