Built on

M. S. Albergo, G. Kanwar, and P. E. Shanahan, Flow-based generative models for Markov chain Monte Carlo in lattice field theory, Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
K. A. Nicoli, S. Nakajima, N. Strodthoff, W. Samek, K.-R. Müller, and P. Kessel, Asymptotically unbiased estimation of physical observables with neural samplers, Phys. Rev. E 101
Original
1910
Earlier work this paper cites.
S. Mandelstam, Charge - Monopole Duality and the Phases of Nonabelian Gauge Theories, Phys. Rev. D 19
1979
Earlier work this paper cites.
Charge - Monopole Duality and the Phases of Nonabelian Gauge Theories
S. Mandelstam · 1979
Earlier work this paper cites.
H. Nicolai, Supersymmetry and Functional Integration Measures, Nucl. Phys. B 176
1980
Earlier work this paper cites.
R. H. Swendsen and J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
U. Wolff, Collective Monte Carlo Updating for Spin Systems, Phys. Rev. Lett. 62
1989
Earlier work this paper cites.
P. E. Crouch and R. Grossman, Numerical integration of ordinary differential equations on manifolds, Journal of Nonlinear Science 3
1993
Earlier work this paper cites.
G. Kanwar, M. S. Albergo, D. Boyda, K. Cranmer, D. C. Hackett, S. Racanière, D. J. Rezende, and P. E. Shanahan, Equivariant flow-based sampling for lattice gauge theory, Phys. Rev. Lett. 125
Original
2003
Earlier work this paper cites.
M. Lüscher, Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD, Comput. Phys. Commun. 165
2005
Earlier work this paper cites.
M. Thomas and A. T. Joy, Elements of information theory (Wiley-Interscience, 2006)
2006
Earlier work this paper cites.
Elements of information theory
M. Thomas and A. T. Joy · 2006
Earlier work this paper cites.
K. A. Nicoli, C. J. Anders, L. Funcke, T. Hartung, K. Jansen, P. Kessel, S. Nakajima, and P. Stornati, Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models, Phys. Rev. Lett. 126
Original
2007
Earlier work this paper cites.
D. Boyda, G. Kanwar, S. Racanière, D. J. Rezende, M. S. Albergo, K. Cranmer, D. C. Hackett, and P. E. Shanahan, Sampling using S U ( N ) SU(N) gauge equivariant flows, Phys. Rev. D 103
Original
2008
Earlier work this paper cites.

Similar

M. Lüscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun. Math. Phys. 293
Original
2010
Cited alongside, same era.
M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi, Solving Lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181
Original
2010
Cited alongside, same era.
G. P. Engel and S. Schaefer, Testing trivializing maps in the Hybrid Monte Carlo algorithm, Comput. Phys. Commun. 182
Original
2011
Cited alongside, same era.
S. Schaefer, R. Sommer, and F. Virotta (ALPHA), Critical slowing down and error analysis in lattice QCD simulations, Nucl. Phys. B 845
Original
2011
Cited alongside, same era.
B. Sengupta, K. J. Friston, and W. D. Penny, Efficient gradient computation for dynamical models, NeuroImage 98

Then

P. de Haan, C. Rainone, M. C. N. Cheng, and R. Bondesan, Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows, (2021), arXiv:2110.02673 [cs.LG]
Original
2021
Later among the works it cites.
L. Falorsi, Continuous normalizing flows on manifolds, (2021), arXiv:2104.14959
Original
2021
Later among the works it cites.
I. Katsman, A. Lou, D. Lim, Q. Jiang, S. N. Lim, and C. M. De Sa, Equivariant manifold flows, Advances in Neural Information Processing Systems 34
2021
Later among the works it cites.
M. S. Albergo, D. Boyda, K. Cranmer, D. C. Hackett, G. Kanwar, S. Racanière, D. J. Rezende, F. Romero-López, P. E. Shanahan, and J. M. Urban, Flow-based sampling in the lattice Schwinger model at criticality, Phys. Rev. D 106
Original
2022
Closest in time.
R. Abbott et al. , Sampling QCD field configurations with gauge-equivariant flow models, in 39th International Symposium on Lattice Field Theory (2022) arXiv:2208.03832 [hep-lat]

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2022

Learning Trivializing Gradient Flows for Lattice Gauge Theories

Bacchio, Simone, Kessel, Pan, Schaefer, Stefan et al.

