  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
