This work proposes a method for using any generator network as the foundation of an Energy-Based Model (EBM). Our formulation posits that observed images are the sum of unobserved latent variables passed through the generator network and a residual random variable that spans the gap between the generator output and the image manifold. One can then define an EBM that includes the generator as part of its forward pass, which we call the Hat EBM. The model can be trained without inferring the latent variables of the observed data or calculating the generator Jacobian determinant. This enables explicit probabilistic modeling of the output distribution of any type of generator network. Experiments show strong performance of the proposed method on (1) unconditional ImageNet synthesis at 128$\times$128 resolution, (2) refining the output of existing generators, and (3) learning EBMs that incorporate non-probabilistic generators. Code and pretrained models to reproduce our results are available at https://github.com/point0bar1/hat-ebm.

Latent variable models for text, when trained successfully, accurately model the data distribution and capture global semantic and syntactic features of sentences.The prominent approach to train such models is variational autoencoders (VAE).It is nevertheless challenging to train and often results in a trivial local optimum where the latent variable is ignored and its posterior collapses into the prior, an issue known as posterior collapse.Various techniques have been proposed to mitigate this issue.Most of them focus on improving the inference model to yield latent codes of higher quality.The present work proposes a short run dynamics for inference.It is initialized from the prior distribution of the latent variable and then runs a small number (e.g., 20) of Langevin dynamics steps guided by its posterior distribution.The major advantage of our method is that it does not require a separate inference model or assume simple geometry of the posterior distribution, thus rendering an automatic, natural and flexible inference engine.We show that the models trained with short run dynamics more accurately model the data, compared to strong language model and VAE baselines, and exhibit no sign of posterior collapse.Analyses of the latent space show that interpolation in the latent space is able to generate coherent sentences with smooth transition and demonstrate improved classification over strong baselines with latent features from unsupervised pretraining.These results together expose a well-structured latent space of our generative model.

Erik Nijkamp, Bo Pang, Ying Nian Wu, Caiming Xiong. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. We find that many of the techniques used to stabilize training in previous studies are not necessary. ML learning with a ConvNet potential requires only a few hyper-parameters and no regularization. Using this minimal framework, we identify a variety of ML learning outcomes that depend solely on the implementation of MCMC sampling.On one hand, we show that it is easy to train an energy-based model which can sample realistic images with short-run Langevin. ML can be effective and stable even when MCMC samples have much higher energy than true steady-state samples throughout training. Based on this insight, we introduce an ML method with purely noise-initialized MCMC, high-quality short-run synthesis, and the same budget as ML with informative MCMC initialization such as CD or PCD. Unlike previous models, our energy model can obtain realistic high-diversity samples from a noise signal after training.On the other hand, ConvNet potentials learned with non-convergent MCMC do not have a valid steady-state and cannot be considered approximate unnormalized densities of the training data because long-run MCMC samples differ greatly from observed images. We show that it is much harder to train a ConvNet potential to learn a steady-state over realistic images. To our knowledge, long-run MCMC samples of all previous models lose the realism of short-run samples. With correct tuning of Langevin noise, we train the first ConvNet potentials for which long-run and steady-state MCMC samples are realistic images.

Open-domain dialogue generation has gained increasing attention in Natural Language Processing.Its evaluation requires a holistic means.Human ratings are deemed as the gold standard.As human evaluation is inefficient and costly, an automated substitute is highly desirable.In this paper, we propose holistic evaluation metrics that capture different aspects of open-domain dialogues.Our metrics consist of (1) GPT-2 based context coherence between sentences in a dialogue, (2) GPT-2 based fluency in phrasing, (3) n-gram based diversity in responses to augmented queries, and (4) textual-entailment-inference based logical self-consistency.The empirical validity of our metrics is demonstrated by strong correlations with human judgments.We open source the code and relevant materials.1

This paper proposes a joint training method to learn both the variational auto-encoder (VAE) and the latent energy-based model (EBM). The joint training of VAE and latent EBM are based on an objective function that consists of three Kullback-Leibler divergences between three joint distributions on the latent vector and the image, and the objective function is of an elegant symmetric and anti-symmetric form of divergence triangle that seamlessly integrates variational and adversarial learning. In this joint training scheme, the latent EBM serves as a critic of the generator model, while the generator model and the inference model in VAE serve as the approximate synthesis sampler and inference sampler of the latent EBM. Our experiments show that the joint training greatly improves the synthesis quality of the VAE. It also enables learning of an energy function that is capable of detecting out of sample examples for anomaly detection.

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 implicit probability distribution defined by a generator model, our method estimates two explicit probabilistic distributions on the data. Using the proposed method we demonstrate a significant improvement on the synthesis quality of the flow model, and show the effectiveness of unsupervised feature learning by the learned energy-based model. Furthermore, the proposed training method can be easily adapted to semi-supervised learning. We achieve competitive results to the state-of-the-art semi-supervised learning methods.

We propose an energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network can be learned jointly by maximum likelihood, which involves short-run MCMC sampling from both the prior and posterior distributions of the latent vector. Due to the low dimensionality of the latent space and the expressiveness of the top-down network, a simple EBM in latent space can capture regularities in the data effectively, and MCMC sampling in latent space is efficient and mixes well. We show that the learned model exhibits strong performances in terms of image and text generation and anomaly detection. The one-page code can be found in supplementary materials.

This paper proposes the divergence triangle as a framework for joint training of a 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, and energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data.

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. More interestingly, unlike traditional EBM or MCMC, the learned short-run MCMC is capable of reconstructing observed images and interpolating between images, like generator or flow models. The code can be found in the Appendix.

