Recent research shows that the following two models are equivalent: (a)
infinitely wide neural networks (NNs) trained under l2 loss by gradient descent
with infinitesimally small learning rate (b) kernel regression with respect to
so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An efficient
algorithm to compute the NTK, as well as its convolutional counterparts,
appears in Arora et al. (2019a), which allowed studying performance of
infinitely wide nets on datasets like CIFAR-10. However, super-quadratic
running time of kernel methods makes them best suited for small-data tasks. We
report results suggesting neural tangent kernels perform strongly on low-data
tasks.
1. On a standard testbed of classification/regression tasks from the UCI
database, NTK SVM beats the previous gold standard, Random Forests (RF), and
also the corresponding finite nets.
2. On CIFAR-10 with 10 - 640 training samples, Convolutional NTK consistently
beats ResNet-34 by 1% - 3%.
3. On VOC07 testbed for few-shot image classification tasks on ImageNet with
transfer learning (Goyal et al., 2019), replacing the linear SVM currently used
with a Convolutional NTK SVM consistently improves performance.
4. Comparing the performance of NTK with the finite-width net it was derived
from, NTK behavior starts at lower net widths than suggested by theoretical
analysis(Arora et al., 2019a). NTK's efficacy may trace to lower variance of
output.

该研究表明：(a) 在无穷宽度神经网络 (NNs) 上应用 l2 损失 (通过梯度下降法) 训练，并将学习率设置为无穷小，与 (b) 基于所谓的神经切向核 (NTK) 的核回归是相等的。在此基础上，对 NTK 进行高效计算的算法已被提出，表明 NTK 在低数据任务上表现良好。