HARNESSING THE POWER OF INFINITELY WIDE DEEP NETS ON SMALL-DATA TASKS

Sanjeev Arora, Simon S. Du, Zhiyuan Li, Ruslan Salakhutdinov, Ruosong Wang, Dingli Yu

Research output: Contribution to conferencePaperpeer-review

53 Scopus citations

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.

Original languageEnglish (US)
StatePublished - 2020
Event8th International Conference on Learning Representations, ICLR 2020 - Addis Ababa, Ethiopia
Duration: Apr 30 2020 → …

Conference

Conference8th International Conference on Learning Representations, ICLR 2020
Country/TerritoryEthiopia
CityAddis Ababa
Period4/30/20 → …

All Science Journal Classification (ASJC) codes

  • Education
  • Linguistics and Language
  • Language and Linguistics
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'HARNESSING THE POWER OF INFINITELY WIDE DEEP NETS ON SMALL-DATA TASKS'. Together they form a unique fingerprint.

Cite this