This paper proposes a method for generative learning of hierarchical random field models. The resulting model, which we call the hierarchical sparse FRAME (Filters, Random field, And Maximum Entropy) model, is a generalization of the original sparse FRAME model by decomposing it into multiple parts that are allowed to shift their locations, scales and rotations, so that the resulting model becomes a hierarchical deformable template. The model can be trained by an EM-type algorithm that alternates the following two steps: (1) Inference: Given the current model, we match it to each training image by inferring the unknown locations, scales, and rotations of the object and its parts by recursive sum-max maps, and (2) Re-learning: Given the inferred geometric configurations of the objects and their parts, we re-learn the model parameters by maximum likelihood estimation via stochastic gradient algorithm. Experiments show that the proposed method is capable of learning meaningful and interpretable templates that can be used for object detection, classification and clustering.

We provide a novel algorithm to approximately factor large matrices with millions of rows, millions of columns, and billions of nonzero elements. Our approach rests on stochastic gradient descent (SGD), an iterative stochastic optimization algorithm. We first develop a novel "stratified" SGD variant (SSGD) that applies to general loss-minimization problems in which the loss function can be expressed as a weighted sum of "stratum losses." We establish sufficient conditions for convergence of SSGD using results from stochastic approximation theory and regenerative process theory. We then specialize SSGD to obtain a new matrix-factorization algorithm, called DSGD, that can be fully distributed and run on web-scale datasets using, e.g., MapReduce. DSGD can handle a wide variety of matrix factorizations. We describe the practical techniques used to optimize performance in our DSGD implementation. Experiments suggest that DSGD converges significantly faster and has better scalability properties than alternative algorithms.

Large-scale data analysis applications require processing and analyzing of Terabytes or even Petabytes of data, particularly in the areas of web analysis or scientific data management. This trend has been discussed as "web-scale data management" in a panel at VLDB 2009. Formerly, parallel data processing was the domain of parallel database systems. Today, novel requirements like scaling out to thousands of machines, improved fault-tolerance, and schema free processing have made a case for new approaches.

Dynamic authority-based keyword search algorithms, such as ObjectRank and personalized PageRank, leverage semantic link information to provide high quality, high recall search in databases, and the Web. Conceptually, these algorithms require a query-time PageRank-style iterative computation over the full graph. This computation is too expensive for large graphs, and not feasible at query time. Alternatively, building an index of precomputed results for some or all keywords involves very expensive preprocessing. We introduce BinRank, a system that approximates ObjectRank results by utilizing a hybrid approach inspired by materialized views in traditional query processing. We materialize a number of relatively small subsets of the data graph in such a way that any keyword query can be answered by running ObjectRank on only one of the subgraphs. BinRank generates the subgraphs by partitioning all the terms in the corpus based on their co-occurrence, executing ObjectRank for each partition using the terms to generate a set of random walk starting points, and keeping only those objects that receive non-negligible scores. The intuition is that a subgraph that contains all objects and links relevant to a set of related terms should have all the information needed to rank objects with respect to one of these terms. We demonstrate that BinRank can achieve subsecond query execution time on the English Wikipedia data set, while producing high-quality search results that closely approximate the results of ObjectRank on the original graph. The Wikipedia link graph contains about 10^8 edges, which is at least two orders of magnitude larger than what prior state of the art dynamic authority-based search systems have been able to demonstrate. Our experimental evaluation investigates the trade-off between query execution time, quality of the results, and storage requirements of BinRank.

Dynamic authority-based keyword search algorithms, such as ObjectRank and personalized PageRank, leverage semantic link information to provide high quality, high recall search in databases and the Web. Conceptually, these algorithms require a query-time PageRank-style iterative computation over the full graph. This computation is too expensive for large graphs, and not feasible at query time. Alternatively, building an index of pre-computed results for some or all keywords involves very expensive preprocessing. We introduce BinRank, a system that approximates ObjectRank results by utilizing a hybrid approach inspired by materialized views in traditional query processing. We materialize a number of relatively small subsets of the data graph in such a way that any keyword query can be answered by running ObjectRank on only one of the sub-graphs. BinRank generates the sub-graphs by partitioning all the terms in the corpus based on their co-occurrence, executing ObjectRank for each partition using the terms to generate a set of random walk starting points, and keeping only those objects that receive non-negligible scores. The intuition is that a sub-graph that contains all objects and links relevant to a set of related terms should have all the information needed to rank objects with respect to one of these terms. We demonstrate that BinRank can achieve sub-second query execution time on the English Wikipedia dataset, while producing high quality search results that closely approximate the results of ObjectRank on the original graph. The Wikipedia link graph contains about 108edges, which is at least two orders of magnitude larger than what prior state of the art dynamic authority-based search systems have been able to demonstrate. Our experimental evaluation investigates the trade-off between query execution time, quality of the results, and storage requirements of BinRank.

DBPubs is a system for effectively analyzing and exploring the content of database publications by combining keyword search with OLAP-style aggregations, navigation, and reporting. DBPubs starts with keyword search over the content of publications. The publications' metadata such as title, authors, venues, year, and so on, provide traditional OLAP static dimensions, which are combined with dynamic dimensions discovered from the content of the publications in the search result, such as frequent phrases, relevant phrases, and topics. We compute publication ranks based on the link structure between documents, i.e., citations, and aggregate them to find seminal papers, discover trends, and rank authors. We deploy an OLAP tool for multidimensional content exploration through traditional OLAP rollup-drilldown operations on the static and dynamic dimensions, solutions for multi-cube analysis, dynamic navigation of the content, and highlighting of interesting dices of the multidimensional content dataspace.