Project's name: Convexity Regularizer for Neural Optimal Transport

Member of Project

• Nikita Gushchin-TA

Team's name: BinKoff (Group 31)

• Bintang Alam Semesta W.A.M)-1st year master student, Advanced Computational Science
• Fidele Koffivi Gbagbe-1st year master student, Advanced Computational Science

Research Idea

The method proposed in the research paper uses adversarial training (kind of GANs). which is not very stable to compute the optimal transport map $T$. From the theory, the method's optimal "discriminator" must be convex, and its gradient can be used for inverse mapping from the target distribution to the source distribution.

Objectives

Add a convexity regularizer in the loss of neural optimal transport algorithm to improve its stability during direct, i.e. source-to-target or training-to-test map as well as to test the quality of generated images during inverse, i.e. target-to-source or test-to-training map.

Environment (Dependencies)

• POT
• wandb
• torch
• torchvision
• numpy
• tqdm
• matplotlib

how to install:

• pip3 install -r dependencies.txt or
• pip install -r dependencies.txt

Repository Structure

• NOT-Group 31

  • notebooks & custom modules ---documentation of source codes and corresponding modules

    • jupyter notebook files:
      • NOT_training_strong.ipynb
      • NOT_inverse_map_true.ipynb
      • NOT_Regularized.ipynb
      • color_MNIST.ipynb
    • modules:
      • src
      • stats

  • images

    • fixed-test-images-53900
    • random-test-images-53900
    • digits-3
    • digits-3 to digits-2
    • Reg-NOT algorithm
    • NOT algorithm

  • references

  • LICENSE

  • README.md

  • presentation

  • project report

Dataset

color-MNIST

Credits

• weight and biases --> data logging for machine learning
• FID score --> a metric for evaluating the quality of generated images and specifically developed to evaluate the performance of generative adversarial networks

References

1. Alexander Korotin, Daniil Selikhanovych, Evgeny Burnaev. Neural Optimal Transport.Eleventh International Conference on Learning Representations.arXiv:2201.12220v3 [cs.LG] 1 Mar 2023

2. Alexander Korotin. Neural Optimal Transport Presentation (August, 9th 2022)