Discrete Neural Flow Samplers with Locally Equivariant Transformer

• URL: http://arxiv.org/abs/2505.17741v1
• Date: Fri, 23 May 2025 11:06:06 GMT
• Title: Discrete Neural Flow Samplers with Locally Equivariant Transformer
• Authors: Zijing Ou, Ruixiang Zhang, Yingzhen Li,
• Abstract summary: We propose Discrete Neural Flow Samplers (DNFS), a trainable and efficient framework for discrete sampling.<n>DNFS learns the rate matrix of a continuous-time Markov chain such that the resulting dynamics satisfy the Kolmogorov equation.<n>To further facilitate computational efficiency, we propose locally equivaraint Transformer, a novel parameterisation of the rate matrix.
• Score: 25.911046280803586
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sampling from unnormalised discrete distributions is a fundamental problem across various domains. While Markov chain Monte Carlo offers a principled approach, it often suffers from slow mixing and poor convergence. In this paper, we propose Discrete Neural Flow Samplers (DNFS), a trainable and efficient framework for discrete sampling. DNFS learns the rate matrix of a continuous-time Markov chain such that the resulting dynamics satisfy the Kolmogorov equation. As this objective involves the intractable partition function, we then employ control variates to reduce the variance of its Monte Carlo estimation, leading to a coordinate descent learning algorithm. To further facilitate computational efficiency, we propose locally equivaraint Transformer, a novel parameterisation of the rate matrix that significantly improves training efficiency while preserving powerful network expressiveness. Empirically, we demonstrate the efficacy of DNFS in a wide range of applications, including sampling from unnormalised distributions, training discrete energy-based models, and solving combinatorial optimisation problems.

Related papers

• LEAPS: A discrete neural sampler via locally equivariant networks [3.5032660973169727]
  We propose LEAPS, an algorithm to sample from discrete distributions known up to normalization by learning a rate matrix of a continuous-time Markov chain (CTMC)<n> LEAPS can be seen as a continuous-time formulation of annealed importance sampling and sequential Monte Carlo methods, extended so that the variance of the importance weights is offset by the inclusion of the CTMC.<n>We demonstrate the efficacy of LEAPS on problems in statistical physics.
  arXiv  Detail & Related papers  (2025-02-15T16:16:45Z)
• Accelerated Parallel Tempering via Neural Transports [31.81728174953862]
  Parallel Tempering (PT) enhances MCMC's sample efficiency through parallel computation.<n>We introduce a framework that accelerates PT by leveraging neural samplers.<n>We demonstrate theoretically and empirically on a variety of multimodal sampling problems that our method improves sample quality.
  arXiv  Detail & Related papers  (2025-02-14T17:41:44Z)
• Neural Flow Samplers with Shortcut Models [19.81513273510523]
  Flow-based samplers generate samples by learning a velocity field that satisfies the continuity equation.<n>While importance sampling provides an approximation, it suffers from high variance.
  arXiv  Detail & Related papers  (2025-02-11T07:55:41Z)
• Adaptive Sampling for Continuous Group Equivariant Neural Networks [5.141137421503899]
  We introduce an adaptive sampling approach that dynamically adjusts the sampling process to the symmetries in the data. Our findings demonstrate improved model performance, and a marginal increase in memory efficiency.
  arXiv  Detail & Related papers  (2024-09-13T11:50:09Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Adaptive Annealed Importance Sampling with Constant Rate Progress [68.8204255655161]
  Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution. We propose the Constant Rate AIS algorithm and its efficient implementation for $alpha$-divergences.
  arXiv  Detail & Related papers  (2023-06-27T08:15:28Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC [83.48593305367523]
  Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. We introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.
  arXiv  Detail & Related papers  (2021-02-04T02:21:08Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)
• Stochastic Normalizing Flows [2.323220706791067]
  We show that normalizing flows can be used to learn the transformation of a simple prior distribution. We derive an efficient training procedure by which both the sampler's and the flow's parameters can be optimized end-to-end. We illustrate the representational power, sampling efficiency and correctness of SNFs on several benchmarks including applications to molecular sampling systems in equilibrium.
  arXiv  Detail & Related papers  (2020-02-16T23:29:32Z)

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.