Pacific Interdisciplinary hub on Optimal Transport | PIMS - Pacific Institute for the Mathematical Sciences

2021 — 2024

The Pacific Interdisciplinary hub on Optimal Transport (PIHOT) is a Collaborative Research Group examining the research and applications of Optimal Transportation across a wide audience of researchers, students, industry, policy makers and the general public.

The Kantorovich Initiative is a dedicated website to help foster a community around the topic of Optimal Transportation.

Denoising Diffusion models have revolutionized generative modeling. Conceptually, these methods define a transport mechanism from a noise distribution to a data distribution. Recent advancements have extended this framework to define transport maps...

Measures provide valuable insights into long-term and global behaviors across a broad range of dynamical systems. In this talk, we present our recent research efforts that employ measure theory and optimal transport to tackle core challenges in...

Gradient flows have emerged as a powerful framework for analyzing machine learning and statistical inference algorithms. Motivated by several applications in statistical inference, generative models, generalization, and robustness of learning...

The quadratically regularized optimal transport problem (QOT) has emerged in the literature as a sparse alternative to entropic regularization (EOT). Unlike EOT, whose solutions always have full support—even for small regularization parameters—QOT...

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for...

What happens to Wasserstein gradient flows if one uses entropic optimal transport instead of classical optimal transport? I will explain why it may be relevant to use Sinkhorn divergences, built on entropic optimal transport, as they allow the...

I will introduce our recent work on parameterising OT problems with elastic costs, i.e. ground costs that mix the classic squared Euclidean distance with a regularizer (e.g. L1 norm). After highlighting the properties of OT maps that follow such...

While Einstein’s theory of gravity is formulated in a smooth setting, the celebrated singularity theorems of Hawking and Penrose describe many physical situations in which this smoothness must eventually breakdown. In positive-definite signature...

Optimal transport operates on empirical distributions which may contain acquisition artifacts, such as outliers or noise, thereby hindering a robust calculation of the OT map. Additionally, it necessitates equal mass between the two distributions...

Density functional theory (DFT) is one of the workhorses of quantum chemistry and material science. In principle, the joint probability of finding a specific electron configuration in a material is governed by a Schrödinger wave equation. But...

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Soumik Pal

Professor of Mathematics, University of Washington

Young-Heon Kim

Professor of Mathematics, University of British Columbia

Brendan Pass

Associate Professor of Mathematics, University of Alberta