Federated learning (FL) is a privacy-preserving paradigm where multiple participants jointly solve a machine learning problem without sharing raw data. Unlike traditional distributed learning, a unique characteristic of FL is statistical heterogeneity, namely, data distributions across participants are different from each other. Meanwhile, recent advances in the interpretation of neural networks have seen a wide use of neural tangent kernels (NTKs) for convergence analyses. In this paper, we propose a novel FL paradigm empowered by the NTK framework. The paradigm addresses the challenge of statistical heterogeneity by transmitting update data that are more expressive than those of the conventional FL paradigms. Specifically, sample-wise Jacobian matrices, rather than model weights/gradients, are uploaded by participants. The server then constructs an empirical kernel matrix to update a global model without explicitly performing gradient descent. We further develop a variant with improved communication efficiency and enhanced privacy. Numerical results show that the proposed paradigm can achieve the same accuracy while reducing the number of communication rounds by an order of magnitude compared to federated averaging.