Learning to Continually Learn with the Bayesian Principle

TL;DR

This work tackles catastrophic forgetting in continual learning by marrying neural networks with exact sequential Bayesian updates over exponential-family posteriors. It introduces Sequential Bayesian Meta-Continual Learning (SB-MCL), where a meta-learned neural bridge processes data and a simple statistical model performs sequential updates, ensuring forgetting is avoided as the neural components remain fixed during continual learning. The framework unifies prior methods (GeMCL, PN, ALPaCA) as special cases and demonstrates strong performance and efficiency across diverse tasks, including supervised, unsupervised, and deep generative modeling, with broad applicability. It shifts the focus from optimization-driven forgetting prevention to leveraging representational capacity and principled Bayesian updates, while outlining future directions to expand posterior families and scale to larger datasets.

Abstract

In the present era of deep learning, continual learning research is mainly focused on mitigating forgetting when training a neural network with stochastic gradient descent on a non-stationary stream of data. On the other hand, in the more classical literature of statistical machine learning, many models have sequential Bayesian update rules that yield the same learning outcome as the batch training, i.e., they are completely immune to catastrophic forgetting. However, they are often overly simple to model complex real-world data. In this work, we adopt the meta-learning paradigm to combine the strong representational power of neural networks and simple statistical models' robustness to forgetting. In our novel meta-continual learning framework, continual learning takes place only in statistical models via ideal sequential Bayesian update rules, while neural networks are meta-learned to bridge the raw data and the statistical models. Since the neural networks remain fixed during continual learning, they are protected from catastrophic forgetting. This approach not only achieves significantly improved performance but also exhibits excellent scalability. Since our approach is domain-agnostic and model-agnostic, it can be applied to a wide range of problems and easily integrated with existing model architectures.

Figures (15)

• Figure 1: Graphical models of MCL. For each episode $e$, training examples $(x_t^e, y_t^e)$ (or just $x_t^e$) are produced conditioned on the time step $t$ and the episode-wise latent variable $z^e$.
• Figure 2: Schematic diagram of our SB-MCL in a single supervised CL episode. In SB-MCL, CL is formulated as the sequential Bayesian update of an exponential family posterior $q_\phi(z|x_{1:t}, y_{1:t})$. The meta-learned neural networks (the learner and the model) remain fixed during CL to protect themselves from catastrophic forgetting.
• Figure 3: Generalization to longer training streams with more tasks and shots after meta-training with 10-task 10-shot on CASIA.
• Figure 4: Notations for architecture diagrams.
• Figure 5: Architectures for classification experiments.