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Efficient sampling from high-dimensional and multimodal unnormalized probability distributions is a central challenge in many areas of science and machine learning. We focus on Boltzmann generators (BGs) that aim to sample the Boltzmann…

Machine Learning · Computer Science 2026-03-03 Christopher von Klitzing , Denis Blessing , Henrik Schopmans , Pascal Friederich , Gerhard Neumann

Boltzmann machines are the basis of several deep learning methods that have been successfully applied to both supervised and unsupervised machine learning tasks. These models assume that a dataset is generated according to a Boltzmann…

Quantum Physics · Physics 2021-01-25 Richard Y. Li , Tameem Albash , Daniel A. Lidar

Boltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples in thermodynamic equilibrium. The equilibrium distribution is usually defined…

Statistical Mechanics · Physics 2022-09-07 Manuel Dibak , Leon Klein , Andreas Krämer , Frank Noé

A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as…

Quantum Physics · Physics 2022-07-21 Siddhartha Srivastava , Veera Sundararaghavan

Energy-based generative models, such as restricted Boltzmann machines (RBMs), require unbiased Boltzmann samples for effective training. Classical Markov chain Monte Carlo methods, however, converge slowly and yield correlated samples,…

Quantum Physics · Physics 2026-03-16 Gilhan Kim , Ju-Yeon Gyhm , Daniel K. Park

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators tackle this problem by pairing normalizing flows with importance sampling to obtain uncorrelated…

Machine Learning · Computer Science 2026-01-21 Charlie B. Tan , Avishek Joey Bose , Chen Lin , Leon Klein , Michael M. Bronstein , Alexander Tong

The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a…

Machine Learning · Statistics 2025-02-04 Leon Klein , Frank Noé

Boltzmann generators approach the sampling problem in many-body physics by combining a normalizing flow and a statistical reweighting method to generate samples of a physical system's equilibrium density. The equilibrium distribution is…

Computational Physics · Physics 2020-12-02 Manuel Dibak , Leon Klein , Frank Noé

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…

Machine Learning · Statistics 2022-02-25 Vincent Stimper , Bernhard Schölkopf , José Miguel Hernández-Lobato

Normalizing flows can transform a simple prior probability distribution into a more complex target distribution. Here, we evaluate the ability and efficiency of generative machine learning methods to sample the Boltzmann distribution of an…

Soft Condensed Matter · Physics 2024-09-16 Gerhard Jung , Giulio Biroli , Ludovic Berthier

Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics. Boltzmann Generators (BGs) tackle it by combining a generative model with a Monte Carlo (MC) correction step to obtain asymptotically…

Machine Learning · Statistics 2026-01-30 Louis Grenioux , Maxence Noble

Efficient sampling from the Boltzmann distribution given its energy function is a key challenge for modeling complex physical systems such as molecules. Boltzmann Generators address this problem by leveraging continuous normalizing flows to…

Machine Learning · Computer Science 2025-10-17 Rishal Aggarwal , Jacky Chen , Nicholas M. Boffi , David Ryan Koes

Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its…

Machine Learning · Computer Science 2025-03-05 Jiajun He , Wenlin Chen , Mingtian Zhang , David Barber , José Miguel Hernández-Lobato

Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More…

Machine Learning · Computer Science 2025-12-03 Kentaro Kubo , Hayato Goto

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but practical…

Machine Learning · Computer Science 2026-05-29 Weilong Chen , Bojun Zhao , Jan Eckwert , Julija Zavadlav

The use of generative models to sample equilibrium distributions of many-body systems, as first demonstrated by Boltzmann Generators, has attracted substantial interest due to their ability to produce unbiased and uncorrelated samples in…

Statistical Mechanics · Physics 2025-10-23 Maximilian Schebek , Frank Noé , Jutta Rogal

Generative models based on invertible transformations provide a physics-aware route to sample equilibrium configurations directly from the Boltzmann distribution, enabling efficient exploration of complex thermodynamic landscapes. Here, we…

Statistical Mechanics · Physics 2026-03-06 Luigi de Santis , John Russo , Andrea Ninarello

Simulation-free training frameworks have been at the forefront of the generative modelling revolution in continuous spaces, leading to large-scale diffusion and flow matching models. However, such modern generative models suffer from…

Machine Learning · Computer Science 2025-10-31 Danyal Rehman , Oscar Davis , Jiarui Lu , Jian Tang , Michael Bronstein , Yoshua Bengio , Alexander Tong , Avishek Joey Bose

Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their…

Disordered Systems and Neural Networks · Physics 2016-02-11 Marylou Gabrié , Eric W. Tramel , Florent Krzakala

Generating a Boltzmann distribution in high dimension has recently been achieved with Normalizing Flows, which enable fast and exact computation of the generated density, and thus unbiased estimation of expectations. However, current…

Machine Learning · Computer Science 2023-01-16 Loris Felardos , Jérôme Hénin , Guillaume Charpiat
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