In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization of the generative model and requires only the evaluation of its data likelihood. Moreover, the metric leads to the conceptual definition of generative distances and generative geodesics, whose computation can be done efficiently in the data space. Their approximations are proven to converge to their true values under mild conditions. We showcase three proof-of-concept applications of this global metric, including clustering, data visualization, and data interpolation, thus providing new tools to support the geometrical understanding of generative models.
University of Science and Technology Beijing（北京科技大学）；Technical University of Denmark（丹麦技术大学）
Deep generative models are tremendously successful in learning low-dimensional latent representations that well-describe the data. These representations, however, tend to much distort relationships between points, i.e. pairwise distances tend to not reflect semantic similarities well. This renders unsupervised tasks, such as clustering, difficult when working with the latent representations. We demonstrate that taking the geometry of the generative model into account is sufficient to make simple clustering algorithms work well over latent representations. Leaning on the recent finding that dee…
Interpolating between points is a problem connected simultaneously with finding geodesics and study of generative models. In the case of geodesics, we search for the curves with the shortest length, while in the case of generative models we typically apply linear interpolation in the latent space. However, this interpolation uses implicitly the fact that Gaussian is unimodal. Thus the problem of interpolating in the case when the latent density is non-Gaussian is an open problem. In this paper, we present a general and unified approach to interpolation, which simultaneously allows us to search…
Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit int…
The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the computational complexity of solving a non-convex optimisation problem. We propose finding shortest paths in a finite graph of samples from the aggregate approximate posterior, that can be solved exactly, at greatly reduced runtime, and without a notable loss in quality. Our approach, therefore, is hence applicable to high-dimensional problems, e.g., in the visual…
DTU Compute, Technical University of Denmark, Kongens Lyngby, Denmark（丹麦技术大学计算机系）；Department of Computer Science, University of Virginia, Charlottesville (VA), USA（弗吉尼亚大学计算机科学系）；Department of Electrical and Computer Engineering, University of Virginia, Charlottesville (VA), USA（弗吉尼亚大学电气与计算机工程系）
Probabilistic generative deep learning for molecular design involves the discovery and design of new molecules and analysis of their structure, properties and activities by probabilistic generative models using the deep learning approach. It leverages the existing huge databases and publications of experimental results, and quantum-mechanical calculations, to learn and explore molecular structure, properties and activities. We discuss the major components of probabilistic generative deep learning for molecular design, which include molecular structure, molecular representations, deep generativ…
Technical University of Munich（慕尼黑工业大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
The underlying geometrical structure of the latent space in deep generative models is in most cases not Euclidean, which may lead to biases when comparing interpolation capabilities of two models. Smoothness and plausibility of linear interpolations in latent space are associated with the quality of the underlying generative model. In this paper, we show that not all such interpolations are comparable as they can deviate arbitrarily from the shortest interpolation curve given by the geodesic. This deviation is revealed by computing curve lengths with the pull-back metric of the generative mode…
It is argued that deep learning is efficient for data that is generated from hierarchal generative models. Examples of such generative models include wavelet scattering networks, functions of compositional structure, and deep rendering models. Unfortunately so far, for all such models, it is either not rigorously known that they can be learned efficiently, or it is not known that "deep algorithms" are required in order to learn them. We propose a simple family of "generative hierarchal models" which can be efficiently learned and where "deep" algorithm are necessary for learning. Our definitio…
Deep generative models have demonstrated effectiveness in learning compact and expressive design representations that significantly improve geometric design optimization. However, these models do not consider the uncertainty introduced by manufacturing or fabrication. Past work that quantifies such uncertainty often makes simplified assumptions on geometric variations, while the "real-world" uncertainty and its impact on design performance are difficult to quantify due to the high dimensionality. To address this issue, we propose a Generative Adversarial Network-based Design under Uncertainty …
Deparment of Mechanical Engineering Massachussetts Institute of Technology
