% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{Nicoli:623656,
      author       = {Nicoli, Kim A. and Anders, Christopher J. and Hartung,
                      Tobias and Jansen, Karl and Kessel, Pan and Nakajima,
                      Shinichi},
      title        = {{D}etecting and mitigating mode-collapse for flow-based
                      sampling of lattice field theories},
      journal      = {Physical review / D},
      volume       = {108},
      number       = {11},
      issn         = {2470-0010},
      address      = {Ridge, NY},
      publisher    = {American Physical Society},
      reportid     = {PUBDB-2025-00725, arXiv:2302.14082},
      pages        = {114501},
      year         = {2023},
      note         = {16 pages, 7 figures, 6 pages of supplement material},
      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.},
      keywords     = {Monte Carlo: Markov chain (INSPIRE) / flow (INSPIRE) /
                      tunneling (INSPIRE) / lattice field theory (INSPIRE) /
                      lattice (INSPIRE) / U(1) (INSPIRE) / SU(N) (INSPIRE) /
                      statistical analysis (INSPIRE) / energy: density (INSPIRE) /
                      collapse (INSPIRE) / partition function (INSPIRE) /
                      spontaneous symmetry breaking (INSPIRE) / thermodynamical
                      (INSPIRE) / free energy (INSPIRE)},
      cin          = {CQTA},
      ddc          = {530},
      cid          = {I:(DE-H253)CQTA-20221102},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / QUEST -
                      QUantum computing for Excellence in Science and Technology
                      (101087126) / AQTIVATE - Advanced computing, quantum
                      algorithms, and data-driven approaches for science,
                      technology and engineering (101072344)},
      pid          = {G:(DE-HGF)POF4-611 / G:(EU-Grant)101087126 /
                      G:(EU-Grant)101072344},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {2302.14082},
      howpublished = {arXiv:2302.14082},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2302.14082;\%\%$},
      UT           = {WOS:001137344800005},
      doi          = {10.1103/PhysRevD.108.114501},
      url          = {https://bib-pubdb1.desy.de/record/623656},
}