Related papers: FlashSinkhorn: IO-Aware Entropic Optimal Transport…
In this paper, we propose a practical primal-dual algorithm with theoretical guarantees and develop a GPU-based solver, which we dub PDOT, for solving large-scale optimal transport problems. Compared to Sinkhorn algorithm or classic LP…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
We consider the numerical solution of the discrete multi-marginal optimal transport (MOT) by means of the Sinkhorn algorithm. In general, the Sinkhorn algorithm suffers from the curse of dimensionality with respect to the number of…
In long-context decoding for LLMs and LMMs, attention becomes increasingly memory-bound because each decoding step must load a large amount of KV-cache data from GPU memory. Existing acceleration strategies often trade efficiency for…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
Unbalanced optimal transport (UOT) has been widely used as a fundamental tool in many application domains, where it often dominates the application running time. While many researchers have proposed various optimizations for UOT, few have…
Non-Markovian (renewal) epidemic simulation on multi-million-node contact networks is essential for realistic forecasting under general age-dependent holding-time distributions (log-normal, Weibull, Erlang, and similar), but the…
The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…
We study long-context balanced entropic optimal transport (OT) attention on TPU hardware through a stopped-base, fixed-depth tail-refinement surrogate. After a stopped $T$-step Sinkhorn solve, we unroll a short refinement tail and…
Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…
Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
Photonic computing has emerged as a promising substrate for accelerating the dense linear-algebra operations at the heart of AI, yet adoption for large Transformer models remains in its infancy. We identify two bottlenecks: (1) costly…
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the…
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT problem, the entropic OT problem, which allows to implement…
Attention accounts for an increasingly dominant fraction of total computation during inference for mixture-of-experts (MoE) models, making efficient acceleration critical. Emerging domain-specific accelerators for large model inference are…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
Partial Optimal Transport (POT) addresses the problem of transporting only a fraction of the total mass between two distributions, making it suitable when marginals have unequal size or contain outliers. While Sinkhorn-based methods are…
Numerically solving multi-marginal optimal transport (MMOT) problems is computationally prohibitive, even for moderate-scale instances involving $l\ge4$ marginals with support sizes of $N\ge1000$. The cost in MMOT is represented as a tensor…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…