No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers

TL;DR

This paper explores simulation-free training of neural samplers for sampling from complex distributions, highlighting the importance of Langevin preconditioning and proposing a baseline combining MCMC with generative models.

Contribution

It introduces a modified simulation-free training method using time-dependent normalizing flows and systematically analyzes the role of Langevin preconditioning in neural samplers.

Findings

Simulation-free training faces mode collapse without Langevin preconditioning.

Most neural samplers fail to cover simple target distributions without proper preconditioning.

Combining MCMC with generative models provides a strong baseline for future research.

Abstract

We consider the sampling problem, where the aim is to draw samples from a distribution whose density is known only up to a normalization constant. Recent breakthroughs in generative modeling to approximate a high-dimensional data distribution have sparked significant interest in developing neural network-based methods for this challenging problem. However, neural samplers typically incur heavy computational overhead due to simulating trajectories during training. This motivates the pursuit of simulation-free training procedures of neural samplers. In this work, we propose an elegant modification to previous methods, which allows simulation-free training with the help of a time-dependent normalizing flow. However, it ultimately suffers from severe mode collapse. On closer inspection, we find that nearly all successful neural samplers rely on Langevin preconditioning to avoid mode collapsing. We systematically analyze several popular methods with various objective functions and demonstrate that, in the absence of Langevin preconditioning, most of them fail to adequately cover even a simple target. Finally, we draw attention to a strong baseline by combining the state-of-the-art MCMC method, Parallel Tempering (PT), with an additional generative model to shed light on future explorations of neural samplers.