Optimal Transport Problems on GPUs with FlashSinkhorn 2
Optimal transport theory is becoming increasingly important in machine learning and data analytics areas, the calculation cost is a big obstacle. The new FlashSinkhorn 2 (FS2) study published in ArXiv offers a practical solution on this challenge.
Based on entropi-based optimal transport (EOT) problems, the basic features of the new solver are:
- Two-stage approach uses the GPU memory more efficient and prevents the evaluation of all point pairs
- Large discrete EOT problems using square-transmitting distance in low-sized spot clouds in a certain error tolerance
- Starting with a cell-based rough stage, the heavy part of the calculation removes from pre-procession
- It does not require extra hardware investment thanks to it can work on a single GPU
- All n×m spot pairs of the previous FlashSinkhorn version exceeds the limit required in each pusheration
Sinkhorn algorithm has been standard method for the pusher solution of optimal transport problems. But in large scale applications, storage and processing of dense core matrix leads to serious memory problems. FlashSinkhorn 2 relieves this problem by using block-click structure (block-sparse structure).
Research has potential to provide practical results in areas such as learning data distribution in particularly machine learning applications, Wasserstein based loss calculation and effective brain mapping. These types of algorithms that use the parallelization power of GPUs more intelligent will be able to work with larger and complex problems of artificial intelligence researchers.