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2023

Fixed point actions from convolutional neural networks

Holland, Kieran, Ipp, Andreas, Müller, David I. et al.

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Lattice gauge-equivariant convolutional neural networks (L-CNNs) can be used to form arbitrarily shaped Wilson loops and can approximate any gauge-covariant or gauge-invariant function on the lattice.

Here we use L-CNNs to describe fixed point (FP) actions which are based on renormalization group transformations.
FP actions are classically perfect, i.e., they have no lattice artifacts on classical gauge-field configurations satisfying the equations of motion, and therefore possess scale invariant instanton solutions.
FP actions are tree-level Symanzik-improved to all orders in the lattice spacing and can produce physical predictions with very small lattice artifacts even on coarse lattices.

Fixed point actions from convolutional neural networks · Around

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P. Hasenfratz, The Theoretical background and properties of perfect actions , in Advanced Summer School on Nonperturbative Quantum Field Physics , pp. 137–199, 3, 1998 · 1998
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2008
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Then

M. Favoni, A. Ipp, D. I. Müller and D. Schuh, Lattice Gauge Equivariant Convolutional Neural Networks , Phys. Rev. Lett. 128
Original
2012
Later among the works it cites.
S. Bacchio, P. Kessel, S. Schaefer and L. Vaitl, Learning trivializing gradient flows for lattice gauge theories , Phys. Rev. D 107
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2023
Closest in time.
2311.03578
Original
L. Wang, G. Aarts and K. Zhou, Generative Diffusion Models for Lattice Field Theory , in 37th Conference on Neural Information Processing Systems , 11, 2023 · 2023
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