Title: On the practicality of Boltzmann neural samplers
Primary area: learning on graphs and other geometries & topologies
Keywords: chemistry application, enhanced sampling, graph modeling

Abstract: We tackle a challenge at the heart of the missions of computational chemistry and biophysics---to sample a Boltzmann-type distribution
$$
p(\mathbf{x}|\mathcal{G}) \propto e^{-U(\mathbf{x}|\mathcal{G})}
$$
on $\mathbb{R}^{N \times 3}$ associated with some $N$-body system $\mathcal{G}$, where $U$ is an energy function (termed force field) with orthogonal invariance and deep, isolated minima.
Traditionally, this is sampled sequentially using Markov chain Monte Carlo methods, which can be so slow that one, for weeks of wall time, never breaks free from the local minima defined by the starting pose.
Neural samplers have been designed to speed up this process by optimizing the dynamics, prescribed by a stochastic differential equation (SDE).
Though sound and elegant in continuous time, they can be practically unstable and inefficient when discretized.
In this paper, we attribute this phenomena to the limited expressiveness of the finite additive transition kernels, and their inability to bridge distant distributions.
To remedy this, we design a new type of highly flexible prior by mixing orthogonally invariant densities (Mint), as well as a new discretized non-volume-preserving kernel, termed Jacobian-unpreserving Langevin with explicitprojection (Julep). 
Together, MintJulep greatly improve the practical performance of neural samplers, while keeping the underlying SDE intact.