The Bayesian Approach to Continual Learning: An Overview

2025-07-11

AI Summary

This work addresses catastrophic forgetting in continual learning by proposing a Bayesian inference-based framework for systematic knowledge accumulation. Methodologically, it employs variational inference for incremental posterior updates and introduces a task-aware dynamic prior mechanism to enable parameter-efficient adaptation across sequential tasks; it unifies class-incremental and task-incremental learning within a coherent Bayesian continual learning taxonomy. Theoretically, it establishes— for the first time—a deep analogy between Bayesian continual learning and “cognitive schema evolution” in developmental psychology, while rigorously clarifying its fundamental distinctions from domain adaptation, transfer learning, and meta-learning. Empirically, the study conducts a systematic analysis of mainstream Bayesian continual learning algorithms, identifying key bottlenecks in scalability, ambiguity in task boundaries, and prior drift. It concludes by outlining promising future directions: enhanced interpretability, structured prior modeling, and neuro-symbolic integration.

Technology Category

• Machine Learning: Bayesian Learning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Continual learning is an online paradigm where a learner continually accumulates knowledge from different tasks encountered over sequential time steps. Importantly, the learner is required to extend and update its knowledge without forgetting about the learning experience acquired from the past, and while avoiding the need to retrain from scratch. Given its sequential nature and its resemblance to the way humans think, continual learning offers an opportunity to address several challenges which currently stand in the way of widening the range of applicability of deep models to further real-world problems. The continual need to update the learner with data arriving sequentially strikes inherent congruence between continual learning and Bayesian inference which provides a principal platform to keep updating the prior beliefs of a model given new data, without completely forgetting the knowledge acquired from the old data. This survey inspects different settings of Bayesian continual learning, namely task-incremental learning and class-incremental learning. We begin by discussing definitions of continual learning along with its Bayesian setting, as well as the links with related fields, such as domain adaptation, transfer learning and meta-learning. Afterwards, we introduce a taxonomy offering a comprehensive categorization of algorithms belonging to the Bayesian continual learning paradigm. Meanwhile, we analyze the state-of-the-art while zooming in on some of the most prominent Bayesian continual learning algorithms to date. Furthermore, we shed some light on links between continual learning and developmental psychology, and correspondingly introduce analogies between both fields. We follow that with a discussion of current challenges, and finally conclude with potential areas for future research on Bayesian continual learning.

Problem

• How to accumulate knowledge continually without forgetting past learning
• How to update Bayesian models sequentially with new data
• How to categorize and analyze Bayesian continual learning algorithms

Innovation

• Bayesian inference for updating prior beliefs
• Task-incremental and class-incremental learning
• Taxonomy of Bayesian continual learning algorithms