Applications of Tropical Geometry in Deep Neural Networks

  • Motasem Alfarra

Student thesis: Master's Thesis

Abstract

This thesis tackles the problem of understanding deep neural network with piece- wise linear activation functions. We leverage tropical geometry, a relatively new field in algebraic geometry to characterize the decision boundaries of a single hidden layer neural network. This characterization is leveraged to understand, and reformulate three interesting applications related to deep neural network. First, we give a geo- metrical demonstration of the behaviour of the lottery ticket hypothesis. Moreover, we deploy the geometrical characterization of the decision boundaries to reformulate the network pruning problem. This new formulation aims to prune network pa- rameters that are not contributing to the geometrical representation of the decision boundaries. In addition, we propose a dual view of adversarial attack that tackles both designing perturbations to the input image, and the equivalent perturbation to the decision boundaries.
Date of AwardApr 2020
Original languageEnglish (US)
Awarding Institution
  • Computer, Electrical and Mathematical Science and Engineering
SupervisorBernard Ghanem (Supervisor)

Keywords

  • Deep Learning
  • Deep Neural Networks
  • Tropical Geometry
  • Network Pruning
  • Lottery Ticket Hypothesis
  • Adversarial Attacks

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