Understanding and eliminating spurious modes in variational Monte Carlo using collective variables

• URL: http://arxiv.org/abs/2211.09767v1
• Date: Fri, 11 Nov 2022 20:13:10 GMT
• Title: Understanding and eliminating spurious modes in variational Monte Carlo using collective variables
• Abstract summary: We show that a collective-variable-based penalization yields a substantially more robust training procedure. Because the penalization scheme is cheap to implement and is not specific to the particular model studied here, it can be extended to other applications of VMC.
• Score: 6.389320429740539
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The use of neural network parametrizations to represent the ground state in variational Monte Carlo (VMC) calculations has generated intense interest in recent years. However, as we demonstrate in the context of the periodic Heisenberg spin chain, this approach can produce unreliable wave function approximations. One of the most obvious signs of failure is the occurrence of random, persistent spikes in the energy estimate during training. These energy spikes are caused by regions of configuration space that are over-represented by the wave function density, which are called ``spurious modes'' in the machine learning literature. After exploring these spurious modes in detail, we demonstrate that a collective-variable-based penalization yields a substantially more robust training procedure, preventing the formation of spurious modes and improving the accuracy of energy estimates. Because the penalization scheme is cheap to implement and is not specific to the particular model studied here, it can be extended to other applications of VMC where a reasonable choice of collective variable is available.

Related papers

• Why SGD is not Brownian Motion: A New Perspective on Stochastic Dynamics [92.39053980710702]
  Gradient Descent (SGD) is commonly modeled as a Langevin process, assuming that minibatch noise acts as Brownian motion.<n>This approximation relies on a continuous-time limit and a sqrt(eta) noise scaling that does not match the discrete SGD update at finite learning rate.<n>We propose an alternative formulation of SGD as deterministic dynamics in a fluctuating loss landscape induced by minibatch sampling.
  arXiv  Detail & Related papers  (2026-05-21T15:50:40Z)
• Removing nodal and support-mismatch pathologies in Variational Monte Carlo via blurred sampling [5.276073131901768]
  Variational Monte Carlo (VMC) is a powerful and fast-growing method for optimizing and evolving parameterized body wave functions.<n>In practice, however, without the backbone of the method can become unstable or biased due to the presence of nodes.<n>We introduce blurred sampling to address these difficulties.
  arXiv  Detail & Related papers  (2026-03-18T18:00:05Z)
• Entropy Production in Machine Learning Under Fokker-Planck Probability Flow [0.0]
  We propose an entropy-based retraining framework grounded in non-equilibrium cost dynamics.<n>We show that entropy-triggered retraining achieves predictive performance comparable to high-frequency retraining.
  arXiv  Detail & Related papers  (2026-01-02T04:01:57Z)
• Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks [0.0]
  We show that Generative Adversarial Networks (GANs) may be fruitfully exploited to learn dynamics.<n>We showcase the application to a two-dimensional, many-particle system, focusing on surface-step fluctuations and on the related time-dependent roughness.
  arXiv  Detail & Related papers  (2025-07-29T12:48:03Z)
• Numerical Generalized Randomized Hamiltonian Monte Carlo for piecewise smooth target densities [0.0]
  Generalized Hamiltonian Monte Carlo processes for sampling continuous densities with discontinuous gradient and piecewise smooth targets are proposed. It is argued that the techniques lead to GRHMC processes that admit the desired target distribution as the invariant distribution in both scenarios.
  arXiv  Detail & Related papers  (2025-04-25T09:41:57Z)
• Nonequilibrium Universality of Rydberg-Excitation Spreading on a Dynamic Network [0.0]
  An absorbing-state phase transition (ASPT) of Rydberg-excitation spreading occurs in a laser-driven gas of mobile atoms. It occurs on an irregular graph, set by the random atom positions in the gas and, depending on temperature, changes its character from static to dynamic. We study the potential modification of the universality class by losses as a function of dissipation strength.
  arXiv  Detail & Related papers  (2025-02-20T17:31:37Z)
• Probing the many-body localized spin-glass phase through quench dynamics [0.0]
  We characterize the dynamical properties of a disordered spin chain, focusing on the spin-glass regime. We explain these oscillations deep in the many-body localized spin glass regime via a simple theoretical model. Our work suggests that RG predictions can be quantitatively tested against numerical simulations and experiments, potentially enabling microscopic descriptions of dynamical phases in large systems.
  arXiv  Detail & Related papers  (2025-02-12T08:05:22Z)
• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Deterministic Uncertainty Propagation for Improved Model-Based Offline Reinforcement Learning [12.490614705930676]
  We present a theoretical result demonstrating the strong dependency of suboptimality on the number of Monte Carlo samples taken per Bellman target calculation. Our main contribution is a deterministic approximation to the Bellman target that uses progressive moment matching. We show that it is possible to provide tighter guarantees for the suboptimality of MOMBO than the existing Monte Carlo sampling approaches.
  arXiv  Detail & Related papers  (2024-06-06T13:58:41Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Machine learning in and out of equilibrium [58.88325379746631]
  Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium. We propose a new variation of Langevin dynamics (SGLD) that harnesses without replacement minibatching.
  arXiv  Detail & Related papers  (2023-06-06T09:12:49Z)
• On Uncertainty in Deep State Space Models for Model-Based Reinforcement Learning [21.63642325390798]
  We show that RSSMs use a suboptimal inference scheme and that models trained using this inference overestimate the aleatoric uncertainty of the ground truth system. We propose an alternative approach building on well-understood components for modeling aleatoric and epistemic uncertainty, dubbed Variational Recurrent Kalman Network (VRKN) Our experiments show that using the VRKN instead of the RSSM improves performance in tasks where appropriately capturing aleatoric uncertainty is crucial.
  arXiv  Detail & Related papers  (2022-10-17T16:59:48Z)
• DynaConF: Dynamic Forecasting of Non-Stationary Time Series [4.286546152336783]
  We propose a new method to model non-stationary conditional distributions over time. We show that our model can adapt to non-stationary time series better than state-of-the-art deep learning solutions.
  arXiv  Detail & Related papers  (2022-09-17T21:40:02Z)
• Training Discrete Deep Generative Models via Gapped Straight-Through Estimator [72.71398034617607]
  We propose a Gapped Straight-Through ( GST) estimator to reduce the variance without incurring resampling overhead. This estimator is inspired by the essential properties of Straight-Through Gumbel-Softmax. Experiments demonstrate that the proposed GST estimator enjoys better performance compared to strong baselines on two discrete deep generative modeling tasks.
  arXiv  Detail & Related papers  (2022-06-15T01:46:05Z)
• Dealing with collinearity in large-scale linear system identification using Bayesian regularization [3.04585143845864]
  We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses.
  arXiv  Detail & Related papers  (2022-03-25T13:11:26Z)
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states [0.0]
  Neural-network quantum states (NQS) have been shown to be a suitable variational ansatz to simulate out-of-equilibrium dynamics. We show that stable and accurate time propagation can be achieved in regimes of sufficiently regularized variational dynamics.
  arXiv  Detail & Related papers  (2021-05-03T17:55:09Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Targeted free energy estimation via learned mappings [66.20146549150475]
  Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences. FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted Free Energy Perturbation, uses a high-dimensional mapping in configuration space to increase overlap.
  arXiv  Detail & Related papers  (2020-02-12T11:10:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.