On the Power of Shallow Learning

• URL: http://arxiv.org/abs/2106.03186v1
• Date: Sun, 6 Jun 2021 17:25:33 GMT
• Title: On the Power of Shallow Learning
• Authors: James B. Simon, Sajant Anand, Michael R. DeWeese
• Abstract summary: Given a kernel, can one find a network that realizes it? We affirmatively answer this question for fully-connected architectures, completely characterizing the space of achievable kernels. We experimentally verify our construction and demonstrate that, by just choosing the activation function, we can design a wide shallow network that mimics the generalization performance of any wide, deep, fully-connected network.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A deluge of recent work has explored equivalences between wide neural networks and kernel methods. A central theme is that one can analytically find the kernel corresponding to a given wide network architecture, but despite major implications for architecture design, no work to date has asked the converse question: given a kernel, can one find a network that realizes it? We affirmatively answer this question for fully-connected architectures, completely characterizing the space of achievable kernels. Furthermore, we give a surprising constructive proof that any kernel of any wide, deep, fully-connected net can also be achieved with a network with just one hidden layer and a specially-designed pointwise activation function. We experimentally verify our construction and demonstrate that, by just choosing the activation function, we can design a wide shallow network that mimics the generalization performance of any wide, deep, fully-connected network.

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