Machine Learning Trivializing Maps: A First Step Towards Understanding How Flow-Based Samplers Scale Up

Understand

A trivializing map is a field transformation whose Jacobian determinant exactly cancels the interaction terms in the action, providing a representation of the theory in terms of a deterministic transformation of a distribution from which sampling is trivial.

• Recently, a proof-of-principle study by Albergo, Kanwar and Shanahan [arXiv:1904.12072] demonstrated that approximations of trivializing maps can be `machine-learned' by a class of invertible, differentiable neural models called \textit{normalizing flows}.
• By ensuring that the Jacobian determinant can be computed efficiently, asymptotically exact sampling from the theory of interest can be performed by drawing samples from a simple distribution and passing them through the network.
• From a theoretical perspective, this approach has the potential to become more efficient than traditional Markov Chain Monte Carlo sampling techniques, where autocorrelations severely diminish the sampling efficiency as one approaches the continuum limit.