# Genetic Column Generation for Computing Lower Bounds for Adversarial Classification

arXiv: https://arxiv.org/abs/2406.08331 · HTML: https://mlsanity.com/paper/2406.08331/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 15 references that are in the map.
- First posted on arXiv 12 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images](https://mlsanity.com/paper/1412.1897/) (2014)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classification](https://mlsanity.com/paper/2204.12676/) (2022)
- [On the existence of solutions to adversarial training in multiclass classification](https://mlsanity.com/paper/2305.00075/) (2023)
- [An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classification](https://mlsanity.com/paper/2401.09191/) (2024)
- [Genetic column generation: Fast computation of high-dimensional multi-marginal optimal transport problems](https://mlsanity.com/paper/2103.12624/) (2021)
- [The GenCol algorithm for high-dimensional optimal transport: general formulation and application to barycenters and Wasserstein splines](https://mlsanity.com/paper/2209.09081/) (2022)

## Built on by (most cited first, 1 of 1)

- [Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions](https://mlsanity.com/paper/2510.01969/) (2025)

## 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.