Non-saturating generative adversarial network (GAN) training is widely used and has continued to obtain groundbreaking results. However so far this approach has lacked strong theoretical justification, in contrast to alternatives such as f-GANs and Wasserstein GANs which are motivated in terms of approximate divergence minimization. In this paper we show that non-saturating GAN training does in fact approximately minimize a particular f-divergence. We develop general theoretical tools to compare and classify f-divergences and use these to show that the new f-divergence is qualitatively similar to reverse KL. These results help to explain the high sample quality but poor diversity often observed empirically when using this scheme.
Generative adversarial networks (GANs) can be interpreted as an adversarial game between two players, a discriminator D and a generator G, in which D learns to classify real from fake data and G learns to generate realistic data by "fooling" D into thinking that fake data is actually real data. Currently, a dominating view is that G actually learns by minimizing a divergence given that the general objective function is a divergence when D is optimal. However, this view has been challenged due to inconsistencies between theory and practice. In this paper, we discuss of the properties associated…
Generative adversarial networks (GAN) are a powerful subclass of generative models. Despite a very rich research activity leading to numerous interesting GAN algorithms, it is still very hard to assess which algorithm(s) perform better than others. We conduct a neutral, multi-faceted large-scale empirical study on state-of-the art models and evaluation measures. We find that most models can reach similar scores with enough hyperparameter optimization and random restarts. This suggests that improvements can arise from a higher computational budget and tuning more than fundamental algorithmic ch…
Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative model) and a discriminator (a teacher providing training signal) that each minimize their own cost. GANs are designed to reach a Nash equilibrium at which each player cannot reduce their cost without changing the other players' parameters. One useful approach for the theory of GANs is to show that a divergence between the training distribution and the model distr…
Norwegian Defence Research Establishment (FFI)（挪威国防研究机构（FFI））
Generative adversarial networks were introduced with a logistic MiniMax cost formulation, which normally fails to train due to saturation, and a Non-Saturating reformulation. While addressing the saturation problem, NS-GAN also inverts the generator's sample weighting, implicitly shifting emphasis from higher-scoring to lower-scoring samples when updating parameters. We present both theory and empirical results suggesting that this makes NS-GAN prone to mode dropping. We design MM-nsat, which preserves MM-GAN sample weighting while avoiding saturation by rescaling the MM-GAN minibatch gradient…
Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models are expressive and allow efficient computation of samples and derivatives, but cannot be used for computing likelihoods or for marginalization. The generative-adversarial training method allows to train such models through the use of an auxiliary discriminative neural network. We show that the generative-adversarial approach is a special case of an existing…
ETH Zurich（苏黎世联邦理工学院）；Technion-Israel Institute of Technology（以色列理工学院）
Many applications in machine learning can be framed as minimization problems and solved efficiently using gradient-based techniques. However, recent applications of generative models, particularly GANs, have triggered interest in solving min-max games for which standard optimization techniques are often not suitable. Among known problems experienced by practitioners is the lack of convergence guarantees or convergence to a non-optimum cycle. At the heart of these problems is the min-max structure of the GAN objective which creates non-trivial dependencies between the players. We propose to add…
We present a framework to understand GAN training as alternating density ratio estimation and approximate divergence minimization. This provides an interpretation for the mismatched GAN generator and discriminator objectives often used in practice, and explains the problem of poor sample diversity. We also derive a family of generator objectives that target arbitrary $f$-divergences without minimizing a lower bound, and use them to train generative image models that target either improved sample quality or greater sample diversity.
