MDOT-TNT

A Truncated Newton Method for Optimal Transport

MDOT-TNT is a fast, GPU-accelerated solver for entropic-regularized optimal transport (OT) problems. It combines mirror descent with a truncated Newton projection method to achieve high numerical precision while remaining stable under weak regularization.

Key features:

• High Precision: Stable under extremely weak regularization (γ up to 2¹⁸), enabling highly precise approximations of unregularized OT

• GPU Accelerated: Fully compatible with CUDA for fast computation on large problems

• Batched Solving: Solve multiple OT problems simultaneously in batched mode

• Memory Efficient: Log-domain computations and efficient rounding avoid storing full transport plans

• PyTorch Native: Seamless integration with PyTorch, supporting autograd-compatible inputs

Contents

• Installation
  • Prerequisites
  • Install from PyPI
  • Install from Source
  • Verifying the Installation
• Quick Start
  • Single Problem
  • Batched Solving
  • Low-Memory / Point Cloud Solving
  • Performance Tips
• API Reference
  • Main Functions
  • Core Modules
• Tutorial
  • Comparing MDOT-TNT with POT Solvers

Citation

If you use MDOT-TNT in your research, please cite:

@inproceedings{kemertas2025truncated,
  title={A Truncated Newton Method for Optimal Transport},
  author={Kemertas, Mete and Farahmand, Amir-massoud and Jepson, Allan Douglas},
  booktitle={The Thirteenth International Conference on Learning Representations},
  year={2025},
  url={https://openreview.net/forum?id=gWrWUaCbMa}
}

License

This code is released under a non-commercial use license. For commercial licensing inquiries, please contact the authors.

Indices and tables

• Index

• Module Index