Fixed point actions from convolutional neural networks
Kieran Holland Andreas Ipp David I. Müller Urs Wenger
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. We find that L-CNNs are much more accurate at parametrizing the FP
action compared to older approaches. They may therefore provide a way to
circumvent critical slowing down and topological freezing towards the continuum
limit.