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An Inertial Newton Algorithm for Deep Learning

Author

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  • Bolte, Jérôme
  • Castera, Camille
  • Pauwels, Edouard
  • Févotte, Cédric

Abstract

We devise a learning algorithm for possibly nonsmooth deep neural networks featuring inertia and Newtonian directional intelligence only by means of a backpropagation oracle. Our algorithm, called INDIAN, has an appealing mechanical interpretation, making the role of its two hyperparameters transparent. An elementary phase space lifting allows both for its implementation and its theoretical study under very general assumptions. We handle in particular a stochastic version of our method (which encompasses usual mini-batch approaches) for nonsmooth activation functions (such as ReLU). Our algorithm shows high efficiency and reaches state of the art on image classification problems.

Suggested Citation

  • Bolte, Jérôme & Castera, Camille & Pauwels, Edouard & Févotte, Cédric, 2019. "An Inertial Newton Algorithm for Deep Learning," TSE Working Papers 19-1043, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:123630
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    References listed on IDEAS

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    1. Hédy Attouch & Jérôme Bolte & Patrick Redont & Antoine Soubeyran, 2010. "Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 438-457, May.
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    Cited by:

    1. Samir Adly & Hedy Attouch & Van Nam Vo, 2023. "Convergence of Inertial Dynamics Driven by Sums of Potential and Nonpotential Operators with Implicit Newton-Like Damping," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 290-331, July.
    2. Bolte, Jérôme & Le, Tam & Pauwels, Edouard & Silveti-Falls, Antonio, 2022. "Nonsmooth Implicit Differentiation for Machine Learning and Optimization," TSE Working Papers 22-1314, Toulouse School of Economics (TSE).
    3. Claire Boyer & Antoine Godichon-Baggioni, 2023. "On the asymptotic rate of convergence of Stochastic Newton algorithms and their Weighted Averaged versions," Computational Optimization and Applications, Springer, vol. 84(3), pages 921-972, April.
    4. Emilie Chouzenoux & Jean-Baptiste Fest, 2022. "SABRINA: A Stochastic Subspace Majorization-Minimization Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 919-952, December.
    5. Bolte, Jérôme & Pauwels, Edouard, 2019. "Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning," TSE Working Papers 19-1044, Toulouse School of Economics (TSE).
    6. Bolte, Jérôme & Glaudin, Lilian & Pauwels, Edouard & Serrurier, Matthieu, 2021. "A Hölderian backtracking method for min-max and min-min problems," TSE Working Papers 21-1243, Toulouse School of Economics (TSE).
    7. Bolte, Jérôme & Pauwels, Edouard, 2021. "A mathematical model for automatic differentiation in machine learning," TSE Working Papers 21-1184, Toulouse School of Economics (TSE).

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