Hyperbolic Multimodal Continual Learning

2026-08-10

AI Summary

This work addresses catastrophic forgetting in multimodal continual learning under hyperspherical geometry, identifying its root causes as semantic relation drift and hierarchical structure distortion. To mitigate these issues, the study establishes, for the first time, a theoretical foundation for representation preservation in hyperbolic space and introduces a structure-preserving continual learning framework. This framework enforces shared isometric transformations across modalities to jointly maintain the geometric invariance of both semantic relationships and hierarchical structures. Experimental results demonstrate that the proposed approach significantly alleviates catastrophic forgetting on multimodal continual learning benchmarks while simultaneously enhancing adaptability to new tasks.

Abstract

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.

Problem

• hyperbolic geometry
• multimodal learning
• continual learning
• catastrophic forgetting
• hierarchical structure

Innovation

• hyperbolic geometry
• multimodal continual learning
• cross-modal invariance
• hierarchical structure preservation
• representation stability