We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated $f$-divergences. We then focus on $α$-GAN, defined via the $α$-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by $α$-GAN equivalently converge, for all $α\in \mathbb{R}_{>0}\cup\{\infty\}$. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a funct…
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative model minimizing a divergence measure, e.g. the Jensen-Shannon (JS) divergence, to the data distribution. However, in practice the discriminator is constrained to be in a smaller class $\mathcal{F}$ such as neural nets. Then, a natural question is how the divergence minimization …
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…
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…
Rutgers University（罗格斯大学）；University of Patras（帕特雷大学）
Generative adversarial networks (GANs) are designed with the help of min-max optimization problems that are solved with stochastic gradient-type algorithms which are known to be non-robust. In this work we revisit a non-adversarial method based on kernels which relies on a pure minimization problem and propose a simple stochastic gradient algorithm for the computation of its solution. Using simplified tools from Stochastic Approximation theory we demonstrate that batch versions of the algorithm or smoothing of the gradient do not improve convergence. These observations allow for the developmen…
Institute of Applied and Computational Mathematics（应用与计算数学研究所）；Foundation for Research & Technology - Hellas（希腊研究与技术基金会）；Computer Science Department（计算机科学系）；University of Crete（克里特大学）；Institute of Computer Science（计算机科学研究所）；Department of Mathematics and Statistics（数学与统计系）；University of Massachusetts at Amherst（马萨诸塞大学阿默斯特分校）
In this paper, we propose a novel loss function for training Generative Adversarial Networks (GANs) aiming towards deeper theoretical understanding as well as improved stability and performance for the underlying optimization problem. The new loss function is based on cumulant generating functions giving rise to \emph{Cumulant GAN}. Relying on a recently-derived variational formula, we show that the corresponding optimization problem is equivalent to R{é}nyi divergence minimization, thus offering a (partially) unified perspective of GAN losses: the R{é}nyi family encompasses Kullback-Leibler d…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Shanghai Jiao Tong University（上海交通大学）
Conditional generative models aim to learn the underlying joint distribution of data and labels to achieve conditional data generation. Among them, the auxiliary classifier generative adversarial network (AC-GAN) has been widely used, but suffers from the problem of low intra-class diversity of the generated samples. The fundamental reason pointed out in this paper is that the classifier of AC-GAN is generator-agnostic, which therefore cannot provide informative guidance for the generator to approach the joint distribution, resulting in a minimization of the conditional entropy that decreases …
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
Generative Adversarial Networks (GANs) have gained momentum for their ability to model image distributions. They learn to emulate the training set and that enables sampling from that domain and using the knowledge learned for useful applications. Several methods proposed enhancing GANs, including regularizing the loss with some feature matching. We seek to push GANs beyond the data in the training and try to explore unseen territory in the image manifold. We first propose a new regularizer for GAN based on K-nearest neighbor (K-NN) selective feature matching to a target set Y in high-level fea…
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Google Brain（谷歌大脑）
Allowing effective inference of latent vectors while training GANs can greatly increase their applicability in various downstream tasks. Recent approaches, such as ALI and BiGAN frameworks, develop methods of inference of latent variables in GANs by adversarially training an image generator along with an encoder to match two joint distributions of image and latent vector pairs. We generalize these approaches to incorporate multiple layers of feedback on reconstructions, self-supervision, and other forms of supervision based on prior or learned knowledge about the desired solutions. We achieve …
OMRON SINIC X（欧姆龙 SINIC X 研究院）；OMRON Corporation（欧姆龙公司）
This work addresses a new problem that learns generative adversarial networks (GANs) from multiple data collections that are each i) owned separately by different clients and ii) drawn from a non-identical distribution that comprises different classes. Given such non-iid data as input, we aim to learn a distribution involving all the classes input data can belong to, while keeping the data decentralized in each client storage. Our key contribution to this end is a new decentralized approach for learning GANs from non-iid data called Forgiver-First Update (F2U), which a) asks clients to train a…
