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About this paper
Kurt Pasque, Christopher Teska, Ruriko Yoshida, Keiji Miura, Jefferson Huang
A tropical convolutional neural network architecture is introduced, leveraging tropical geometry to achieve inherent robustness against adversarial attacks. This model maintains computational efficiency and accuracy on clean inputs while demonstrating improved performance against various attacks like CW and PGD compared to standard CNNs.
Key insights
- Tropical geometry offers a framework for robust decision boundaries, interpreting piecewise linear networks as tropical rational functions.
- Tropical decision boundaries, formed by tropical bisectors, create stable regions in the input space due to their piecewise linear structure.
- The sparse and constant-magnitude gradients of the tropical distance function make it challenging for adversarial attacks to find effective small perturbations.
Summary by alphaXiv.
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