Deep Generative Machine Learning Models (DGMs) have been growing in popularity across the design community thanks to their ability to learn and mimic complex data distributions. DGMs are conventionally trained to minimize statistical divergence between the distribution over generated data and distribution over the dataset on which they are trained. While sufficient for the task of generating "realistic" fake data, this objective is typically insufficient for design synthesis tasks. Instead, design problems typically call for adherence to design requirements, such as performance targets and con…
Deep generative models provide a powerful set of tools to understand real-world data. But as these models improve, they increase in size and complexity, so their computational cost in memory and execution time grows. Using binary weights in neural networks is one method which has shown promise in reducing this cost. However, whether binary neural networks can be used in generative models is an open problem. In this work we show, for the first time, that we can successfully train generative models which utilize binary neural networks. This reduces the computational cost of the models massively.…
Warsaw University of Technology（华沙理工大学）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
Diffusion-based Deep Generative Models (DDGMs) offer state-of-the-art performance in generative modeling. Their main strength comes from their unique setup in which a model (the backward diffusion process) is trained to reverse the forward diffusion process, which gradually adds noise to the input signal. Although DDGMs are well studied, it is still unclear how the small amount of noise is transformed during the backward diffusion process. Here, we focus on analyzing this problem to gain more insight into the behavior of DDGMs and their denoising and generative capabilities. We observe a fluid…
Queen Mary University of London（伦敦玛丽女王大学）；Goldsmiths, University of London（伦敦大学金史密斯学院）；University of the Arts London（伦敦艺术大学）；Aalto University（阿尔托大学）；Finnish Center for Artificial Intelligence（芬兰人工智能中心）；Monash University（莫纳什大学）
We present a framework for automating generative deep learning with a specific focus on artistic applications. The framework provides opportunities to hand over creative responsibilities to a generative system as targets for automation. For the definition of targets, we adopt core concepts from automated machine learning and an analysis of generative deep learning pipelines, both in standard and artistic settings. To motivate the framework, we argue that automation aligns well with the goal of increasing the creative responsibility of a generative system, a central theme in computational creat…
We present doubly stochastic gradient MCMC, a simple and generic method for (approximate) Bayesian inference of deep generative models (DGMs) in a collapsed continuous parameter space. At each MCMC sampling step, the algorithm randomly draws a mini-batch of data samples to estimate the gradient of log-posterior and further estimates the intractable expectation over hidden variables via a neural adaptive importance sampler, where the proposal distribution is parameterized by a deep neural network and learnt jointly. We demonstrate the effectiveness on learning various DGMs in a wide range of ta…
We propose Intermediate Layer Optimization (ILO), a novel optimization algorithm for solving inverse problems with deep generative models. Instead of optimizing only over the initial latent code, we progressively change the input layer obtaining successively more expressive generators. To explore the higher dimensional spaces, our method searches for latent codes that lie within a small $l_1$ ball around the manifold induced by the previous layer. Our theoretical analysis shows that by keeping the radius of the ball relatively small, we can improve the established error bound for compressed se…
Deep Generative Machine Learning Models have been growing in popularity across the design community thanks to their ability to learn and mimic complex data distributions. While early works are promising, further advancement will depend on addressing several critical considerations such as design quality, feasibility, novelty, and targeted inverse design. We propose the Design Target Achievement Index (DTAI), a differentiable, tunable metric that scores a design's ability to achieve designer-specified minimum performance targets. We demonstrate that DTAI can drastically improve the performance …
Wasserstein-Fisher-Rao (WFR) distance is a family of metrics to gauge the discrepancy of two Radon measures, which takes into account both transportation and weight change. Spherical WFR distance is a projected version of WFR distance for probability measures so that the space of Radon measures equipped with WFR can be viewed as metric cone over the space of probability measures with spherical WFR. Compared to the case for Wasserstein distance, the understanding of geodesics under the spherical WFR is less clear and still an ongoing research focus. In this paper, we develop a deep learning fra…
University of Utah（犹他大学）；IBM Research AI（IBM人工智能研究院）
Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to ge…
CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks
Extreme Conditions Physics Research Laboratory（极端条件物理研究实验室）；Center of Excellence in Physics of Energy Materials (CE:PEM), Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand（能源材料物理卓越中心，物理系，科学学院，朱拉隆梭大学，Bangkok 10330，泰国）；Thailand Center of Excellence in Physics, Ministry of Higher Education, Science, Research（泰国物理卓越中心，教育部，科学，研究）；Department of Chemistry（化学系）；Biochemistry, University of South Carolina, South Carolina 29208, USA（生物化学，南卡罗来纳大学，South Carolina 29208，美国）；Complex Systems Lab, Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand（复杂系统实验室，物理系，科学学院，朱拉隆梭大学，Bangkok 10330，泰国）；Theoretical Physics Division, Department of Physics, Chemistry（理论物理 division，物理系，化学）
University of Central Florida（中佛罗里达大学）；University of Pennsylvania（宾夕法尼亚大学）；Boston Children’s Hospital（波士顿儿童医院）；Harvard Medical School（哈佛医学院）
The performance of the state-of-the-art image segmentation methods heavily relies on the high-quality annotations, which are not easily affordable, particularly for medical data. To alleviate this limitation, in this study, we propose a weakly supervised image segmentation method based on a deep geodesic prior. We hypothesize that integration of this prior information can reduce the adverse effects of weak labels in segmentation accuracy. Our proposed algorithm is based on a prior information, extracted from an auto-encoder, trained to map objects geodesic maps to their corresponding binary ma…
FAAGC: Feature Augmentation on Adaptive Geodesic Curve Based on the shape space theory
School of Computer Engineering and Science, Shanghai University（上海大学计算机工程与科学学院）；Key Laboratory of Silicate Cultural Relics Conservation (Shanghai University), Ministry of Education（上海大学硅酸盐文物保护重点实验室（教育部））
Latent representations are the essence of deep generative models and determine their usefulness and power. For latent representations to be useful as generative concept representations, their latent space must support latent space interpolation, attribute vectors and concept vectors, among other things. We investigate and discuss latent variable modeling, including latent variable models, latent representations and latent spaces, particularly hierarchical latent representations and latent space vectors and geometry. Our focus is on that used in variational autoencoders and generative adversari…
Many deep models have been recently proposed for anomaly detection. This paper presents comparison of selected generative deep models and classical anomaly detection methods on an extensive number of non--image benchmark datasets. We provide statistical comparison of the selected models, in many configurations, architectures and hyperparamaters. We arrive to conclusion that performance of the generative models is determined by the process of selection of their hyperparameters. Specifically, performance of the deep generative models deteriorates with decreasing amount of anomalous samples used …
University of Minnesota, Twin Cities（明尼苏达大学双城分校）；University of Oxford（牛津大学）
Several deep learning methods for phase retrieval exist, but most of them fail on realistic data without precise support information. We propose a novel method based on single-instance deep generative prior that works well on complex-valued crystal data.
Multimodal learning is a framework for building models that make predictions based on different types of modalities. Important challenges in multimodal learning are the inference of shared representations from arbitrary modalities and cross-modal generation via these representations; however, achieving this requires taking the heterogeneous nature of multimodal data into account. In recent years, deep generative models, i.e., generative models in which distributions are parameterized by deep neural networks, have attracted much attention, especially variational autoencoders, which are suitable…
Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering the discriminative ability of DGMs on making accurate predictions. This paper presents max-margin deep generative models (mmDGMs), which explore the strongly discriminative principle of max-margin learning to improve the discriminative power of DGMs, while retaining the generative capability. We develop an efficient doubly stochastic subgradient algorithm for…
Exploiting the deep generative model's remarkable ability of learning the data-manifold structure, some recent researches proposed a geometric data interpolation method based on the geodesic curves on the learned data-manifold. However, this interpolation method often gives poor results due to a topological difference between the model and the dataset. The model defines a family of simply-connected manifolds, whereas the dataset generally contains disconnected regions or holes that make them non-simply-connected. To compensate this difference, we propose a novel density regularizer that make t…
École Polytechnique（巴黎综合理工学院）；University of California, Berkeley（加州大学伯克利分校）
Class labels are often imperfectly observed, due to mistakes and to genuine ambiguity among classes. We propose a new semi-supervised deep generative model that explicitly models noisy labels, called the Mislabeled VAE (M-VAE). The M-VAE can perform better than existing deep generative models which do not account for label noise. Additionally, the derivation of M-VAE gives new theoretical insights into the popular M1+M2 semi-supervised model.