Understand

We propose a unifying approach that starts from the perturbative construction of trivializing maps by L\"uscher and then improves on it by learning.

The resulting continuous normalizing flow model can be implemented using common tools of lattice field theory and requires several orders of magnitude fewer parameters than any existing machine learning approach.
Specifically, our model can achieve competitive performance with as few as 14 parameters while existing deep-learning models have around 1 million parameters for $SU(3)$ Yang--Mills theory on a $16^2$ lattice.
This has obvious consequences for training speed and interpretability.

Built on

M. S. Albergo, G. Kanwar, and P. E. Shanahan, Flow-based generative models for Markov chain Monte Carlo in lattice field theory, Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
K. A. Nicoli, S. Nakajima, N. Strodthoff, W. Samek, K.-R. Müller, and P. Kessel, Asymptotically unbiased estimation of physical observables with neural samplers, Phys. Rev. E 101
Original
1910
Earlier work this paper cites.
S. Mandelstam, Charge - Monopole Duality and the Phases of Nonabelian Gauge Theories, Phys. Rev. D 19
1979
Earlier work this paper cites.
Charge - Monopole Duality and the Phases of Nonabelian Gauge Theories
S. Mandelstam · 1979
Earlier work this paper cites.
H. Nicolai, Supersymmetry and Functional Integration Measures, Nucl. Phys. B 176
1980
Earlier work this paper cites.
R. H. Swendsen and J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58
1987
Earlier work this paper cites.
U. Wolff, Collective Monte Carlo Updating for Spin Systems, Phys. Rev. Lett. 62
1989
Earlier work this paper cites.
P. E. Crouch and R. Grossman, Numerical integration of ordinary differential equations on manifolds, Journal of Nonlinear Science 3
1993
Earlier work this paper cites.
G. Kanwar, M. S. Albergo, D. Boyda, K. Cranmer, D. C. Hackett, S. Racanière, D. J. Rezende, and P. E. Shanahan, Equivariant flow-based sampling for lattice gauge theory, Phys. Rev. Lett. 125
Original
2003
Earlier work this paper cites.
M. Lüscher, Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD, Comput. Phys. Commun. 165
2005
Earlier work this paper cites.
M. Thomas and A. T. Joy, Elements of information theory (Wiley-Interscience, 2006)
2006
Earlier work this paper cites.
Elements of information theory
M. Thomas and A. T. Joy · 2006
Earlier work this paper cites.
K. A. Nicoli, C. J. Anders, L. Funcke, T. Hartung, K. Jansen, P. Kessel, S. Nakajima, and P. Stornati, Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models, Phys. Rev. Lett. 126
Original
2007
Earlier work this paper cites.
D. Boyda, G. Kanwar, S. Racanière, D. J. Rezende, M. S. Albergo, K. Cranmer, D. C. Hackett, and P. E. Shanahan, Sampling using S U ( N ) SU(N) gauge equivariant flows, Phys. Rev. D 103
Original
2008
Earlier work this paper cites.

Similar

M. Lüscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun. Math. Phys. 293
Original
2010
Cited alongside, same era.
M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi, Solving Lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181
Original
2010
Cited alongside, same era.
G. P. Engel and S. Schaefer, Testing trivializing maps in the Hybrid Monte Carlo algorithm, Comput. Phys. Commun. 182
Original
2011
Cited alongside, same era.
S. Schaefer, R. Sommer, and F. Virotta (ALPHA), Critical slowing down and error analysis in lattice QCD simulations, Nucl. Phys. B 845
Original
2011
Cited alongside, same era.
B. Sengupta, K. J. Friston, and W. D. Penny, Efficient gradient computation for dynamical models, NeuroImage 98

Then

P. de Haan, C. Rainone, M. C. N. Cheng, and R. Bondesan, Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows, (2021), arXiv:2110.02673 [cs.LG]
Original
2021
Later among the works it cites.
L. Falorsi, Continuous normalizing flows on manifolds, (2021), arXiv:2104.14959
Original
2021
Later among the works it cites.
I. Katsman, A. Lou, D. Lim, Q. Jiang, S. N. Lim, and C. M. De Sa, Equivariant manifold flows, Advances in Neural Information Processing Systems 34
2021
Later among the works it cites.
M. S. Albergo, D. Boyda, K. Cranmer, D. C. Hackett, G. Kanwar, S. Racanière, D. J. Rezende, F. Romero-López, P. E. Shanahan, and J. M. Urban, Flow-based sampling in the lattice Schwinger model at criticality, Phys. Rev. D 106
Original
2022
Closest in time.
R. Abbott et al. , Sampling QCD field configurations with gauge-equivariant flow models, in 39th International Symposium on Lattice Field Theory (2022) arXiv:2208.03832 [hep-lat]

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2014

Cited alongside, same era.

