Meta-Learning with Neural Tangent Kernels

Yufan Zhou, Zhenyi Wang, Jiayi Xian, Changyou Chen, Jinhui Xu

Keywords: meta-learning, neural tangent kernel

Abstract: Model Agnostic Meta-Learning (MAML) has emerged as a standard framework for meta-learning, where a meta-model is learned with the ability of fast adapting to new tasks. However, as a double-looped optimization problem, MAML needs to differentiate through the whole inner-loop optimization path for every outer-loop training step, which may lead to both computational inefficiency and sub-optimal solutions. In this paper, we generalize MAML to allow meta-learning to be defined in function spaces, and propose the first meta-learning paradigm in the Reproducing Kernel Hilbert Space (RKHS) induced by the meta-model's Neural Tangent Kernel (NTK). Within this paradigm, we introduce two meta-learning algorithms in the RKHS, which no longer need a sub-optimal iterative inner-loop adaptation as in the MAML framework. We achieve this goal by 1) replacing the adaptation with a fast-adaptive regularizer in the RKHS; and 2) solving the adaptation analytically based on the NTK theory. Extensive experimental studies demonstrate advantages of our paradigm in both efficiency and quality of solutions compared to related meta-learning algorithms. Another interesting feature of our proposed methods is that they are demonstrated to be more robust to adversarial attacks and out-of-distribution adaptation than popular baselines, as demonstrated in our experiments.

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One-sentence Summary: First work to define meta learning in RKHS induced by Neural Tangent Kernel

Data: [CUB-200-2011](https://paperswithcode.com/dataset/cub-200-2011), [FC100](https://paperswithcode.com/dataset/fc100), [mini-Imagenet](https://paperswithcode.com/dataset/mini-imagenet)