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Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a…

Machine Learning · Computer Science 2020-01-10 Dieterich Lawson , George Tucker , Bo Dai , Rajesh Ranganath

We study a new approach to learning energy-based models (EBMs) based on adversarial training (AT). We show that (binary) AT learns a special kind of energy function that models the support of the data distribution, and the learning process…

Machine Learning · Computer Science 2022-12-29 Xuwang Yin , Shiying Li , Gustavo K. Rohde

This paper studies the fundamental problem of learning energy-based model (EBM) in the latent space of the generator model. Learning such prior model typically requires running costly Markov Chain Monte Carlo (MCMC). Instead, we propose to…

Machine Learning · Computer Science 2022-09-20 Zhisheng Xiao , Tian Han

Several density estimation methods have shown to fail to detect out-of-distribution (OOD) samples by assigning higher likelihoods to anomalous data. Energy-based models (EBMs) are flexible, unnormalized density models which seem to be able…

Machine Learning · Computer Science 2021-07-20 Sven Elflein , Bertrand Charpentier , Daniel Zügner , Stephan Günnemann

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point…

Machine Learning · Computer Science 2023-10-31 Sangwoong Yoon , Young-Uk Jin , Yung-Kyun Noh , Frank C. Park

Energy-Based Models (EBMs) provide a flexible framework for generative modeling, but their training remains theoretically challenging due to the need to approximate normalization constants and efficiently sample from complex, multi-modal…

Machine Learning · Computer Science 2025-06-10 Davide Carbone

We study the problem of learning associative memory -- a system which is able to retrieve a remembered pattern based on its distorted or incomplete version. Attractor networks provide a sound model of associative memory: patterns are stored…

Machine Learning · Statistics 2021-04-21 Sergey Bartunov , Jack W Rae , Simon Osindero , Timothy P Lillicrap

Recently there has been a lot of interest in non-autoregressive (non-AR) models for speech synthesis, such as FastSpeech 2 and diffusion models. Unlike AR models, these models do not have autoregressive dependencies among outputs which…

Sound · Computer Science 2023-10-20 Wanli Sun , Zehai Tu , Anton Ragni

A new approach to maximum likelihood learning of discrete graphical models and RBM in particular is introduced. Our method, Perturb and Descend (PD) is inspired by two ideas (I) perturb and MAP method for sampling (II) learning by…

Neural and Evolutionary Computing · Computer Science 2014-05-08 Siamak Ravanbakhsh , Russell Greiner , Brendan Frey

We propose Energy-based generator matching (EGM), a modality-agnostic approach to train generative models from energy functions in the absence of data. Extending the recently proposed generator matching, EGM enables training of arbitrary…

Machine Learning · Computer Science 2025-11-20 Dongyeop Woo , Minsu Kim , Minkyu Kim , Kiyoung Seong , Sungsoo Ahn

Energy-based models (EBMs) are a simple yet powerful framework for generative modeling. They are based on a trainable energy function which defines an associated Gibbs measure, and they can be trained and sampled from via well-established…

Machine Learning · Computer Science 2021-05-06 Carles Domingo-Enrich , Alberto Bietti , Eric Vanden-Eijnden , Joan Bruna

Deep neural networks (DNNs) are easily fooled by adversarial perturbations that are imperceptible to humans. Adversarial training, a process where adversarial examples are added to the training set, is the current state-of-the-art defense…

Machine Learning · Computer Science 2024-01-23 Siddharth Mansingh , Michal Kucer , Garrett Kenyon , Juston Moore , Michael Teti

In the last decades, energy-based models (EBMs) have become an important class of probabilistic models in which a component of the likelihood is intractable and therefore cannot be evaluated explicitly. Consequently, parameter estimation in…

Computational Engineering, Finance, and Science · Computer Science 2026-04-10 Luca Martino

Generative models have shown strong generation ability while efficient likelihood estimation is less explored. Energy-based models~(EBMs) define a flexible energy function to parameterize unnormalized densities efficiently but are notorious…

Machine Learning · Computer Science 2024-06-11 Cong Geng , Tian Han , Peng-Tao Jiang , Hao Zhang , Jinwei Chen , Søren Hauberg , Bo Li

While energy-based models (EBMs) exhibit a number of desirable properties, training and sampling on high-dimensional datasets remains challenging. Inspired by recent progress on diffusion probabilistic models, we present a diffusion…

Machine Learning · Computer Science 2021-03-30 Ruiqi Gao , Yang Song , Ben Poole , Ying Nian Wu , Diederik P. Kingma

In this paper, we attack the anomaly detection problem by directly modeling the data distribution with deep architectures. We propose deep structured energy based models (DSEBMs), where the energy function is the output of a deterministic…

Machine Learning · Computer Science 2016-06-17 Shuangfei Zhai , Yu Cheng , Weining Lu , Zhongfei Zhang

Energy-based models (EBMs) offer a flexible framework for parameterizing probability distributions using neural networks. However, learning EBMs by exact maximum likelihood estimation (MLE) is generally intractable, due to the need to…

Machine Learning · Computer Science 2025-08-20 Michael E. Sander , Vincent Roulet , Tianlin Liu , Mathieu Blondel

Energy-based models (EBMs) are versatile density estimation models that directly parameterize an unnormalized log density. Although very flexible, EBMs lack a specified normalization constant of the model, making the likelihood of the model…

Machine Learning · Computer Science 2024-02-20 Louis Grenioux , Éric Moulines , Marylou Gabrié

Discrete structures play an important role in applications like program language modeling and software engineering. Current approaches to predicting complex structures typically consider autoregressive models for their tractability, with…

Machine Learning · Computer Science 2020-11-12 Hanjun Dai , Rishabh Singh , Bo Dai , Charles Sutton , Dale Schuurmans

Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function,…

Machine Learning · Statistics 2022-03-17 Erik Nijkamp , Ruiqi Gao , Pavel Sountsov , Srinivas Vasudevan , Bo Pang , Song-Chun Zhu , Ying Nian Wu