Journal Article

PUBDB-2025-00725

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Detecting and mitigating mode-collapse for flow-based sampling of lattice field theories

Nicoli, K. A. (Corresponding author) ; Anders, C. J. ; Hartung, T. ; Jansen, K.DESY* ; Kessel, P. ; Nakajima, S.

2023
American Physical Society Ridge, NY

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Please use a persistent id in citations: doi:10.1103/PhysRevD.108.114501  doi:10.3204/PUBDB-2025-00725

Report No.: arXiv:2302.14082

Abstract: We study the consequences of mode-collapse of normalizing flows in the context of lattice field theory. Normalizing flows allow for independent sampling. For this reason, it is hoped that they can avoid the tunneling problem of local-update Markov Chain Monte Carlo algorithms for multimodal distributions. In this work, we first point out that the tunneling problem is also present for normalizing flows but is shifted from the sampling to the algorithm’s training phase. Specifically, normalizing flows often suffer from mode-collapse for which the training process assigns vanishingly low probability mass to relevant modes of the physical distribution. This may result in a significant bias when the flow is used as a sampler in a Markov-Chain or with importance sampling. We propose a metric to quantify the degree of mode-collapse and derive a bound on the resulting bias. Furthermore, we propose various mitigation strategies in particular in the context of estimating thermodynamic observables, such as the free energy.

Keyword(s): Monte Carlo: Markov chain ; flow ; tunneling ; lattice field theory ; lattice ; U(1) ; SU(N) ; statistical analysis ; energy: density ; collapse ; partition function ; spontaneous symmetry breaking ; thermodynamical ; free energy

Note: 16 pages, 7 figures, 6 pages of supplement material

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Contributing Institute(s):

1. Centre f. Quantum Techno. a. Application (CQTA)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF4-611) (POF4-611)
2. QUEST - QUantum computing for Excellence in Science and Technology (101087126) (101087126)
3. AQTIVATE - Advanced computing, quantum algorithms, and data-driven approaches for science, technology and engineering (101072344) (101072344)

Experiment(s):

1. No specific instrument

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF >= 5 ; JCR ; SCOAP3 sponsored Journal ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Preprint Nicoli, K. A. (Corresponding author) ; Anders, C. J. ; Hartung, T. ; Jansen, K.DESY* ; Kessel, P. ; Nakajima, S.
Detecting and mitigating mode-collapse for flow-based sampling of lattice field theories
(2023) [10.3204/PUBDB-2025-01127]2023     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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