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Sampling using $SU(N)$ gauge equivariant flows

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arxiv 2008.05456 v2 pith:G6PPSRMN submitted 2020-08-12 hep-lat cs.LGstat.ML

Denis Boyda , Gurtej Kanwar , Sébastien Racanière , Danilo Jimenez Rezende , Michael S. Albergo , Kyle Cranmer , Daniel C. Hackett , Phiala E. Shanahan This is my paper · ORCID
classification hep-latcs.LGstat.ML
keywords gaugeflow-basedflowslatticesamplingvariablealgorithmalternative
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We develop a flow-based sampling algorithm for $SU(N)$ lattice gauge theories that is gauge-invariant by construction. Our key contribution is constructing a class of flows on an $SU(N)$ variable (or on a $U(N)$ variable by a simple alternative) that respect matrix conjugation symmetry. We apply this technique to sample distributions of single $SU(N)$ variables and to construct flow-based samplers for $SU(2)$ and $SU(3)$ lattice gauge theory in two dimensions.

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