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Life sciences · Preprint
arXiv · August 10, 2026
Posted before peer review. The findings may change or fail to hold.
This preprint presents a theoretical analysis of forgetting in hyperbolic multimodal continual learning and proposes a framework to preserve cross-modal geometric structure. The work establishes that prevention of forgetting requires cross-modal invariance under shared hyperbolic isometry and identifies two types of distortion (semantic relation drift and hierarchy-related distortion). Experimental validation is claimed but not quantified in the abstract.
Preprint. Intervention: Continual learning framework preserving cross-modal geometric structure in hyperbolic space.
Forgetting in hyperbolic continual learning involves both semantic relation drift and hierarchy-related distortion Prevention of forgetting requires cross-modal invariance under a shared hyperbolic isometry Proposed framework preserves cross-modal relational structure and hierarchical geometry while enabling adaptation to new tasks
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This is an unrefereed computational work presenting theoretical framework and algorithm design for continual learning in hyperbolic geometry, with experimental validation but no peer review.
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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.
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