# Neural Collapse Inspired Feature-Classifier Alignment for Few-Shot Class Incremental Learning

arXiv: https://arxiv.org/abs/2302.03004 · HTML: https://mlsanity.com/paper/2302.03004/

## Key facts

- Cited by 116 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 65 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Learning to Compare: Relation Network for Few-Shot Learning](https://mlsanity.com/paper/1711.06025/) (2017)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (2018)
- [Dreaming to Distill: Data-free Knowledge Transfer via DeepInversion](https://mlsanity.com/paper/1912.08795/) (2019)
- [Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2004.10956/) (2020)
- [A Geometric Analysis of Neural Collapse with Unconstrained Features](https://mlsanity.com/paper/2105.02375/) (2021)
- [Few-Shot Incremental Learning with Continually Evolved Classifiers](https://mlsanity.com/paper/2104.03047/) (2021)
- [Exploring Deep Neural Networks via Layer-Peeled Model: Minority Collapse in Imbalanced Training](https://mlsanity.com/paper/2101.12699/) (2021)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Neural collapse with unconstrained features](https://mlsanity.com/paper/2011.11619/) (2020)
- [Negative Margin Matters: Understanding Margin in Few-shot Classification](https://mlsanity.com/paper/2003.12060/) (2020)
- [Forward Compatible Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2203.06953/) (2022)
- [Overcoming Catastrophic Forgetting in Incremental Few-Shot Learning by Finding Flat Minima](https://mlsanity.com/paper/2111.01549/) (2021)
- [Semantic-aware Knowledge Distillation for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2103.04059/) (2021)
- [Extended Unconstrained Features Model for Exploring Deep Neural Collapse](https://mlsanity.com/paper/2202.08087/) (2022)
- [On the Role of Neural Collapse in Transfer Learning](https://mlsanity.com/paper/2112.15121/) (2021)
- [On the Optimization Landscape of Neural Collapse under MSE Loss: Global Optimality with Unconstrained Features](https://mlsanity.com/paper/2203.01238/) (2022)
- [Self-Promoted Prototype Refinement for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2107.08918/) (2021)
- [Constrained Few-shot Class-incremental Learning](https://mlsanity.com/paper/2203.16588/) (2022)
- [Few-Shot Class-Incremental Learning by Sampling Multi-Phase Tasks](https://mlsanity.com/paper/2203.17030/) (2022)
- [An Unconstrained Layer-Peeled Perspective on Neural Collapse](https://mlsanity.com/paper/2110.02796/) (2021)
- [Few-Shot Class-Incremental Learning from an Open-Set Perspective](https://mlsanity.com/paper/2208.00147/) (2022)
- [Few-Shot Class-Incremental Learning via Entropy-Regularized Data-Free Replay](https://mlsanity.com/paper/2207.11213/) (2022)

