Summary of An Optimal Transport Approach For Computing Adversarial Training Lower Bounds in Multiclass Classification, by Nicolas Garcia Trillos et al.
An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification
by Nicolas Garcia Trillos, Matt Jacobs, Jakwang Kim, Matthew Werenski
First submitted to arxiv on: 17 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC); Machine Learning (stat.ML)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This research paper proposes novel numerical algorithms for computing universal lower bounds on the optimal adversarial risk and identifying optimal classifiers in deep learning-based algorithms. The authors leverage a connection between adversarial training (AT) in multiclass classification settings and multimarginal optimal transport (MOT). They develop computationally tractable methods using linear programming (LP) and entropic regularization (Sinkhorn), which can be applied to real-world datasets such as MNIST and CIFAR-10. The proposed algorithms demonstrate improved robustness against adversarial attacks. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This study aims to improve the robustness of deep learning models by developing new algorithms for computing lower bounds on adversarial risk and finding optimal classifiers. The authors find a connection between adversarial training and multimarginal optimal transport, which helps them create efficient methods using linear programming and entropic regularization. They test these methods on popular datasets like MNIST and CIFAR-10 to show their effectiveness. |
Keywords
* Artificial intelligence * Classification * Deep learning * Regularization
