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

TL;DR

This paper introduces a topology-aware hierarchical classifier and a topology alignment method to improve class-incremental learning by capturing complex feature manifold structures and adapting to non-linear feature drift.

Contribution

It proposes HC-SOINN and STAR, novel techniques that model feature manifolds topologically and adapt to feature drift, enhancing classifier robustness in CIL.

Findings

HC-SOINN improves classification accuracy across multiple methods.

STAR effectively aligns feature topology to handle non-linear drift.

Framework demonstrates resilience to 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.