Hyperbolic Multimodal Continual Learning

Hyperbolic geometry has recently emerged as a powerful representation space for multimodal learning, as it naturally captures hierarchical semantic structure across modalities. Despite this progress, how such representations behave under continual learning poses fundamentally different challenges that remain underexplored. This work provides a geometric perspective on this problem and establishes a theoretical foundation for representation preservation in hyperbolic space, showing that preventing forgetting requires cross-modal invariance under a shared hyperbolic isometry. We further show that forgetting in hyperbolic continual learning involves both semantic relation drift and hierarchy-related distortion, motivating preservation of both cross-modal relational structure and hierarchical geometry. Guided by these insights, a principled continual learning framework is derived that preserves essential geometric structure while allowing effective adaptation to new tasks. Experiments on continual multimodal benchmarks corroborate the effectiveness of the proposed approach.

Modern AI systems often learn from multiple kinds of data, such as images and text, and they need to keep useful knowledge when new tasks arrive over time. This paper studies how to help such systems avoid forgetting while preserving the meaningful relationships they have already learned. We focus on representations that organize concepts in a hierarchy, from specific ideas to more general ones. Our method encourages the model to keep both the relationships between images and text and the broader structure of this hierarchy as it learns continuously. Experiments show that this approach improves stability and performance across several multimodal learning settings.