Deep learning based generative models such as deepfake have been able to generate amazing images and videos. However, these models may need significant transformation when applied to generate crystal materials structures in which the building blocks, the physical atoms are very different from the pixels. Naively transferred generative models tend to generate a large portion of physically infeasible crystal structures that are not stable or synthesizable. Herein we show that by exploiting and adding physically oriented data augmentation, loss function terms, and post processing, our deep advers…
Generative concept representations have three major advantages over discriminative ones: they can represent uncertainty, they support integration of learning and reasoning, and they are good for unsupervised and semi-supervised learning. We discuss probabilistic and generative deep learning, which generative concept representations are based on, and the use of variational autoencoders and generative adversarial networks for learning generative concept representations, particularly for concepts whose data are sequences, structured data or graphs.
Florida State University（佛罗里达州立大学）；University of South Florida（南佛罗里达大学）
Complex analyses involving multiple, dependent random quantities often lead to graphical models - a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tool…
University of Guelph（圭尔夫大学）；Vector Institute（向量研究所）
Generative models are now used to create a variety of high-quality digital artifacts. Yet their use in designing physical objects has received far less attention. In this paper, we advocate for the construction toy, LEGO, as a platform for developing generative models of sequential assembly. We develop a generative model based on graph-structured neural networks that can learn from human-built structures and produce visually compelling designs. Our code is released at: https://github.com/uoguelph-mlrg/GenerativeLEGO.
The University of Chicago（芝加哥大学）；The Grossman Institute for Neuroscience, Quantitative Biology and Human Behavior（格罗斯曼神经科学、定量生物学与人类行为研究所）
Variational inference (VI) and Markov chain Monte Carlo (MCMC) are two main approximate approaches for learning deep generative models by maximizing marginal likelihood. In this paper, we propose using annealed importance sampling for learning deep generative models. Our proposed approach bridges VI with MCMC. It generalizes VI methods such as variational auto-encoders and importance weighted auto-encoders (IWAE) and the MCMC method proposed in (Hoffman, 2017). It also provides insights into why running multiple short MCMC chains can help learning deep generative models. Through experiments, w…
Goldsmiths, University of London（伦敦大学金史密斯学院）；University of The Arts London（伦敦艺术大学）
We introduce a new framework for manipulating and interacting with deep generative models that we call network bending. We present a comprehensive set of deterministic transformations that can be inserted as distinct layers into the computational graph of a trained generative neural network and applied during inference. In addition, we present a novel algorithm for analysing the deep generative model and clustering features based on their spatial activation maps. This allows features to be grouped together based on spatial similarity in an unsupervised fashion. This results in the meaningful m…
We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we argue that it might be advantageous to use more flexible code distributions. We demonstrate how these distributions can be induced directly from the data. The benefits include: more powerful generative models, better modeling of latent structure and explicit control of the degree of generalization.
