A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers
#Neural Networks #Optimal Transport #Adversarial Methods #Statistical Learning #Generalization Error #Semi-dual Formulations #Generative Modeling
📌 Key Takeaways
- Researchers established theoretical bounds on generalization error for neural optimal transport methods
- The paper focuses on semi-dual adversarial formulations of optimal transport problems
- Findings could extend to general optimal transport cases, opening new research directions
- Authors provide experimental illustrations available online for verification
- Research addresses critical theoretical gap in rapidly evolving field of generative modeling
📖 Full Retelling
Researchers Roman Tarasov, Petr Mokrov, Milena Gazdieva, Evgeny Burnaev, and Alexander Korotin published a comprehensive paper on neural optimal transport solvers on arXiv on February 24, 2026, addressing theoretical gaps in adversarial minimax approaches that have shown promise in generative modeling but lacked statistical learning foundations. The paper, titled 'A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers,' introduces upper bounds on the generalization error of approximate optimal transport maps recovered by minimax quadratic solvers, providing crucial theoretical validation for these increasingly popular methods. Neural network-based optimal transport has emerged as a fruitful direction in the generative modeling community with applications spanning domain translation, image super-resolution, and computational biology, yet the theoretical foundations of adversarial minimax solvers based on semi-dual formulations remained underexplored. The researchers' analysis establishes that the theoretical bounds depend solely on standard statistical and mathematical properties of neural network functional classes, offering a pathway to better understand the reliability of these complex computational methods.
🏷️ Themes
Machine Learning, Optimal Transport, Statistical Learning
📚 Related People & Topics
Neural network
Structure in biology and artificial intelligence
A neural network is a group of interconnected units called neurons that send signals to one another. Neurons can be either biological cells or mathematical models. While individual neurons are simple, many of them together in a network can perform complex tasks.
Entity Intersection Graph
Connections for Neural network:
🌐
Deep learning
3 shared
🌐
Large language model
2 shared
🌐
Mechanistic interpretability
2 shared
🌐
Interpretability
2 shared
Mentioned Entities
Original Source
--> Computer Science > Machine Learning arXiv:2502.01310 [Submitted on 3 Feb 2025 ( v1 ), last revised 24 Feb 2026 (this version, v4)] Title: A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers Authors: Roman Tarasov , Petr Mokrov , Milena Gazdieva , Evgeny Burnaev , Alexander Korotin View a PDF of the paper titled A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers, by Roman Tarasov and 4 other authors View PDF HTML Abstract: Neural network-based optimal transport is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online this https URL . Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2502.01310 [cs.LG] (or arXiv:2502.01310v4 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2502.01310 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Petr Mokrov [ view email ] [v1] Mon, 3 Feb 2025 12:37:20 UTC (148 KB) [v2] Thu, 29 May 2025 12:15:10 UTC (195 KB) [v3] Sun, 28 Sep 2025 12:46:45 UTC (283 KB) [v4] Tue, 24 Feb 2026 08:13:3...
Read full article at source