A Simple Baseline for Bayesian Uncertainty in Deep Learning

TLDR

Stochastic Weight Averaging (SWA) improves deep‑learning generalization by averaging SGD iterates with a modified learning‑rate schedule. The authors introduce SWA‑Gaussian (SWAG), a scalable method for uncertainty representation and calibration in deep learning. SWAG fits a Gaussian whose mean is the SWA solution and whose low‑rank plus diagonal covariance is derived from SGD iterates, then samples from this distribution for Bayesian model averaging. SWAG accurately approximates the true posterior shape and outperforms alternatives on out‑of‑sample detection, calibration, and transfer‑learning tasks.

Abstract

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been shown to improve generalization in deep learning. With SWAG, we fit a Gaussian using the SWA solution as the first moment and a low rank plus diagonal covariance also derived from the SGD iterates, forming an approximate posterior distribution over neural network weights; we then sample from this Gaussian distribution to perform Bayesian model averaging. We empirically find that SWAG approximates the shape of the true posterior, in accordance with results describing the stationary distribution of SGD iterates. Moreover, we demonstrate that SWAG performs well on a wide variety of tasks, including out of sample detection, calibration, and transfer learning, in comparison to many popular alternatives including MC dropout, KFAC Laplace, SGLD, and temperature scaling.