text: 151,124,1403147732215156745,960527787428900864,Michael Albergo,"*New paper* with the @MIT crew, @DaniloJRezende @sracaniere @DeepMind , @KyleCranmer and Julian Urban! We construct normalizing flows that are compatible with sampling path integrals of quantum field theories involving fermions. Fermions make this tricky! <LINK> <LINK> A primary goal in lattice field theory is to compute path integral expectations arising from the ""action"" of the theory. For a theory involving bosons and fermions, that may look something like this equation. These integrals are generally evaluated with Markov chain Monte Carlo: <LINK> The second set of integration measures here refer to integrals over the fermion fields ψ, which aren't like bosonic, scalar fields. They are defined by Grassmann numbers, which are elements of the exterior algebra over the complex numbers. Grassmann numbers anti-commute! Because of this, the ""Grassmann"" part of these integrals can be analytically solved, which sounds like a blessing but can make the rest of the MCMC process difficult! For theories that we want to study, this means we have to compute the determinant of some pretty gnarly matrices: <LINK> We present a number of MCMC samplers to deal with this fact that primarily rely on the equivalence of these determinant calculations with a Gaussian integral over a set of auxiliary fields that are called ""pseudofermions"": <LINK> We then construct a variety of normalizing flows compatible with each of the samplers, making sure each captures the translational equivariance quirks (anti-periodicity in time) that arise from the fermionic degrees of freedom: <LINK> We apply these ideas to a Yukawa theory, where bosons are coupled to mass-degenerate fermions, to show how it works! <LINK> These tools should be applicable to a bunch of problems in lattice field theory and condensed matter, so we are excited to see where it takes us :)",https://arxiv.org/abs/2106.05934,"Algorithms based on normalizing flows are emerging as promising machine learning approaches to sampling complicated probability distributions in a way that can be made asymptotically exact. In the context of lattice field theory, proof-of-principle studies have demonstrated the effectiveness of this approach for scalar theories, gauge theories, and statistical systems. This work develops approaches that enable flow-based sampling of theories with dynamical fermions, which is necessary for the technique to be applied to lattice field theory studies of the Standard Model of particle physics and many condensed matter systems. As a practical demonstration, these methods are applied to the sampling of field configurations for a two-dimensional theory of massless staggered fermions coupled to a scalar field via a Yukawa interaction. ",Flow-based sampling for fermionic lattice field theories,8,"['*New paper* with the @MIT crew, @DaniloJRezende @sracaniere @DeepMind , @KyleCranmer and Julian Urban! We construct normalizing flows that are compatible with sampling path integrals of quantum field theories involving fermions. Fermions make this tricky! <LINK> <LINK>', 'A primary goal in lattice field theory is to compute path integral expectations arising from the ""action"" of the theory. For a theory involving bosons and fermions, that may look something like this equation. These integrals are generally evaluated with Markov chain Monte Carlo: https://t.co/HpNlUqfo3Y', ""The second set of integration measures here refer to integrals over the fermion fields ψ, which aren't like bosonic, scalar fields. They are defined by Grassmann numbers, which are elements of the exterior algebra over the complex numbers. Grassmann numbers anti-commute!"", 'Because of this, the ""Grassmann"" part of these integrals can be analytically solved, which sounds like a blessing but can make the rest of the MCMC process difficult! For theories that we want to study, this means we have to compute the determinant of some pretty gnarly matrices: https://t.co/116GNPqwl1', 'We present a number of MCMC samplers to deal with this fact that primarily rely on the equivalence of these determinant calculations with a Gaussian integral over a set of auxiliary fields that are called ""pseudofermions"": https://t.co/h9ehhuTdMW', 'We then construct a variety of normalizing flows compatible with each of the samplers, making sure each captures the translational equivariance quirks (anti-periodicity in time) that arise from the fermionic degrees of freedom: https://t.co/TrcDd3Vwko', 'We apply these ideas to a Yukawa theory, where bosons are coupled to mass-degenerate fermions, to show how it works! https://t.co/rwmLqC68Rb', 'These tools should be applicable to a bunch of problems in lattice field theory and condensed matter, so we are excited to see where it takes us :)']",21,06,1853