In standard generative adversarial network (SGAN), the discriminator estimates the probability that the input data is real. The generator is trained to increase the probability that fake data is real. We argue that it should also simultaneously decrease the probability that real data is real because 1) this would account for a priori knowledge that half of the data in the mini-batch is fake, 2) this would be observed with divergence minimization, and 3) in optimal settings, SGAN would be equivalent to integral probability metric (IPM) GANs. We show that this property can be induced by using a …
The Swiss AI Lab, IDSIA, USI & SUPSI（瑞士人工智能实验室（IDSIA，意大利瑞士大学与瑞士意大利语区应用科学大学））；NNAISENSE
I review unsupervised or self-supervised neural networks playing minimax games in game-theoretic settings: (i) Artificial Curiosity (AC, 1990) is based on two such networks. One network learns to generate a probability distribution over outputs, the other learns to predict effects of the outputs. Each network minimizes the objective function maximized by the other. (ii) Generative Adversarial Networks (GANs, 2010-2014) are an application of AC where the effect of an output is 1 if the output is in a given set, and 0 otherwise. (iii) Predictability Minimization (PM, 1990s) models data distribut…
Learning Domain Invariant Representations by Joint Wasserstein Distance Minimization
Technische Universität Berlin（柏林工业大学）；Berlin Institute for the Foundations of Learning and Data – BIFOLD（柏林学习与数据基础研究所（BIFOLD））；Tokyo Institute of Technology（东京工业大学）；Fujitsu Laboratories Ltd.（富士通实验室有限公司）；RIKEN AIP（理化学研究所人工智能研究中心）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Korea University（高丽大学）；Google Deepmind（谷歌DeepMind）；Freie Universität Berlin（柏林自由大学）
Adam-type methods, the extension of adaptive gradient methods, have shown great performance in the training of both supervised and unsupervised machine learning models. In particular, Adam-type optimizers have been widely used empirically as the default tool for training generative adversarial networks (GANs). On the theory side, however, despite the existence of theoretical results showing the efficiency of Adam-type methods in minimization problems, the reason of their wonderful performance still remains absent in GAN's training. In existing works, the fast convergence has long been consider…
Preserving Privacy in GANs Against Membership Inference Attack
École de technologie supérieure（高等技术学院）；Universidad de Buenos Aires（布宜诺斯艾利斯大学）；McGill University（麦吉尔大学）；ILLS - International Laboratory on Learning Systems（国际学习系统实验室）；MILA - Quebec AI Institute（魁北克人工智能研究所）；CNRS（法国国家科学研究中心）；CentraleSupélec（巴黎中央理工-高等电力学院）
Robust quantization improves the tolerance of networks for various implementations, allowing reliable output in different bit-widths or fragmented low-precision arithmetic. In this work, we perform extensive analyses to identify the sources of quantization error and present three insights to robustify a network against quantization: reduction of error propagation, range clamping for error minimization, and inherited robustness against quantization. Based on these insights, we propose two novel methods called symmetry regularization (SymReg) and saturating nonlinearity (SatNL). Applying the pro…
The University of Iowa（爱荷华大学）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the underlying factors driving their empirical success in min-max problems such as GANs remain unclear. In this paper, we aim at bridging this gap from both theoretical and empirical perspectives. First, we analyze a variant of Optimistic Stochastic Gradient (OSG) proposed in~\citep{daskalakis2017training} for solving a class of non-convex non-concave min-max problem a…
The min-max optimization problem, also known as the saddle point problem, is a classical optimization problem which is also studied in the context of zero-sum games. Given a class of objective functions, the goal is to find a value for the argument which leads to a small objective value even for the worst case function in the given class. Min-max optimization problems have recently become very popular in a wide range of signal and data processing applications such as fair beamforming, training generative adversarial networks (GANs), and robust machine learning, to just name a few. The overarch…
University of Minnesota（明尼苏达大学）；Virginia Tech（弗吉尼亚理工大学）；Criteo AI Lab（Criteo人工智能实验室）；LinkedIn Corporation（领英公司）
This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been applied for regression and has shown to be advantageous over the other standard approaches like Gaussian Process Regression, given its ability to implicitly model complex noise forms. However, the current CGAN implementation for regression uses the classical generator-discriminator architecture with the minimax optimization approach, which is notorious for b…
Neuromorphic data carries information in spatio-temporal patterns encoded by spikes. Accordingly, a central problem in neuromorphic computing is training spiking neural networks (SNNs) to reproduce spatio-temporal spiking patterns in response to given spiking stimuli. Most existing approaches model the input-output behavior of an SNN in a deterministic fashion by assigning each input to a specific desired output spiking sequence. In contrast, in order to fully leverage the time-encoding capacity of spikes, this work proposes to train SNNs so as to match distributions of spiking signals rather …