## Built on by (most cited first, 30 of 116)

- [Investigating the Catastrophic Forgetting in Multimodal Large Language Models](https://mlsanity.com/paper/2309.10313/) (2023)
- [A Comprehensive Survey of Forgetting in Deep Learning Beyond Continual Learning](https://mlsanity.com/paper/2307.09218/) (2023)
- [No Fear of Classifier Biases: Neural Collapse Inspired Federated Learning with Synthetic and Fixed Classifier](https://mlsanity.com/paper/2303.10058/) (2023)
- [Model Tailor: Mitigating Catastrophic Forgetting in Multi-modal Large Language Models](https://mlsanity.com/paper/2402.12048/) (2024)
- [A Survey on Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2304.08130/) (2023)
- [CorDA: Context-Oriented Decomposition Adaptation of Large Language Models for Task-Aware Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2406.05223/) (2024)
- [Generalized Neural Collapse for a Large Number of Classes](https://mlsanity.com/paper/2310.05351/) (2023)
- [Pre-trained Vision and Language Transformers Are Few-Shot Incremental Learners](https://mlsanity.com/paper/2404.02117/) (2024)
- [OrCo: Towards Better Generalization via Orthogonality and Contrast for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2403.18550/) (2024)
- [Catastrophic Forgetting in Deep Learning: A Comprehensive Taxonomy](https://mlsanity.com/paper/2312.10549/) (2023)
- [DiGeo: Discriminative Geometry-Aware Learning for Generalized Few-Shot Object Detection](https://mlsanity.com/paper/2303.09674/) (2023)
- [Compositional Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2405.17022/) (2024)
- [An Upload-Efficient Scheme for Transferring Knowledge From a Server-Side Pre-trained Generator to Clients in Heterogeneous Federated Learning](https://mlsanity.com/paper/2403.15760/) (2024)
- [CoFInAl: Enhancing Action Quality Assessment with Coarse-to-Fine Instruction Alignment](https://mlsanity.com/paper/2404.13999/) (2024)
- [Neural Collapse Terminus: A Unified Solution for Class Incremental Learning and Its Variants](https://mlsanity.com/paper/2308.01746/) (2023)
- [Neural Collapse in Multi-label Learning with Pick-all-label Loss](https://mlsanity.com/paper/2310.15903/) (2023)
- [Rethinking Few-shot Class-incremental Learning: Learning from Yourself](https://mlsanity.com/paper/2407.07468/) (2024)
- [Navigate Beyond Shortcuts: Debiased Learning through the Lens of Neural Collapse](https://mlsanity.com/paper/2405.05587/) (2024)
- [Learning Prompt with Distribution-Based Feature Replay for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2401.01598/) (2024)
- [Cross Entropy versus Label Smoothing: A Neural Collapse Perspective](https://mlsanity.com/paper/2402.03979/) (2024)
- [CLOSER: Towards Better Representation Learning for Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2410.05627/) (2024)
- [EPA: Neural Collapse Inspired Robust Out-of-Distribution Detector](https://mlsanity.com/paper/2401.01710/) (2024)
- [FedLoGe: Joint Local and Generic Federated Learning under Long-tailed Data](https://mlsanity.com/paper/2401.08977/) (2024)
- [Quantifying the Variability Collapse of Neural Networks](https://mlsanity.com/paper/2306.03440/) (2023)
- [Calibrating Higher-Order Statistics for Few-Shot Class-Incremental Learning with Pre-trained Vision Transformers](https://mlsanity.com/paper/2404.06622/) (2024)
- [Memory-efficient Continual Learning with Neural Collapse Contrastive](https://mlsanity.com/paper/2412.02865/) (2024)
- [Revisiting Pool-based Prompt Learning for Few-shot Class-incremental Learning](https://mlsanity.com/paper/2507.09183/) (2025)
- [A Study of Neural Collapse Phenomenon: Grassmannian Frame, Symmetry and Generalization](https://mlsanity.com/paper/2304.08914/) (2023)
- [Towards Demystifying the Generalization Behaviors When Neural Collapse Emerges](https://mlsanity.com/paper/2310.08358/) (2023)
- [Contrastive Augmented Graph2Graph Memory Interaction for Few Shot Continual Learning](https://mlsanity.com/paper/2403.04140/) (2024)

## Abstract (arXiv)

Few-shot class-incremental learning (FSCIL) has been a challenging problem as only a few training samples are accessible for each novel class in the new sessions. Finetuning the backbone or adjusting the classifier prototypes trained in the prior sessions would inevitably cause a misalignment between the feature and classifier of old classes, which explains the well-known catastrophic forgetting problem. In this paper, we deal with this misalignment dilemma in FSCIL inspired by the recently discovered phenomenon named neural collapse, which reveals that the last-layer features of the same class will collapse into a vertex, and the vertices of all classes are aligned with the classifier prototypes, which are formed as a simplex equiangular tight frame (ETF). It corresponds to an optimal geometric structure for classification due to the maximized Fisher Discriminant Ratio. We propose a neural collapse inspired framework for FSCIL. A group of classifier prototypes are pre-assigned as a simplex ETF for the whole label space, including the base session and all the incremental sessions. During training, the classifier prototypes are not learnable, and we adopt a novel loss function that drives the features into their corresponding prototypes. Theoretical analysis shows that our method holds the neural collapse optimality and does not break the feature-classifier alignment in an incremental fashion. Experiments on the miniImageNet, CUB-200, and CIFAR-100 datasets demonstrate that our proposed framework outperforms the state-of-the-art performances. Code address: https://github.com/NeuralCollapseApplications/FSCIL