title: Low-Precision Stochastic Gradient Langevin Dynamics
abstract: Low-precision optimization is widely used to accelerate large-scale deep learning. Despite providing better uncertainty estimation and generalization, sampling methods remain mostly unexplored in this space. In this paper, we provide the first study of low-precision Stochastic Gradient Langevin Dynamics (SGLD), arguing that it is particularly suited to low-bit arithmetic due to its intrinsic ability to handle system noise. We prove the convergence of low-precision SGLD on strongly log-concave distributions, showing that with full-precision gradient accumulators, SGLD is more robust to quantization error than SGD; however, with low-precision gradient accumulators, SGLD can diverge arbitrarily far from the target distribution with small stepsizes. To remedy this issue, we develop a new quantization function that preserves the correct variance in each update step. We demonstrate that the resulting low-precision SGLD algorithm is comparable to full-precision SGLD and outperforms low-precision SGD on deep learning tasks.
authors: Ruqi Zhang Andrew Gordon Wilson Christopher De Sa
hIndex: Andrew Gordon Wilson 42