# Rethinking Continual Learning with Progressive Neural Collapse

arXiv: https://arxiv.org/abs/2505.24254 · HTML: https://mlsanity.com/paper/2505.24254/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 62 references that are in the map.
- First posted on arXiv 30 May 2025.

## Builds on (most cited first, 30 of 50)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [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)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Dynamic Few-Shot Visual Learning without Forgetting](https://mlsanity.com/paper/1804.09458/) (2018)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [Co2L: Contrastive Continual Learning](https://mlsanity.com/paper/2106.14413/) (2021)
- [Overcoming Catastrophic Forgetting by Incremental Moment Matching](https://mlsanity.com/paper/1703.08475/) (2017)
- [Compacting, Picking and Growing for Unforgetting Continual Learning](https://mlsanity.com/paper/1910.06562/) (2019)
- [Coresets via Bilevel Optimization for Continual Learning and Streaming](https://mlsanity.com/paper/2006.03875/) (2020)
- [Revisiting Class-Incremental Learning with Pre-Trained Models: Generalizability and Adaptivity are All You Need](https://mlsanity.com/paper/2303.07338/) (2023)

## Built on by (most cited first, 4 of 4)

- [Beyond Static Models: An Evolving Framework for Continual Learning in Large Language Models across Training Stages](https://mlsanity.com/paper/2603.12658/) (2026)
- [Heads collapse, features stay: Why Replay needs big buffers](https://mlsanity.com/paper/2512.07400/) (2025)
- [FreeMOCA: Memory-Free Continual Learning for Malicious Code Analysis](https://mlsanity.com/paper/2605.09664/) (2026)
- [Distribution-Conditioned Task Routing for Class-Incremental Learning](https://mlsanity.com/paper/2609.34503/) (2026)

## Abstract (arXiv)

Continual Learning (CL) seeks to build an agent that can continuously learn a sequence of tasks, where a key challenge, namely Catastrophic Forgetting, persists due to the potential knowledge interference among different tasks. On the other hand, deep neural networks (DNNs) are shown to converge to a terminal state termed Neural Collapse during training, where all class prototypes geometrically form a static simplex equiangular tight frame (ETF). These maximally and equally separated class prototypes make the ETF an ideal target for model learning in CL to mitigate knowledge interference. Thus inspired, several studies have emerged very recently to leverage a fixed global ETF in CL, which however suffers from key drawbacks, such as impracticability and limited performance.To address these challenges and fully unlock the potential of ETF in CL, we propose Progressive Neural Collapse (ProNC), a novel framework that completely removes the need of a fixed global ETF in CL. Specifically, ProNC progressively expands the ETF target in a principled way by adding new class prototypes as vertices for new tasks, ensuring maximal separability across all encountered classes with minimal shifts from the previous ETF. We next develop a new CL framework by plugging ProNC into commonly used CL algorithm designs, where distillation is further leveraged to balance between target shifting for old classes and target aligning for new classes. Extensive experiments show that our approach significantly outperforms related baselines while maintaining superior flexibility, simplicity, and efficiency. Our code is available at https://github.com/Continue-Edge-AI-Lab/ProNC