Contrastive divergence is a popular method of training energy-based models, but is known to have difficulties with training stability. We propose an adaptation to improve contrastive divergence training by scrutinizing a gradient term that is difficult to calculate and is often left out for convenience. We show that this gradient term is numerically significant and in practice is important to avoid training instabilities, while being tractable to estimate. We further highlight how data augmentation and multi-scale processing can be used to improve model robustness and generation quality. Finally, we empirically evaluate stability of model architectures and show improved performance on a host of benchmarks and use cases,such as image generation, OOD detection, and compositional generation.
Energy-based models (EBMs) offer flexible distribution parametrization. However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation. In this paper, we propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum likelihood learning of EBMs. PS-CD is derived from the maximization of a family of strictly proper homogeneous scoring rules, which avoids the computation of the intractable partition function and provides a generalized family of learning objectives that include contrastive divergence as a …
The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the impressive results obtained in image generation by parameterizing the distribution with Convolutional Neural Networks (CNN). However, the motivation and theoretical foundations behind modern EBMs are often absent from recent papers and this sometimes results in some confusion. In particular, the theoretical justifications behind the popular MCMC-based learning…
We propose a number of new algorithms for learning deep energy models and demonstrate their properties. We show that our SteinCD performs well in term of test likelihood, while SteinGAN performs well in terms of generating realistic looking images. Our results suggest promising directions for learning better models by combining GAN-style methods with traditional energy-based learning.
Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learning
Korea Institute for Advanced Study（韩国高等研究院）；University of Seoul（首尔市立大学）；Seoul National University（首尔国立大学）；Hanyang University（汉阳大学）；Saige Research（赛奇研究院）
Generative Adversarial Networks (GANs) have shown great promise in modeling high dimensional data. The learning objective of GANs usually minimizes some measure discrepancy, \textit{e.g.}, $f$-divergence~($f$-GANs) or Integral Probability Metric~(Wasserstein GANs). With $f$-divergence as the objective function, the discriminator essentially estimates the density ratio, and the estimated ratio proves useful in further improving the sample quality of the generator. However, how to leverage the information contained in the discriminator of Wasserstein GANs (WGAN) is less explored. In this paper, …
Technion - Israel Institute of Technology（以色列理工学院）
Contrastive divergence (CD) learning is a classical method for fitting unnormalized statistical models to data samples. Despite its wide-spread use, the convergence properties of this algorithm are still not well understood. The main source of difficulty is an unjustified approximation which has been used to derive the gradient of the loss. In this paper, we present an alternative derivation of CD that does not require any approximation and sheds new light on the objective that is actually being optimized by the algorithm. Specifically, we show that CD is an adversarial learning procedure, whe…
Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distribution. While KL divergence has many desirable properties, other f-divergences have shown advantages in training implicit density generative models such as generative adversarial networks. In this paper, we propose a general variational framework termed f-EBM to train EBMs using a…
Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution, especially in high-dimensional domains. Previous works have explored modelling the noise distribution as a separate generative model, and then concurrently training this noise model with the EBM. While this method allows for more effective noise-contrastive estimation, it comes at the cost of extra memory and training complexity. Instead, this thesis proposes …
Department of Statistics, UCLA（统计学系，加州大学洛杉矶分校（UCLA））
This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle…
Restricted Boltzmann Machines (RBMs) are probabilistic generative models that can be trained by maximum likelihood in principle, but are usually trained by an approximate algorithm called Contrastive Divergence (CD) in practice. In general, a CD-k algorithm estimates an average with respect to the model distribution using a sample obtained from a k-step Markov Chain Monte Carlo Algorithm (e.g., block Gibbs sampling) starting from some initial configuration. Choices of k typically vary from 1 to 100. This technical report explores if it's possible to leverage a simple approximate sampling algor…
TRIPODS Institute for Theoretical Foundations of Data Science（TRIPODS 数据科学理论基础研究所）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Brown University（布朗大学）；Foundation for Research and Technology - Hellas（希腊研究与技术基金会）
We develop a rigorous and general framework for constructing information-theoretic divergences that subsume both $f$-divergences and integral probability metrics (IPMs), such as the $1$-Wasserstein distance. We prove under which assumptions these divergences, hereafter referred to as $(f,Γ)$-divergences, provide a notion of `distance' between probability measures and show that they can be expressed as a two-stage mass-redistribution/mass-transport process. The $(f,Γ)$-divergences inherit features from IPMs, such as the ability to compare distributions which are not absolutely continuous, as we…
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used to decide whether the approximation provided by the CD algorithm is good enough, though several authors (Schulz et al., 2010; Fischer & Igel, 2010) have raised doubts concerning the feasibility of this procedure. However, not many alternatives to the reconstruction error have been…
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.
