Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks

TL;DR

The paper investigates Neural Tangent Kernels (NTKs) as the infinite-width limit of neural networks trained with the $l_2$ loss and an infinitesimal learning rate, showing that NTK-based kernel regression can rival or exceed traditional small-data methods. It derives CNTK/NTK formulations, implements efficient kernel-based learning, and evaluates on UCI datasets, a small CIFAR-10 subset, and VOC07 few-shot transfer, demonstrating strong performance in low-data regimes. NTK-based SVMs outperform Random Forests and Gaussian kernels on numerous UCI tasks, while CNTK-based classifiers outperform ResNet-34 on CIFAR-10 with limited data, highlighting practical advantages of NTKs as off-the-shelf drop-in classifiers. The results motivate further exploration of NTK generalization and architecture-specific kernels, including extensions to recurrent and graph domains, for robust low-data learning.

Abstract

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.

Figures (2)

• Figure 1: Performance comparisons between NTK and other classifiers.
• Figure 2: Performance Comparisons between NTK and NN.