mlsanityData to 7 Oct 2026

Genetic Column Generation for Computing Lower Bounds for Adversarial Classification

arXiv 2406.08331 ↗First posted 12 Jun 2024math.NA cs.LG cs.NAcited by 1

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Abstract (arXiv)

Recent theoretical results on adversarial multi-class classification showed a similarity to the multi-marginal formulation of Wasserstein-barycenter in optimal transport. Unfortunately, both problems suffer from the curse of dimension, making it hard to exploit the nice linear program structure of the problems for numerical calculations. We investigate how ideas from Genetic Column Generation for multi-marginal optimal transport can be used to overcome the curse of dimension in computing the minimal adversarial risk in multi-class classification.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 12 of its 15 references that are in the map. First posted on arXiv 12 Jun 2024.

Builds on

12 of 15 references.

References · 12

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  3. 2014Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Imagescited by 774
  4. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  5. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 285
  6. 2021Recent Advances in Adversarial Training for Adversarial Robustnesscited by 276
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  8. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  9. 2023On the existence of solutions to adversarial training in multiclass classificationcited by 9
  10. 2024An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classificationcited by 5
  11. 2021Genetic column generation: Fast computation of high-dimensional multi-marginal optimal transport problemscited by 3
  12. 2022The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splinescited by 1

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Citing papers per year: 2025: 1.

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  1. 2025Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functionscited by 1