# Scalable Class-Incremental Learning Based on Parametric Neural Collapse

arXiv: https://arxiv.org/abs/2512.21845 · HTML: https://mlsanity.com/paper/2512.21845/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Distillation for continual learning, one of 12 directions in Knowledge distillation.
- Builds on 28 of its 40 references that are in the map.
- First posted on arXiv 26 Dec 2025.

## Placed in

- Knowledge distillation / [Distillation for continual learning](https://mlsanity.com/distill/distillation-for-continual-learning/)

## Builds on (most cited first, 28 of 28)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Progress & Compress: A scalable framework for continual learning](https://mlsanity.com/paper/1805.06370/) (2018)
- [Supervision Exists Everywhere: A Data Efficient Contrastive Language-Image Pre-training Paradigm](https://mlsanity.com/paper/2110.05208/) (2021)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)
- [DER: Dynamically Expandable Representation for Class Incremental Learning](https://mlsanity.com/paper/2103.16788/) (2021)
- [Maintaining Discrimination and Fairness in Class Incremental Learning](https://mlsanity.com/paper/1911.07053/) (2019)
- [S-Prompts Learning with Pre-trained Transformers: An Occam's Razor for Domain Incremental Learning](https://mlsanity.com/paper/2207.12819/) (2022)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [FOSTER: Feature Boosting and Compression for Class-Incremental Learning](https://mlsanity.com/paper/2204.04662/) (2022)
- [Reinforced Continual Learning](https://mlsanity.com/paper/1805.12369/) (2018)
- [Class-incremental Learning via Deep Model Consolidation](https://mlsanity.com/paper/1903.07864/) (2019)
- [Constrained Few-shot Class-incremental Learning](https://mlsanity.com/paper/2203.16588/) (2022)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Lightweight Adaptive Feature De-drifting for Compressed Image Classification](https://mlsanity.com/paper/2401.01724/) (2024)
- [Incorporating Neuro-Inspired Adaptability for Continual Learning in Artificial Intelligence](https://mlsanity.com/paper/2308.14991/) (2023)
- [Elastic Feature Consolidation for Cold Start Exemplar-Free Incremental Learning](https://mlsanity.com/paper/2402.03917/) (2024)
- [DS-AL: A Dual-Stream Analytic Learning for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2403.17503/) (2024)
- [Continuous Temporal Domain Generalization](https://mlsanity.com/paper/2405.16075/) (2024)
- [Task-Agnostic Guided Feature Expansion for Class-Incremental Learning](https://mlsanity.com/paper/2503.00823/) (2025)
- [An Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/1910.09388/) (2019)
- [Koopman Operators in Robot Learning](https://mlsanity.com/paper/2408.04200/) (2024)
- [Multi-View Class Incremental Learning](https://mlsanity.com/paper/2306.09675/) (2023)

## Abstract (arXiv)

Incremental learning often encounter challenges such as overfitting to new data and catastrophic forgetting of old data. Existing methods can effectively extend the model for new tasks while freezing the parameters of the old model, but ignore the necessity of structural efficiency to lead to the feature difference between modules and the class misalignment due to evolving class distributions. To address these issues, we propose scalable class-incremental learning based on parametric neural collapse (SCL-PNC) that enables demand-driven, minimal-cost backbone expansion by adapt-layer and refines the static into a dynamic parametric Equiangular Tight Frame (ETF) framework according to incremental class. This method can efficiently handle the model expansion question with the increasing number of categories in real-world scenarios. Additionally, to counteract feature drift in serial expansion models, the parallel expansion framework is presented with a knowledge distillation algorithm to align features across expansion modules. Therefore, SCL-PNC can not only design a dynamic and extensible ETF classifier to address class misalignment due to evolving class distributions, but also ensure feature consistency by an adapt-layer with knowledge distillation between extended modules. By leveraging neural collapse, SCL-PNC induces the convergence of the incremental expansion model through a structured combination of the expandable backbone, adapt-layer, and the parametric ETF classifier. Experiments on standard benchmarks demonstrate the effectiveness and efficiency of our proposed method. Our code is available at https://github.com/zhangchuangxin71-cyber/dynamic_ ETF2. Keywords: Class incremental learning; Catastrophic forgetting; Neural collapse;Knowledge distillation; Expanded model.