D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, (2014), arXiv:1412.6980

Original

2014

Cited alongside, same era.

W. Grathwohl, R. T. Chen, J. Bettencourt, I. Sutskever, and D. Duvenaud, Ffjord: Free-form continuous dynamics for scalable reversible generative models, (2018), arXiv:1810.01367

Original

2018

Cited alongside, same era.

J. Köhler, L. Klein, and F. Noé, Equivariant flows: exact likelihood generative learning for symmetric densities, in International conference on machine learning (PMLR, 2020) pp. 5361–5370

2020

Cited alongside, same era.

E. Mathieu and M. Nickel, Riemannian continuous normalizing flows, Advances in Neural Information Processing Systems 33

2020

Cited alongside, same era.

A. Lou, D. Lim, I. Katsman, L. Huang, Q. Jiang, S. N. Lim, and C. M. De Sa, Neural manifold ordinary differential equations, Advances in Neural Information Processing Systems 33

2020

Cited alongside, same era.

L. Richter, A. Boustati, N. Nüsken, F. Ruiz, and O. D. Akyildiz, VarGrad: a low-variance gradient estimator for variational inference, Advances in Neural Information Processing Systems 33

2020

Cited alongside, same era.

M. S. Albergo, G. Kanwar, S. Racanière, D. J. Rezende, J. M. Urban, D. Boyda, K. Cranmer, D. C. Hackett, and P. E. Shanahan, Flow-based sampling for fermionic lattice field theories, Phys. Rev. D 104

Original

2021

Cited alongside, same era.

Original

2022

Closest in time.

L. Del Debbio, J. M. Rossney, and M. Wilson, Machine Learning Trivializing Maps: A First Step Towards Understanding How Flow-Based Samplers Scale Up, PoS LATTICE2021

Original

2022

Closest in time.

K. A. Nicoli, C. J. Anders, L. Funcke, T. Hartung, K. Jansen, P. Kessel, S. Nakajima, and P. Stornati, Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse, PoS LATTICE2021

Original

2022

Closest in time.

M. Gerdes, P. de Haan, C. Rainone, R. Bondesan, and M. C. N. Cheng, Learning Lattice Quantum Field Theories with Equivariant Continuous Flows, (2022), arXiv:2207.00283 [hep-lat]

Original

2022

Closest in time.

J. Finkenrath, Tackling critical slowing down using global correction steps with equivariant flows: the case of the Schwinger model, (2022), arXiv:2201.02216 [hep-lat]

Original

2022

Closest in time.

L. Vaitl, K. A. Nicoli, S. Nakajima, and P. Kessel, Path-gradient estimators for continuous normalizing flows, in International Conference on Machine Learning (PMLR, 2022) pp. 21945–21959

2022

Closest in time.

D. Albandea, L. Del Debbio, P. Hernández, R. Kenway, J. M. Rossney, and A. Ramos, Learning trivializing flows, 39th International Symposium on Lattice Field Theory , (2022), arXiv:2211.12806 [hep-lat]

Original

2022

Closest in time.

S. Bacchio, J. Finkenrath, and C. Stylianou, Lyncs-API: a Python API for Lattice QCD applications, PoS LATTICE2021

Original

2022

Closest in time.

S. Yamamoto, S. Bacchio, and J. Finenrath, Running HMC Simulation with Python via QUDA, (2022), arXiv:2212.06657 [hep-lat]

Original

2022

Closest in time.

Use of Schwinger-Dyson equation in constructing an approximate trivializing map

Original

P. Boyle, T. Izubuchi, L. Jin, C. Jung, C. Lehner, N. Matsumoto, and A. Tomiya · 2023

Closest in time.