Tropical Decision Boundaries for Neural Networks Are Robust Against Adversarial Attacks
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Abstract (arXiv)
We introduce a simple, easy to implement, and computationally efficient tropical convolutional neural network architecture that is robust against adversarial attacks. We exploit the tropical nature of piece-wise linear neural networks by embedding the data in the tropical projective torus in a single hidden layer which can be added to any model. We study the geometry of its decision boundary theoretically and show its robustness against adversarial attacks on image datasets using computational experiments.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 1 Feb 2024.
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22 of 45 references.
References · 22
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2014Explaining and Harnessing Adversarial Examplescited by 7,287
- 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
- 2016Towards Evaluating the Robustness of Neural Networkscited by 2,976
- 2018Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examplescited by 1,259
- 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
- 2017Adversarial Attacks on Neural Network Policiescited by 314
- 2018Adversarial Risk and the Dangers of Evaluating Against Weak Attackscited by 221
- 2013Maxout Networkscited by 186
- 2019Adversarial Training and Robustness for Multiple Perturbationscited by 182
- 2018Universality of Deep Convolutional Neural Networkscited by 176
- 2018Robustness via curvature regularization, and vice versacited by 174
10 more
- 2018Tropical Geometry of Deep Neural Networkscited by 92
- 2019ME-Net: Towards Effective Adversarial Robustness with Matrix Estimationcited by 65
- 2018Provable Robustness of ReLU networks via Maximization of Linear Regionscited by 51
- 2022A Survey of Robust Adversarial Training in Pattern Recognition: Fundamental, Theory, and Methodologiescited by 44
- 2019Provable robustness against all adversarial lp-perturbations for p≥ 1cited by 39
- 2018Theoretical Analysis of Adversarial Learning: A Minimax Approachcited by 31
- 2018A Tropical Approach to Neural Networks with Piecewise Linear Activationscited by 26
- 2023Text Analysis Using Deep Neural Networks in Digital Humanities and Information Sciencecited by 5
- 2023Transformed Low-Rank Parameterization Can Help Robust Generalization for Tensor Neural Networkscited by 4
- 2021Tropical Support Vector Machines: Evaluations and Extension to Function Spacescited by 3
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