Hyperbolic Multimodal Continual Learning
2026-08-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how hyperbolic geometry, which helps represent complex relationships in data, works when a system learns new things over time without forgetting old information. They found that to avoid forgetting, the system needs to keep consistent relationships between different types of data using special geometric rules in hyperbolic space. The authors developed a method that helps preserve these important shapes and relationships while allowing the model to learn new tasks. Their experiments show this approach works well on tests involving multiple types of data learned over time.
Hyperbolic geometryMultimodal learningContinual learningRepresentation preservationIsometrySemantic hierarchyForgettingCross-modal invarianceRelational structureHierarchical geometry
Authors
Jiahong Liu, Ming Shen, Xiaohao Liu, Rex Ying, Menglin Yang, Tat-Seng Chua, Irwin King
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.