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.

本研究通过使用Hamiltonian Monte Carlo（HMC）来执行连续贝叶斯推理，并通过其样本拟合密度估计器将后验作为新任务的先验进行传播，从而检验了访问真实后验能否保证预防神经网络中的灾难性遗忘，并发现这种方法无法预防灾难性遗忘，说明进行神经网络中的顺序贝叶斯推理的困难性。因此，提出了一种概率连续学习生成过程的贝叶斯模型，而非依赖于神经网络权重的顺序贝叶斯推理。此外，还提出了一个名为原型贝叶斯连续学习的简单基线，可用于类增量连续学习视觉基准，与最先进的贝叶斯连续学习方法相竞争。

连续学习的序列贝叶斯推理