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For certain infinitely-wide neural networks, the neural tangent kernel (NTK)theory fully characterizes generalization, but for the networks used inpractice, the empirical NTK only provides a rough first-order approximation.Still, a growing body of work keeps leveraging this approximation tosuccessfully analyze important deep learning phenomena and design algorithmsfor new applications. In our work, we provide strong empirical evidence todetermine the practical validity of such approximation by conducting asystematic comparison of the behavior of different neural networks and theirlinear approximations on different tasks. We show that the linearapproximations can indeed rank the learning complexity of certain tasks forneural networks, even when they achieve very different performances. However,in contrast to what was previously reported, we discover that neural networksdo not always perform better than their kernel approximations, and reveal thatthe performance gap heavily depends on architecture, dataset size and trainingtask. We discover that networks overfit to these tasks mostly due to theevolution of their kernel during training, thus, revealing a new type ofimplicit bias.

What can linearized neural networks actually say about generalization?