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

翻译：小样本类增量学习（FSCIL）一直是一个具有挑战性的问题，因为在新的学习轮次中，每个新类别仅有少量训练样本可用。对先前训练轮次中训练的骨干网络进行微调或调整分类器原型，不可避免地会导致旧类别的特征与分类器之间出现对齐偏差，这解释了著名的灾难性遗忘问题。本文受近期发现的名为"神经坍缩"现象的启发，来应对FSCIL中的这种对齐偏差困境。神经坍缩现象揭示了同一类别的最后一层特征会坍缩为一个顶点，且所有类别的顶点与分类器原型对齐，这些原型构成一个单纯形等角紧框架（ETF）。由于最大化Fisher判别比，这种结构对应于最优的分类几何结构。我们提出了一种基于神经坍缩的FSCIL框架。我们预先为整个标签空间（包括基础会话和所有增量会话）分配一组分类器原型作为单纯形ETF。在训练过程中，分类器原型不可学习，并采用一种新颖的损失函数，将特征驱动到对应的原型中。理论分析表明，我们的方法保持了神经坍缩的最优性，并且不会以增量方式破坏特征-分类器对齐。在miniImageNet、CUB-200和CIFAR-100数据集上的实验表明，我们提出的框架优于现有最先进方法。代码地址：https://github.com/NeuralCollapseApplications/FSCIL