Built on

T. S. Cohen, M. Weiler, B. Kicanaoglu, and M. Welling, (2019), arXiv:1902.04615 [cs.LG]
Original
1902
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H.-Y. Hu, S.-H. Li, L. Wang, and Y.-Z. You, Phys. Rev. Res. 2
Original
1903
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L. Kades, J. M. Pawlowski, A. Rothkopf, M. Scherzer, J. M. Urban, S. J. Wetzel, N. Wink, and F. P. G. Ziegler, Phys. Rev. D 102
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1905
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M. C. Cheng, V. Anagiannis, M. Weiler, P. de Haan, T. S. Cohen, and M. Welling, (2019), arXiv:1906.02481 [cs.LG]
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1906
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H. Xu, Y. Ma, H. Liu, D. Deb, H. Liu, J. Tang, and A. K. Jain, “Adversarial attacks and defenses in images, graphs and text: A review,” (2019), arXiv:1909.08072 [cs.LG]
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1909
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D. Grimmer, I. Melgarejo-Lermas, and E. Martín-Martínez, (2019), arXiv:1910.03637 [quant-ph]
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1910
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Y. Zhang, P. Ginsparg, and E.-A. Kim, Physical Review Research 2
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K. G. Wilson, in Recent Developments in Gauge Theories. Proceedings, Nato Advanced Study Institute, Cargese, France, August 26 - September 8, 1979 , Vol. 59, edited by G. ’t Hooft, C. Itzykson, A. Jaffe, H. Lehmann, P. Mitter, I. Singer, and R. Stora (1980) pp. 363–402
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R. Giles, Phys. Rev. D 24
1981
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K. Symanzik, Nucl. Phys. B 226
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Y. Iwasaki, Nucl. Phys. B 258
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G. Cybenko, Mathematics of control, signals and systems 2
1989
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S. Caracciolo, G. Curci, P. Menotti, and A. Pelissetto, Annals Phys. 197
1990
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J. Ambjørn, T. Askgaard, H. Porter, and M. Shaposhnikov, Nucl. Phys. B 353
1991
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R. Loll, Nucl. Phys. B 400
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G. D. Moore, Nucl. Phys. B 480
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F. Niedermayer, Nucl. Phys. B Proc. Suppl. 53
1997
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Then

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2014
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2014
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2014
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2020

Lattice gauge equivariant convolutional neural networks

Favoni, Matteo, Ipp, Andreas, Müller, David I. et al.

Understand

We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems.

At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers.
Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice.
We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.

Built on

T. S. Cohen, M. Weiler, B. Kicanaoglu, and M. Welling, (2019), arXiv:1902.04615 [cs.LG]
Original
1902
Earlier work this paper cites.
H.-Y. Hu, S.-H. Li, L. Wang, and Y.-Z. You, Phys. Rev. Res. 2
Original
1903
Earlier work this paper cites.
L. Kades, J. M. Pawlowski, A. Rothkopf, M. Scherzer, J. M. Urban, S. J. Wetzel, N. Wink, and F. P. G. Ziegler, Phys. Rev. D 102
Original
1905
Earlier work this paper cites.
M. C. Cheng, V. Anagiannis, M. Weiler, P. de Haan, T. S. Cohen, and M. Welling, (2019), arXiv:1906.02481 [cs.LG]
Original
1906
Earlier work this paper cites.
H. Xu, Y. Ma, H. Liu, D. Deb, H. Liu, J. Tang, and A. K. Jain, “Adversarial attacks and defenses in images, graphs and text: A review,” (2019), arXiv:1909.08072 [cs.LG]
Original
1909
Earlier work this paper cites.
D. Grimmer, I. Melgarejo-Lermas, and E. Martín-Martínez, (2019), arXiv:1910.03637 [quant-ph]
Original
1910
Earlier work this paper cites.
Y. Zhang, P. Ginsparg, and E.-A. Kim, Physical Review Research 2
Original
1912
Earlier work this paper cites.
G. Pólya, Mathematische Annalen 84
1921
Earlier work this paper cites.
K. G. Wilson, Phys. Rev. D 10
1974
Earlier work this paper cites.
A. M. Polyakov, Phys. Lett. B 72
1978
Earlier work this paper cites.
M. Creutz, Phys. Rev. D 21
1980
Earlier work this paper cites.
K. G. Wilson, in Recent Developments in Gauge Theories. Proceedings, Nato Advanced Study Institute, Cargese, France, August 26 - September 8, 1979 , Vol. 59, edited by G. ’t Hooft, C. Itzykson, A. Jaffe, H. Lehmann, P. Mitter, I. Singer, and R. Stora (1980) pp. 363–402
1980
Earlier work this paper cites.
R. Giles, Phys. Rev. D 24
1981
Earlier work this paper cites.
K. Symanzik, Nucl. Phys. B 226
1983
Earlier work this paper cites.
Y. Iwasaki, Nucl. Phys. B 258
1985
Earlier work this paper cites.
G. Cybenko, Mathematics of control, signals and systems 2
1989
Earlier work this paper cites.
S. Caracciolo, G. Curci, P. Menotti, and A. Pelissetto, Annals Phys. 197
1990
Earlier work this paper cites.
J. Ambjørn, T. Askgaard, H. Porter, and M. Shaposhnikov, Nucl. Phys. B 353
1991
Earlier work this paper cites.
R. Loll, Nucl. Phys. B 400
1993
Earlier work this paper cites.
G. D. Moore, Nucl. Phys. B 480
1996
Earlier work this paper cites.
F. Niedermayer, Nucl. Phys. B Proc. Suppl. 53
1997
Earlier work this paper cites.

Similar

J. F. Lagaë and D. K. Sinclair, Phys. Rev. D 59
1998
Cited alongside, same era.
G. S. Bali, Phys. Rept. 343
2001
Cited alongside, same era.
B. Jähne, Digital Image Processing, 5th revised and extended edition (Berlin: Springer-Verlag, 2002)
2002
Cited alongside, same era.
M. Finzi, S. Stanton, P. Izmailov, and A. G. Wilson, (2020), arXiv:2002.12880 [stat.ML]
Original
2002
Cited alongside, same era.
J. Smit, Introduction to Quantum Fields on a Lattice (Cambridge University Press, 2002)
2002
Cited alongside, same era.
S. O. Bilson-Thompson, D. B. Leinweber, and A. G. Williams, Annals Phys. 304
2003
Cited alongside, same era.