While anti-amnesia FSCIL learners often excel in incremental sessions, they
tend to prioritize mitigating knowledge attrition over harnessing the model's
potential for knowledge acquisition. In this paper, we delve into the
foundations of model generalization in FSCIL through the lens of the Neural
Tangent Kernel (NTK). Our primary design focus revolves around ensuring optimal
NTK convergence and NTK-related generalization error, serving as the
theoretical bedrock for exceptional generalization. To attain globally optimal
NTK convergence, we employ a meta-learning mechanism grounded in mathematical
principles to guide the optimization process within an expanded network.
Furthermore, to reduce the NTK-related generalization error, we commence from
the foundational level, optimizing the relevant factors constituting its
generalization loss. Specifically, we initiate self-supervised pre-training on
the base session to shape the initial network weights. Then they are carefully
refined through curricular alignment, followed by the application of dual NTK
regularization tailored specifically for both convolutional and linear layers.
Through the combined effects of these measures, our network acquires robust NTK
properties, significantly enhancing its foundational generalization. On popular
FSCIL benchmark datasets, our NTK-FSCIL surpasses contemporary state-of-the-art
approaches, elevating end-session accuracy by 2.9% to 8.7%.

通过对 FSCIL 中神经切向核（NTK）的基本理论研究，我们设计出一种元学习机制，用数学原理来指导扩展网络内的优化过程，确保全局最优的 NTK 收敛和与 NTK 相关的泛化误差，从而提高网络的基础泛化能力。通过自我监督的预训练、课程对齐和对卷积层和线性层定制的双重 NTK 正则化等方法的综合效果，我们的网络在主流的 FSCIL 基准数据集上优于目前最先进的方法，将最终准确率提升了 2.9% 至 8.7%。