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%.

翻译：尽管抗遗忘的小样本增量学习（FSCIL）学习器在增量会话中表现优异，但其往往优先考虑缓解知识遗忘，而非充分利用模型的知识获取潜力。本文从神经正切核（NTK）视角深入探究FSCIL中模型泛化的理论基础。我们的核心设计围绕确保最优NTK收敛性与NTK相关泛化误差展开，以此作为卓越泛化能力的理论基石。为实现全局最优NTK收敛，我们采用基于数学原理的元学习机制，引导扩展网络中的优化过程。此外，为降低NTK相关泛化误差，我们从基础层面出发，优化构成其泛化损失的相关要素：具体而言，我们在基会话阶段启动自监督预训练以塑造初始网络权重，随后通过课程对齐进行精细调整，最终对卷积层与线性层分别施加双重NTK正则化。通过上述措施的协同作用，我们的网络获得了鲁棒的NTK特性，显著增强了其基础泛化能力。在主流FSCIL基准数据集上，我们提出的NTK-FSCIL方法超越了当前最先进技术，将最终会话准确率提升了2.9%至8.7%。