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A Universal Approximation Result for Difference of log-sum-exp Neural Networks

Giuseppe C. Calafiore 1 Stéphane Gaubert 2 Corrado Possieri 1
2 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We show that a neural network whose output is obtained as the difference of the outputs of two feedforward networks with exponential activation function in the hidden layer and logarithmic activation function in the output node (LSE networks) is a smooth universal approximator of continuous functions over convex, compact sets. By using a logarithmic transform, this class of networks maps to a family of subtraction-free ratios of generalized posynomials, which we also show to be universal approximators of positive functions over log-convex, compact subsets of the positive orthant. The main advantage of Difference-LSE networks with respect to classical feedforward neural networks is that, after a standard training phase, they provide surrogate models for design that possess a specific difference-of-convex-functions form, which makes them optimizable via relatively efficient numerical methods. In particular, by adapting an existing difference-of-convex algorithm to these models, we obtain an algorithm for performing effective optimization-based design. We illustrate the proposed approach by applying it to data-driven design of a diet for a patient with type-2 diabetes.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-02423871
Contributor : Stephane Gaubert <>
Submitted on : Thursday, December 26, 2019 - 10:56:12 AM
Last modification on : Friday, April 30, 2021 - 9:54:16 AM

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  • HAL Id : hal-02423871, version 1
  • ARXIV : 1905.08503

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Giuseppe C. Calafiore, Stéphane Gaubert, Corrado Possieri. A Universal Approximation Result for Difference of log-sum-exp Neural Networks. 2019. ⟨hal-02423871⟩

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