Brenier Meets Adversarial Training: Optimal Transport Geometry for Robust Learning XB8NYRD86J
| URI | m2://res/XB8NYRD86J |
|---|---|
| Kind | preprint |
| Creators | Alireza Abdollahpoorrostam, Ehsan Sharifian, Buse Şen, Marco Cuturi, Daniel Kuhn |
| Date | 2026-09-25 |
| Subjects | arxiv cs.LG, arxiv math.OC, arxiv stat.ML |
| Scope | border |
Expressions
e1: version, preprint
| Date | 2026-09-25 |
|---|---|
| Ids | arXiv 2609.31363 |
Items in this resource
The mentions of the inventory that name this resource. Each name links to the card of its inventory row.
| Item | Kind | Where | Source |
|---|---|---|---|
| Global optimality guarantee of MPA | statement | theorem D.2 | arxiv |
| 3B0NHSMT8B | statement | theorem 4.1 | arxiv |
| Strict positivity of $\underline{p}(\epsilon)$ | statement | lemma D.6 | arxiv |
| Wasserstein distance | definition | definition 2.1 | arxiv |
| Properties of the Ascent and Reassignment Operators | statement | lemma D.3 | arxiv |
| Ascent Operators | definition | definition D.1 | arxiv |
| 6HV4CTBR40 | statement | lemma D.1 | arxiv |
| Monge gap | definition | definition 2.3 | arxiv |
| Sample complexity of MPA | statement | corollary D.2 | arxiv |
| Outliers are rare | statement | lemma D.5 | arxiv |
| Suboptimality from wasteful transport | statement | proposition 3.2 | arxiv |
| DD41GKS108 | statement | corollary D.1 | arxiv |
| Assignment-stationarity | definition | definition 4.1 | arxiv |
| E15XPXJHE0 | statement | lemma 4.1 | arxiv |
| Monotonicity of $T_{\mathrm{pa}}$ when $m=1$ | statement | proposition 4.1 | arxiv |
| Finite termination of exact MPA | statement | theorem D.1 | arxiv |
| Superlevel sets | statement | lemma D.8 | arxiv |
| Cyclical monotonicity | definition | definition 2.2 | arxiv |
| KHFSXTFK9S | statement | proposition 3.3 | arxiv |
| Square integrability of the optimal adversarial map | statement | lemma D.4 | arxiv |
| $T_{\mathrm{pa}}$ violates cyclical monotonicity | example | example 4.1 | arxiv |
| Uncovered inliers are rare | statement | lemma D.7 | arxiv |
| R0J15DAD0H | statement | theorem 4.2 | arxiv |
| RGQ5YQV8MF | statement | lemma D.2 | arxiv |
| Adversarial risk | statement | proposition B.2 | arxiv |
| Convex-potential representation | statement | theorem 5.1 | arxiv |
| Measurability and well-definedness of \texorpdfstring{$T^\star$}{T* | statement | proposition B.1 | arxiv |
| Reassignment Operator | definition | definition D.2 | arxiv |
| Convergence with inexact adversary | statement | proposition 3.1 | arxiv |
Catalogue records
- arxiv: 2609.31363 (work)