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This paper studies the fundamental problem of multi-layer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture…

Machine Learning · Computer Science 2023-10-17 Jiali Cui , Ying Nian Wu , Tian Han

Due to the intractable partition function, training energy-based models (EBMs) by maximum likelihood requires Markov chain Monte Carlo (MCMC) sampling to approximate the gradient of the Kullback-Leibler divergence between data and model…

Machine Learning · Statistics 2021-12-28 Jianwen Xie , Zilong Zheng , Ping Li

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

Continual learning has become essential in many practical applications such as online news summaries and product classification. The primary challenge is known as catastrophic forgetting, a phenomenon where a model inadvertently discards…

Machine Learning · Computer Science 2025-01-13 Xiaodi Li , Dingcheng Li , Rujun Gao , Mahmoud Zamani , Latifur Khan

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

Energy-based models (EBMs) have experienced a resurgence within machine learning in recent years, including as a promising alternative for probabilistic regression. However, energy-based regression requires a proposal distribution to be…

Machine Learning · Computer Science 2023-11-08 Fredrik K. Gustafsson , Martin Danelljan , Thomas B. Schön

This work presents strategies to learn an Energy-Based Model (EBM) according to the desired length of its MCMC sampling trajectories. MCMC trajectories of different lengths correspond to models with different purposes. Our experiments cover…

Machine Learning · Statistics 2022-05-25 Mitch Hill , Jonathan Mitchell , Chu Chen , Yuan Du , Mubarak Shah , Song-Chun Zhu

Energy-Based Models (EBMs) have been widely used for generative modeling. Contrastive Divergence (CD), a prevailing training objective for EBMs, requires sampling from the EBM with Markov Chain Monte Carlo methods (MCMCs), which leads to an…

Machine Learning · Computer Science 2023-07-06 Weijian Luo , Hao Jiang , Tianyang Hu , Jiacheng Sun , Zhenguo Li , Zhihua Zhang

Energy-Based Models (EBMs), also known as non-normalized probabilistic models, specify probability density or mass functions up to an unknown normalizing constant. Unlike most other probabilistic models, EBMs do not place a restriction on…

Machine Learning · Computer Science 2021-02-19 Yang Song , Diederik P. Kingma

Variational Auto-Encoders (VAEs) are known to generate blurry and inconsistent samples. One reason for this is the "prior hole" problem. A prior hole refers to regions that have high probability under the VAE's prior but low probability…

Machine Learning · Computer Science 2025-10-02 Debottam Dutta , Chaitanya Amballa , Zhongweiyang Xu , Yu-Lin Wei , Romit Roy Choudhury

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

Maximum likelihood estimation is widely used in training Energy-based models (EBMs). Training requires samples from an unnormalized distribution, which is usually intractable, and in practice, these are obtained by MCMC algorithms such as…

Machine Learning · Computer Science 2021-04-23 Zhisheng Xiao , Qing Yan , Yali Amit

Energy-based modeling is a promising approach to unsupervised learning, which yields many downstream applications from a single model. The main difficulty in learning energy-based models with the "contrastive approaches" is the generation…

Machine Learning · Computer Science 2021-11-30 Kirill Neklyudov , Priyank Jaini , Max Welling

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

This paper introduces novel deep dynamical models designed to represent continuous-time sequences. Our approach employs a neural emission model to generate each data point in the time series through a non-linear transformation of a latent…

Machine Learning · Computer Science 2025-02-06 Sheng Cheng , Deqian Kong , Jianwen Xie , Kookjin Lee , Ying Nian Wu , Yezhou Yang

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only…

Machine Learning · Statistics 2023-07-18 Tobias Schröder , Zijing Ou , Yingzhen Li , Andrew B. Duncan

State-of-the-art pre-trained image models predominantly adopt a two-stage approach: initial unsupervised pre-training on large-scale datasets followed by task-specific fine-tuning using Cross-Entropy loss~(CE). However, it has been…

Computer Vision and Pattern Recognition · Computer Science 2024-11-18 Zijun Long , George Killick , Lipeng Zhuang , Gerardo Aragon-Camarasa , Zaiqiao Meng , Richard Mccreadie

Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to…

Machine Learning · Computer Science 2023-12-14 Davide Carbone , Mengjian Hua , Simon Coste , Eric Vanden-Eijnden

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…

Machine Learning · Computer Science 2022-02-25 Léo Gagnon , Guillaume Lajoie

Maximum likelihood (ML) learning for energy-based models (EBMs) is challenging, partly due to non-convergence of Markov chain Monte Carlo.Several variations of ML learning have been proposed, but existing methods all fail to achieve both…

Machine Learning · Statistics 2023-04-24 Xinwei Zhang , Zhiqiang Tan , Zhijian Ou