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

arXiv: https://arxiv.org/abs/2605.11904 · HTML: https://mlsanity.com/paper/2605.11904/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 35 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 4 of 4)

- [A Model or 603 Exemplars: Towards Memory-Efficient Class-Incremental Learning](https://mlsanity.com/paper/2205.13218/) (2022)
- [Continual Learning with Pre-Trained Models: A Survey](https://mlsanity.com/paper/2401.16386/) (2024)
- [Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learning](https://mlsanity.com/paper/2302.03004/) (2023)
- [Toward Understanding Catastrophic Forgetting in Continual Learning](https://mlsanity.com/paper/1908.01091/) (2019)

## Built on by (most cited first, 1 of 1)

- [Beyond Routing Saturation: A Long-Horizon Class-Incremental Perspective on Expert Routing in Multimodal Continual Instruction Tuning](https://mlsanity.com/paper/2608.01437/) (2026)

## Abstract (arXiv)

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.