LG AI Research（LG人工智能研究院）；KAIST（韩国科学技术院）；Korea University（高丽大学）
An energy-based model (EBM) is a popular generative framework that offers both explicit density and architectural flexibility, but training them is difficult since it is often unstable and time-consuming. In recent years, various training techniques have been developed, e.g., better divergence measures or stabilization in MCMC sampling, but there often exists a large gap between EBMs and other generative frameworks like GANs in terms of generation quality. In this paper, we propose a novel and effective framework for improving EBMs via contrastive representation learning (CRL). To be specific,…
Contrastive Divergence (CD) and Persistent Contrastive Divergence (PCD) are popular methods for training the weights of Restricted Boltzmann Machines. However, both methods use an approximate method for sampling from the model distribution. As a side effect, these approximations yield significantly different biases and variances for stochastic gradient estimates of individual data points. It is well known that CD yields a biased gradient estimate. In this paper we however show empirically that CD has a lower stochastic gradient estimate variance than exact sampling, while the mean of subsequen…
This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the following traits. (1) The update of the energy-based model is based on noise contrastive estimation, with the flow model serving as a strong noise distribution. (2) The update of the flow model approximately minimizes the Jensen-Shannon divergence between the flow model and the data distribution. (3) Unlike generative adversarial networks (GAN) which estimates an im…
LMU Munich（慕尼黑大学）；Google Research（谷歌研究院）；Technical University of Munich（慕尼黑工业大学）
Deep Bregman divergence measures divergence of data points using neural networks which is beyond Euclidean distance and capable of capturing divergence over distributions. In this paper, we propose deep Bregman divergences for contrastive learning of visual representation where we aim to enhance contrastive loss used in self-supervised learning by training additional networks based on functional Bregman divergence. In contrast to the conventional contrastive learning methods which are solely based on divergences between single points, our framework can capture the divergence between distributi…
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used as a stopping criterion for CD, although several authors \cite{schulz-et-al-Convergence-Contrastive-Divergence-2010-NIPSw, fischer-igel-Divergence-Contrastive-Divergence-2010-ICANN} have raised doubts concerning the feasibility of this procedure. In many cases the evolution curve …
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
Contrastive representation learning seeks to acquire useful representations by estimating the shared information between multiple views of data. Here, the choice of data augmentation is sensitive to the quality of learned representations: as harder the data augmentations are applied, the views share more task-relevant information, but also task-irrelevant one that can hinder the generalization capability of representation. Motivated by this, we present a new robust contrastive learning scheme, coined RényiCL, which can effectively manage harder augmentations by utilizing Rényi divergence. Our …
Columbia University（哥伦比亚大学）；University of Cambridge（剑桥大学）；DeepMind（深度思考）
We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To make inference tractable, we introduce the variational contrastive divergence (VCD), a new divergence that replaces the standard Kullback-Leibler (KL) divergence used in VI. The VCD captures a notion of discrepancy between the initial variational distribution and its improved version (obtained after running the MCMC steps), and it converges asymptotically to th…
University of Copenhagen（哥本哈根大学）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias can cause RBM training algorithms such as Contrastive Divergence (CD) learning to deteriorate. We adopt the idea behind Population Monte Carlo (PMC) methods to devise a new RBM training algorithm termed Population-Contrastive-Divergence (pop-CD). Compared to CD, it leads to a consi…
Universitat Politècnica de Catalunya - BarcelonaTech（加泰罗尼亚理工大学-巴塞罗那理工）；Barcelona Supercomputing Center (BSC)（巴塞罗那超级计算中心（BSC））
Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this way one has to resort to approximation schemes for the evaluation of the gradient. This is the case of Restricted Boltzmann Machines (RBM) and its learning algorithm Contrastive Divergence (CD). It is well-known that CD has a number of shortcomings, and its approximation to the gradient has several drawbacks. Overcoming these defects has been the basis of much…
