On Sequential Bayesian Inference for Continual Learning

TL;DR

This paper critically examines the effectiveness of sequential Bayesian inference in continual learning, revealing its limitations due to model misspecification and data imbalance, and proposes a new baseline method for improved performance.

Contribution

The paper demonstrates the failure of sequential Bayesian inference to prevent catastrophic forgetting and introduces Prototypical Bayesian Continual Learning as a competitive alternative.

Findings

Sequential Bayesian inference fails to prevent forgetting in neural networks.

Model misspecification can lead to sub-optimal continual learning performance.

Task data imbalance contributes to forgetting.

Abstract

Sequential Bayesian inference can be used for continual learning to prevent catastrophic forgetting of past tasks and provide an informative prior when learning new tasks. We revisit sequential Bayesian inference and test whether having access to the true posterior is guaranteed to prevent catastrophic forgetting in Bayesian neural networks. To do this we perform sequential Bayesian inference using Hamiltonian Monte Carlo. We propagate the posterior as a prior for new tasks by fitting a density estimator on Hamiltonian Monte Carlo samples. We find that this approach fails to prevent catastrophic forgetting demonstrating the difficulty in performing sequential Bayesian inference in neural networks. From there we study simple analytical examples of sequential Bayesian inference and CL and highlight the issue of model misspecification which can lead to sub-optimal continual learning performance despite exact inference. Furthermore, we discuss how task data imbalances can cause forgetting. From these limitations, we argue that we need probabilistic models of the continual learning generative process rather than relying on sequential Bayesian inference over Bayesian neural network weights. In this vein, we also propose a simple baseline called Prototypical Bayesian Continual Learning, which is competitive with state-of-the-art Bayesian continual learning methods on class incremental continual learning vision benchmarks.