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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…

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…

量子物理 · 物理学 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…

统计力学 · 物理学 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…

量子物理 · 物理学 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,…

量子物理 · 物理学 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…

机器学习 · 计算机科学 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…

机器学习 · 统计学 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…

计算物理 · 物理学 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…

机器学习 · 统计学 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…

软凝聚态物质 · 物理学 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…

机器学习 · 统计学 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…

机器学习 · 计算机科学 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…

机器学习 · 计算机科学 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…

机器学习 · 计算机科学 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…

机器学习 · 计算机科学 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…

统计力学 · 物理学 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…

统计力学 · 物理学 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…

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…

无序系统与神经网络 · 物理学 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…

机器学习 · 计算机科学 2023-01-16 Loris Felardos , Jérôme Hénin , Guillaume Charpiat
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