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Graph interpolating activation improves both natural and robust accuracies in data-efficient deep learning

Part of: Artificial intelligence (68Txx)

Published online by Cambridge University Press:  28 December 2020

BAO WANG Open the ORCID record for BAO WANG [Opens in a new window]  and
STAN J. OSHER
BAO WANG
Affiliation:
Department of Mathematics, Scientific Computing and Imaging (SCI) Institute, University of Utah, Salt Lake City, UT, USA, email: wangbaonj@gmail.com
STAN J. OSHER
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA90095-1555, USA, email: sjo@math.ucla.edu
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Abstract

Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning (DL) research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high-dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace–Beltrami equation on a high-dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation integrates the advantages of both deep learning and manifold learning. Compared to the conventional DNNs with the softmax function as output activation, the new framework demonstrates the following major advantages: First, it is better applicable to data-efficient learning in which we train high capacity DNNs without using a large number of training data. Second, it remarkably improves both natural accuracy on the clean images and robust accuracy on the adversarial images crafted by both white-box and black-box adversarial attacks. Third, it is a natural choice for semi-supervised learning. This paper is a significant extension of our earlier work published in NeurIPS, 2018. For reproducibility, the code is available at https://github.com/BaoWangMath/DNN-DataDependentActivation.

Keywords

Data-dependent activationadversarial defensedata-efficient learning

MSC classification

Primary: 68T01: General
Secondary: 68T10: Pattern recognition, speech recognition
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 3: Connections between Deep learning and Partial Differential Equations , June 2021 , pp. 540 - 569
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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