In our recent paper, we showed that in exponential family, contrastive divergence (CD) with fixed learning rate will give asymptotically consistent estimates \cite{wu2016convergence}. In this paper, we establish consistency and convergence rate of CD with annealed learning rate $η_t$. Specifically, suppose CD-$m$ generates the sequence of parameters $\{θ_t\}_{t \ge 0}$ using an i.i.d. data sample $\mathbf{X}_1^n \sim p_{θ^*}$ of size $n$, then $δ_n(\mathbf{X}_1^n) = \limsup_{t \to \infty} \Vert \sum_{s=t_0}^t η_s θ_s / \sum_{s=t_0}^t η_s - θ^* \Vert$ converges in probability to 0 at a rate of …
Eindhoven University of Technology（埃因霍温理工大学）；University of Pennsylvania（宾夕法尼亚大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Conceived in the early 1990s, Experience Replay (ER) has been shown to be a successful mechanism to allow online learning algorithms to reuse past experiences. Traditionally, ER can be applied to all machine learning paradigms (i.e., unsupervised, supervised, and reinforcement learning). Recently, ER has contributed to improving the performance of deep reinforcement learning. Yet, its application to many practical settings is still limited by the memory requirements of ER, necessary to explicitly store previous observations. To remedy this issue, we explore a novel approach, Online Contrastive…
This paper studies the problem of parameter learning in probabilistic graphical models having latent variables, where the standard approach is the expectation maximization algorithm alternating expectation (E) and maximization (M) steps. However, both E and M steps are computationally intractable for high dimensional data, while the substitution of one step to a faster surrogate for combating against intractability can often cause failure in convergence. We propose a new learning algorithm which is computationally efficient and provably ensures convergence to a correct optimum. Its key idea is…
$f$-MICL: Understanding and Generalizing InfoNCE-based Contrastive Learning
School of Computer Science（计算机科学学院）；University of Waterloo（滑铁卢大学）；Vector Institute（矢量研究院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；National Research Council Canada（加拿大国家研究委员会）；University of Ottawa（渥太华大学）
Reliable detection of out-of-distribution (OOD) inputs is increasingly understood to be a precondition for deployment of machine learning systems. This paper proposes and investigates the use of contrastive training to boost OOD detection performance. Unlike leading methods for OOD detection, our approach does not require access to examples labeled explicitly as OOD, which can be difficult to collect in practice. We show in extensive experiments that contrastive training significantly helps OOD detection performance on a number of common benchmarks. By introducing and employing the Confusion L…
Microsoft Research（微软研究院）；University of Sydney（悉尼大学）
We present an efficient classical algorithm for training deep Boltzmann machines (DBMs) that uses rejection sampling in concert with variational approximations to estimate the gradients of the training objective function. Our algorithm is inspired by a recent quantum algorithm for training DBMs. We obtain rigorous bounds on the errors in the approximate gradients; in turn, we find that choosing the instrumental distribution to minimize the alpha=2 divergence with the Gibbs state minimizes the asymptotic algorithmic complexity. Our rejection sampling approach can yield more accurate gradients t…
Tencent AI Lab（腾讯AI实验室）；Megvii Research Shanghai（上海旷视研究院）；Tsinghua University（清华大学）；Peking University（北京大学）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）
Meta-learning for offline reinforcement learning (OMRL) is an understudied problem with tremendous potential impact by enabling RL algorithms in many real-world applications. A popular solution to the problem is to infer task identity as augmented state using a context-based encoder, for which efficient learning of robust task representations remains an open challenge. In this work, we provably improve upon one of the SOTA OMRL algorithms, FOCAL, by incorporating intra-task attention mechanism and inter-task contrastive learning objectives, to robustify task representation learning against spa…
University of Maryland, College Park（马里兰大学帕克分校）；Capital One（第一资本金融公司）
