Beyond Point-wise Neural Collapse: A Topology-Aware Hierarchical Classifier for Class-Incremental Learning

The Nearest Class Mean (NCM) classifier is widely favored in Class-Incremental Learning (CIL) for its superior resistance to catastrophic forgetting compared to Fully Connected layers. While Neural Collapse (NC) theory supports NCM's optimality by assuming features collapse into single points, non-linear feature drift and insufficient training in CIL often prevent this ideal state. Consequently, classes manifest as complex manifolds rather than collapsed points, rendering the single-point NCM suboptimal. To address this, we propose Hierarchical-Cluster SOINN (HC-SOINN), a novel classifier that captures the topological structure of these manifolds via a ``local-to-global'' representation. Furthermore, we introduce Structure-Topology Alignment via Residuals (STAR) method, which employs a fine-grained pointwise trajectory tracking mechanism to actively deform the learned topology, allowing it to adapt precisely to complex non-linear feature drift. Theoretical analysis and Procrustes distance experiments validate our framework's resilience to manifold deformations. We integrated HC-SOINN into seven state-of-the-art methods by replacing their original classifiers, achieving consistent improvements that highlight the effectiveness and robustness of our approach. Code is available at https://github.com/yhyet/HC_SOINN.

Embedding Space Allocation with Angle-Norm Joint Classifiers for Few-Shot Class-Incremental Learning

Few-shot class-incremental learning (FSCIL) aims to continually learn new classes from only a few samples without forgetting previous ones, requiring intelligent agents to adapt to dynamic environments. FSCIL combines the characteristics and challenges of class-incremental learning and few-shot learning: (i) Current classes occupy the entire feature space, which is detrimental to learning new classes. (ii) The small number of samples in incremental rounds is insufficient for fully training. In existing mainstream virtual class methods, for addressing the challenge (i), they attempt to use virtual classes as placeholders. However, new classes may not necessarily align with the virtual classes. For the challenge (ii), they replace trainable fully connected layers with Nearest Class Mean (NCM) classifiers based on cosine similarity, but NCM classifiers do not account for sample imbalance issues. To address these issues in previous methods, we propose the class-center guided embedding Space Allocation with Angle-Norm joint classifiers (SAAN) learning framework, which provides balanced space for all classes and leverages norm differences caused by sample imbalance to enhance classification criteria. Specifically, for challenge (i), SAAN divides the feature space into multiple subspaces and allocates a dedicated subspace for each session by guiding samples with the pre-set category centers. For challenge (ii), SAAN establishes a norm distribution for each class and generates angle-norm joint logits. Experiments demonstrate that SAAN can achieve state-of-the-art performance and it can be directly embedded into other SOTA methods as a plug-in, further enhancing their performance.