The Ray Tracing Sampler: Bayesian Sampling of Neural Networks for Everyone

TL;DR

This paper introduces a novel ray tracing-based Bayesian sampler for neural networks that offers superior resilience to stochastic gradient heating and can efficiently sample complex posterior distributions, demonstrated on large models like GPT-2.

Contribution

The authors develop a new ray tracing sampler that generalizes existing methods and enables efficient Bayesian inference for large neural networks on consumer hardware.

Findings

Outperforms Hamiltonian Monte Carlo in resilience to heating

Successfully samples posterior of GPT-2 with 1.5 billion parameters

Provides a unified framework encompassing traditional samplers

Abstract

We derive a Markov Chain Monte Carlo sampler based on following ray paths in a medium where the refractive index $n(x)$ is a function of the desired likelihood $\mathcal{L}(x)$. The sampling method propagates rays at constant speed through parameter space, leading to orders of magnitude higher resilience to heating for stochastic gradients as compared to Hamiltonian Monte Carlo (HMC), as well as the ability to cross any likelihood barrier, including holes in parameter space. Using the ray tracing method, we sample the posterior distributions of neural network outputs for a variety of different architectures, up to the 1.5 billion-parameter GPT-2 (Generative Pre-trained Transformer 2) architecture, all on a single consumer-level GPU. We also show that prior samplers including traditional HMC, microcanonical HMC, Metropolis, Gibbs, and even Monte Carlo integration are special cases within a generalized ray tracing framework, which can sample according to an arbitrary weighting function. Public code and documentation for C, JAX, and PyTorch are available at https://bitbucket.org/pbehroozi/ray-tracing-sampler/src