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

该论文通过对神经网络和它们的线性近似在不同任务上的行为进行系统比较，提供了强有力的实证证据来确定近似的实际有效性，发现网络并不总是表现优于其核近似，并揭示了性能差距很大程度上取决于网络架构、数据集大小和训练任务。此外，研究发现网络在训练过程中出现过拟合的原因是其核的演化。由此揭示了一种新的隐式偏差现象。