BEYOND LINEARIZATION: ON QUADRATIC AND HIGHER-ORDER APPROXIMATION OF WIDE NEURAL NETWORKS

Yu Bai, Jason D. Lee

Research output: Contribution to conferencePaperpeer-review

28 Scopus citations

Abstract

Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by the Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the empirical performance of neural networks are observed to exceed their linearized models, suggesting insufficiency of this theory. Towards closing this gap, we investigate the training of over-parametrized neural networks that are beyond the NTK regime yet still governed by the Taylor expansion of the network. We bring forward the idea of randomizing the neural networks, which allows them to escape their NTK and couple with quadratic models. We show that the optimization landscape of randomized two-layer networks are nice and amenable to escaping-saddle algorithms. We prove concrete generalization and expressivity results on these randomized networks, which lead to sample complexity bounds (of learning certain simple functions) that match the NTK and can in addition be better by a dimension factor when mild distributional assumptions are present. We demonstrate that our randomization technique can be generalized systematically beyond the quadratic case, by using it to find networks that are coupled with higher-order terms in their Taylor series.

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

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