From Global to Local: A Scalable Benchmark for Local Posterior Sampling

TL;DR

This paper introduces a scalable benchmark for evaluating local posterior sampling in neural networks, highlighting RMSProp-preconditioned SGLD's effectiveness in capturing local geometry despite limited global convergence guarantees.

Contribution

The paper proposes a novel benchmark for assessing local sampling performance of SGMCMC algorithms and evaluates their effectiveness on large-scale models.

Findings

RMSProp-preconditioned SGLD best captures local posterior geometry

The benchmark scales to models with up to 100 million parameters

Empirical results demonstrate local information extraction without global guarantees

Abstract

Degeneracy is an inherent feature of the loss landscape of neural networks, but it is not well understood how stochastic gradient MCMC (SGMCMC) algorithms interact with this degeneracy. In particular, current global convergence guarantees for common SGMCMC algorithms rely on assumptions which are likely incompatible with degenerate loss landscapes. In this paper, we argue that this gap requires a shift in focus from global to local posterior sampling, and, as a first step, we introduce a novel scalable benchmark for evaluating the local sampling performance of SGMCMC algorithms. We evaluate a number of common algorithms, and find that RMSProp-preconditioned SGLD is most effective at faithfully representing the local geometry of the posterior distribution. Although we lack theoretical guarantees about global sampler convergence, our empirical results show that we are able to extract non-trivial local information in models with up to O(100M) parameters.