mlsanityData to 7 Oct 2026

Explaining the effects of non-convergent sampling in the training of Energy-Based Models

arXiv 2301.09428 ↗First posted 23 Jan 2023cs.LG cond-mat.dis-nn cond-mat.stat-mechcited by 11

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Abstract (arXiv)

In this paper, we quantify the impact of using non-convergent Markov chains to train Energy-Based models (EBMs). In particular, we show analytically that EBMs trained with non-persistent short runs to estimate the gradient can perfectly reproduce a set of empirical statistics of the data, not at the level of the equilibrium measure, but through a precise dynamical process. Our results provide a first-principles explanation for the observations of recent works proposing the strategy of using short runs starting from random initial conditions as an efficient way to generate high-quality samples in EBMs, and lay the groundwork for using EBMs as diffusion models. After explaining this effect in generic EBMs, we analyze two solvable models in which the effect of the non-convergent sampling in the trained parameters can be described in detail. Finally, we test these predictions numerically on a ConvNet EBM and a Boltzmann machine.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 20 of its 53 references that are in the map. First posted on arXiv 23 Jan 2023.

Builds on

20 of 53 references.

References · 20

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,539
  5. 2016A Theory of Generative ConvNetcited by 174
  6. 2019Learning Non-Convergent Non-Persistent Short-Run MCMC Toward Energy-Based Modelcited by 147
  7. 2019On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Modelscited by 105
  8. 2019Maximum Entropy Generators for Energy-Based Modelscited by 55
  9. 2022A Tale of Two Flows: Cooperative Learning of Langevin Flow and Normalizing Flow Toward Energy-Based Modelcited by 44
  10. 2017Inverse statistical problems: from the inverse Ising problem to data sciencecited by 36
  11. 2016Deep Directed Generative Models with Energy-Based Probability Estimationcited by 34
  12. 2020Restricted Boltzmann Machine, recent advances and mean-field theorycited by 31
8 more
  1. 2021Equilibrium and non-Equilibrium regimes in the learning of Restricted Boltzmann Machinescited by 27
  2. 2018Thermodynamics of Restricted Boltzmann Machines and related learning dynamicscited by 25
  3. 2020MCMC Should Mix: Learning Energy-Based Model with Neural Transport Latent Space MCMCcited by 25
  4. 2022Gaussian-Bernoulli RBMs Without Tearscited by 17
  5. 2022Learning a Restricted Boltzmann Machine using biased Monte Carlo samplingcited by 11
  6. 2015Learning FRAME Models Using CNN Filterscited by 4
  7. 2019Robust Multi-Output Learning with Highly Incomplete Data via Restricted Boltzmann Machinescited by 3
  8. 2017Layerwise Systematic Scan: Deep Boltzmann Machines and Beyondcited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 2; 2025: 3; 2026: 2.

11 papers.

  1. 2023Inferring effective couplings with Restricted Boltzmann Machinescited by 8
  2. 2024Fast training and sampling of Restricted Boltzmann Machinescited by 8
  3. 2023Fast and Functional Structured Data Generators Rooted in Out-of-Equilibrium Physicscited by 7
  4. 2023Unsupervised hierarchical clustering using the learning dynamics of RBMscited by 4
  5. 2023Parallel Learning by Multitasking Neural Networkscited by 3
  6. 2025Learning Energy-Based Generative Models via Potential Flow: A Variational Principle Approach to Probability Density Homotopy Matchingcited by 2
  7. 2025Pseudo-likelihood produces associative memories able to generalize, even for asymmetric couplingscited by 2
  8. 2024Absolute abstraction: a renormalisation group approachcited by 0
  9. 2025Emergence of Nonequilibrium Latent Cycles in Unsupervised Generative Modelingcited by 0
  10. 2026Distributional simplicity bias and effective convexity in Energy Based Modelscited by 0
  11. 2026Equilibrium Training of Energy-Based Models with Parallel Trajectory Temperingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Jarzynski Reweighting and Sampling Dynamics for Training Energy-Based Models: Theoretical Analysis of Different Transition Kernels
  2. 2025On scalable and efficient training of diffusion samplers
  3. 2024Energy based diffusion generator for efficient sampling of Boltzmann distributions
  4. 2023Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood
  5. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics
  6. 2026A Diffusive Classification Loss for Learning Energy-based Generative Models
  7. 2023Energy-Based Models For Speech Synthesis
  8. 2026Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking