NTK-Guided Few-Shot Class Incremental Learning

Abstract

The proliferation of Few-Shot Class Incremental Learning (FSCIL) methodologies has highlighted the critical challenge of maintaining robust anti-amnesia capabilities in FSCIL learners. In this paper, we present a novel conceptualization of anti-amnesia in terms of mathematical generalization, leveraging the Neural Tangent Kernel (NTK) perspective. Our method focuses on two key aspects: ensuring optimal NTK convergence and minimizing NTK-related generalization loss, which serve as the theoretical foundation for cross-task generalization. To achieve global NTK convergence, we introduce a principled meta-learning mechanism that guides optimization within an expanded network architecture. Concurrently, to reduce the NTK-related generalization loss, we systematically optimize its constituent factors. Specifically, we initiate self-supervised pre-training on the base session to enhance NTK-related generalization potential. These self-supervised weights are then 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, ensuring optimal convergence and stability of the NTK matrix and minimizing the NTK-related generalization loss, significantly enhancing its theoretical generalization. On popular FSCIL benchmark datasets, our NTK-FSCIL surpasses contemporary state-of-the-art approaches, elevating end-session accuracy by 2.9\% to 9.3\%.