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Class Incremental Learning (CIL) aims to enable models to continually learn new classes while retaining previously learned knowledge. The principal challenge in CIL is catastrophic forgetting, which prior approaches typically address by distilling knowledge from previous model. However, such way is often limited to pairwise alignment, failing to preserve the underlying global manifold structure of feature space—ultimately resulting in semantic drift over time. To capture multi-scale structural patterns in the feature space, we propose a topology-aware distillation framework that leverages persistent homology. Specifically, by enforcing topological alignment across incremental stages, our method ensures structure-consistent knowledge transfer and robust preservation of old classes. Furthermore, we still devise a dual-branch architecture with an inverse sampling and dynamic reweighting mechanism that addresses the inherent data imbalance in standard replay-based frameworks. These innovations coalesce into TaKP (Topology-aware Knowledge Preservation), a unified framework designed to enhance knowledge preservation in CIL. Extensive experiments demonstrate that TaKP achieves state-of-the-art performance on multiple benchmarks, significantly improving old-class preservation and average accuracy.