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework to systematically investigate bias and generalization in deep generative models of images. Inspired by experimental methods from cognitive psychology, we probe each learning algorithm with carefully designed training datasets to characterize when and how existing models generate novel attributes and their combinations. We identify similarities to human psych…
The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances…
University of Chinese Academy of Sciences（中国科学院大学）
Despite its remarkable empirical success as a highly competitive branch of artificial intelligence, deep learning is often blamed for its widely known low interpretation and lack of firm and rigorous mathematical foundation. However, most theoretical endeavor is devoted in discriminative deep learning case, whose complementary part is generative deep learning. To the best of our knowledge, we firstly highlight landscape of empirical error in generative case to complete the full picture through exquisite design of image super resolution under norm based capacity control. Our theoretical advance…
National Institute of Dental and Craniofacial Research (NIDCR), National Institutes of Health (NIH)（美国国立卫生研究院（NIH）国立牙科与颅面研究所（NIDCR））；University of South Dakota Sanford School of Medicine（南达科他大学桑福德医学院）；University of Central Florida（中佛罗里达大学）
In this paper, we propose a novel deep learning framework for anatomy segmentation and automatic landmark- ing. Specifically, we focus on the challenging problem of mandible segmentation from cone-beam computed tomography (CBCT) scans and identification of 9 anatomical landmarks of the mandible on the geodesic space. The overall approach employs three inter-related steps. In step 1, we propose a deep neu- ral network architecture with carefully designed regularization, and network hyper-parameters to perform image segmentation without the need for data augmentation and complex post- processing…
IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Emory University（埃默里大学）
Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards impr…
Ulsan National Institute of Science and Technology（蔚山国立科学技术研究院）；Korea Advanced Institute of Science and Technology（韩国高等科学技术研究院）
Deep generative neural networks (DGNNs) have achieved realistic and high-quality data generation. In particular, the adversarial training scheme has been applied to many DGNNs and has exhibited powerful performance. Despite of recent advances in generative networks, identifying the image generation mechanism still remains challenging. In this paper, we present an explorative sampling algorithm to analyze generation mechanism of DGNNs. Our method efficiently obtains samples with identical attributes from a query image in a perspective of the trained model. We define generative boundaries which …
Despite substantial progress in signal source separation, results for richly structured data continue to contain perceptible artifacts. In contrast, recent deep generative models can produce authentic samples in a variety of domains that are indistinguishable from samples of the data distribution. This paper introduces a Bayesian approach to source separation that uses generative models as priors over the components of a mixture of sources, and noise-annealed Langevin dynamics to sample from the posterior distribution of sources given a mixture. This decouples the source separation problem fro…
The de novo design of molecular structures using deep learning generative models introduces an encouraging solution to drug discovery in the face of the continuously increased cost of new drug development. From the generation of original texts, images, and videos, to the scratching of novel molecular structures, the incredible creativity of deep learning generative models surprised us about the height machine intelligence can achieve. The purpose of this paper is to review the latest advances in generative chemistry which relies on generative modeling to expedite the drug discovery process. Th…
University of Cambridge（剑桥大学）；University of Vienna（维也纳大学）；Microsoft Research Cambridge（微软剑桥研究院）
Deep generative models often perform poorly in real-world applications due to the heterogeneity of natural data sets. Heterogeneity arises from data containing different types of features (categorical, ordinal, continuous, etc.) and features of the same type having different marginal distributions. We propose an extension of variational autoencoders (VAEs) called VAEM to handle such heterogeneous data. VAEM is a deep generative model that is trained in a two stage manner such that the first stage provides a more uniform representation of the data to the second stage, thereby sidestepping the p…
A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning. After learning the deep convolutional dictionary, testing is implemented via deconvolutional inference. To speed up this inference, a new statistical approach is proposed to project the top-layer dictionary elements to the data level. Following this, only one layer of deconvolution is required during testing. Experimental results demonstrate powerful capabil…
Deep generative models have shown promising results in generating realistic images, but it is still non-trivial to generate images with complicated structures. The main reason is that most of the current generative models fail to explore the structures in the images including spatial layout and semantic relations between objects. To address this issue, we propose a novel deep structured generative model which boosts generative adversarial networks (GANs) with the aid of structure information. In particular, the layout or structure of the scene is encoded by a stochastic and-or graph (sAOG), in…
Generative systems have a significant potential to synthesize innovative design alternatives. Still, most of the common systems that have been adopted in design require the designer to explicitly define the specifications of the procedures and in some cases the design space. In contrast, a generative system could potentially learn both aspects through processing a database of existing solutions without the supervision of the designer. To explore this possibility, we review recent advancements of generative models in machine learning and current applications of learning techniques in design. Th…
We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to satisfy given physical laws expressed by partial differential equations. Such physics-informed constraints provide a regularization mechanism for effectively training deep probabilistic models for modeling physical systems in which the cost of data acquisition is high and training data-sets are typically small. This provides a scalable framework for characterizin…
