[Paper Review] Flow-based sampling for multimodal and extended-mode distributions in lattice field theory

Daniel C. Hackett, Chih‐Chen Hsieh+8 more|arXiv (Cornell University)|Jul 1, 2021

Gaussian Processes and Bayesian Inference4 references35 citations

TL;DR

The paper develops flow-based methods to model multimodal distributions in lattice field theory, and proposes composite augmentation with traditional samplers to achieve efficient, exact sampling. It also analyzes training schemes to avoid mode collapse and tests on a two-dimensional real scalar field theory.

ABSTRACT

Recent results have demonstrated that samplers constructed with flow-based generative models are a promising new approach for configuration generation in lattice field theory. In this paper, we present a set of training- and architecture-based methods to construct flow models for targets with multiple separated modes (i.e.~vacua) as well as targets with extended/continuous modes. We demonstrate the application of these methods to modeling two-dimensional real and complex scalar field theories in their symmetry-broken phases. In this context we investigate different flow-based sampling algorithms, including a composite sampling algorithm where flow-based proposals are occasionally augmented by applying updates using traditional algorithms like HMC.

Motivation & Objective

• Motivate and address sampling challenges in lattice field theory with multimodal distributions.
• Develop flow-based models that capture multiple separated modes without explicit mode knowledge.
• Propose composite and augmented MCMC schemes to improve mixing between modes while preserving exactness.
• Investigate training strategies to avoid mode collapse and underweighting of inner tails.
• Apply constructed multimodal flow models to a two-dimensional real scalar field theory and evaluate sampling efficiency.

Proposed method

• Review of update-based MCMC and flow-based sampling with reverse KL self-training.
• Analysis of multimodal sampling pathologies such as mode collapse and inner-tail underweighting.
• Construction of multimodal flow models via mixtures and symmetrized mixtures.
• Training strategies including forwards KL and adiabatic retraining to mitigate mode collapse.
• Composite MCMC combining flow-based proposals with augmented updates like HMC to enhance mode hopping.
• Application to lattice scalar field theory in 2D, with evaluation of flow-based MCMC and augmented schemes.

Experimental results

Research questions

• RQ1 How can flow-based models be trained to accurately represent multimodal target distributions in lattice field theory?
• RQ2 What are effective strategies to prevent mode collapse in flow training for multimodal targets?
• RQ3 Can mixtures and symmetry-based mixture constructions provide robust coverage of all modes?
• RQ4 How do composite or augmented MCMC schemes compare to pure flow-based or traditional MCMC in sampling efficiency for multimodal theories?

Key findings

• Flow models can represent bimodal distributions in a 2D real scalar field theory but may underweight inner tails, affecting pure flow-based MCMC.
• Mixtures of modal flow models and single-model symmetrized mixtures can provide coverage of all modes.
• Augmented MCMC, combining flow proposals with HMC updates, yields more efficient sampling and better reliability than flow-based MCMC alone.
• Training strategies such as forwards KL, adiabatic retraining, and flow-distance regularization help mitigate mode collapse and improve multimodal coverage.
• Composite sampling algorithms leveraging both flow-based proposals and traditional updates can outperform pure HMC and flow-based MCMC in multimodal settings.