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

2026-05-12

AI Summary

This work addresses the limitations of traditional nearest class-mean classifiers, which assume feature collapse to single points and thus fail to capture the complex nonlinear feature manifolds inherent in class-incremental learning, leading to suboptimal performance. To overcome this, the authors propose HC-SOINN, a hierarchical topological-aware classifier that, for the first time, integrates topological structure modeling into class-incremental learning. HC-SOINN constructs class manifolds through a local-to-global hierarchical clustering process and employs a STAR residual-driven topological alignment mechanism to enable dynamic manifold adaptation. Replacing the original classifiers in seven mainstream class-incremental methods with HC-SOINN consistently yields significant performance gains. Theoretical analysis and Procrustes distance experiments further confirm its robustness against feature manifold deformations.

Abstract

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.

Problem

• Class-Incremental Learning
• Neural Collapse
• Feature Manifold
• Catastrophic Forgetting
• Topological Structure

Innovation

• Hierarchical-Cluster SOINN
• Structure-Topology Alignment via Residuals
• Class-Incremental Learning
• Neural Collapse
• Topological Representation