TY  - EJOUR
AU  - Nicoli, Kim A.
AU  - Anders, Christopher J.
AU  - Hartung, Tobias
AU  - Jansen, Karl
AU  - Kessel, Pan
AU  - Nakajima, Shinichi
TI  - Detecting and mitigating mode-collapse for flow-based sampling of lattice field theories
IS  - arXiv:2302.14082
M1  - PUBDB-2025-01127
M1  - arXiv:2302.14082
PY  - 2023
N1  - 16 pages, 7 figures, 6 pages of supplement material
AB  - 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.
KW  - Monte Carlo: Markov chain (INSPIRE)
KW  - flow (INSPIRE)
KW  - tunneling (INSPIRE)
KW  - lattice field theory (INSPIRE)
KW  - lattice (INSPIRE)
KW  - U(1) (INSPIRE)
KW  - SU(N) (INSPIRE)
KW  - statistical analysis (INSPIRE)
KW  - energy: density (INSPIRE)
KW  - collapse (INSPIRE)
KW  - partition function (INSPIRE)
KW  - spontaneous symmetry breaking (INSPIRE)
KW  - thermodynamical (INSPIRE)
KW  - free energy (INSPIRE)
LB  - PUB:(DE-HGF)25
DO  - DOI:10.3204/PUBDB-2025-01127
UR  - https://bib-pubdb1.desy.de/record/625550
ER  -