Tabular data underpins numerous high-impact applications of machine learning from fraud detection to genomics and healthcare. Classical approaches to solving tabular problems, such as gradient boosting and random forests, are widely used by practitioners. However, recent deep learning methods have achieved a degree of performance competitive with popular techniques. We devise a hybrid deep learning approach to solving tabular data problems. Our method, SAINT, performs attention over both rows and columns, and it includes an enhanced embedding method. We also study a new contrastive self-superv…
Multimodal imaging and correlative analysis typically require image alignment. Contrastive learning can generate representations of multimodal images, reducing the challenging task of multimodal image registration to a monomodal one. Previously, additional supervision on intermediate layers in contrastive learning has improved biomedical image classification. We evaluate if a similar approach improves representations learned for registration to boost registration performance. We explore three approaches to add contrastive supervision to the latent features of the bottleneck layer in the U-Nets…
By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood. Interestingly, the traditional contrastive divergence algorithm is a special case of the above formulation and the hyperparameters of the two algorithms can be chosen such that the amount of computation per mini-batch is identical. We show that for a given computational budget the proposed algorithm almost always reaches a higher log-likelihood more rapidly, compar…
This paper proposes a novel formulation of prototypical loss with mixup for speaker verification. Mixup is a simple yet efficient data augmentation technique that fabricates a weighted combination of random data point and label pairs for deep neural network training. Mixup has attracted increasing attention due to its ability to improve robustness and generalization of deep neural networks. Although mixup has shown success in diverse domains, most applications have centered around closed-set classification tasks. In this work, we propose contrastive-mixup, a novel augmentation strategy that le…
University of Cambridge（剑桥大学）；Snap Inc.（Snap公司）；Singapore University of Technology and Design（新加坡科技设计大学）
While Generative Adversarial Networks (GANs) are fundamental to many generative modelling applications, they suffer from numerous issues. In this work, we propose a principled framework to simultaneously mitigate two fundamental issues in GANs: catastrophic forgetting of the discriminator and mode collapse of the generator. We achieve this by employing for GANs a contrastive learning and mutual information maximization approach, and perform extensive analyses to understand sources of improvements. Our approach significantly stabilizes GAN training and improves GAN performance for image synthes…
Enhancing drug and cell line representations via contrastive learning for improved anti-cancer drug prioritization
The Ohio State University（俄亥俄州立大学）；Biomedical Informatics Department, The Ohio State University（俄亥俄州立大学生物医学信息学系）；Computer Science and Engineering Department, The Ohio State University（俄亥俄州立大学计算机科学与工程系）；Translational Data Analytics Institute, The Ohio State University（俄亥俄州立大学转化数据分析研究所）
Georgia Tech（佐治亚理工学院）；Facebook AI Research（Facebook人工智能研究院）；University of California, San Diego（加州大学圣迭戈分校）；Salesforce Research（Salesforce研究院）
Recent research in Visual Question Answering (VQA) has revealed state-of-the-art models to be inconsistent in their understanding of the world -- they answer seemingly difficult questions requiring reasoning correctly but get simpler associated sub-questions wrong. These sub-questions pertain to lower level visual concepts in the image that models ideally should understand to be able to answer the higher level question correctly. To address this, we first present a gradient-based interpretability approach to determine the questions most strongly correlated with the reasoning question on an ima…
Environmental Sound Classification (ESC) is a challenging field of research in non-speech audio processing. Most of current research in ESC focuses on designing deep models with special architectures tailored for specific audio datasets, which usually cannot exploit the intrinsic patterns in the data. However recent studies have surprisingly shown that transfer learning from models trained on ImageNet is a very effective technique in ESC. Herein, we propose SoundCLR, a supervised contrastive learning method for effective environment sound classification with state-of-the-art performance, which…
