Related papers: FlashSinkhorn: IO-Aware Entropic Optimal Transport…

Multi-Head Attention (MHA) is a critical computational kernel in transformer-based AI models. Emerging scalable tile-based accelerator architectures integrate increasing numbers of tightly-packed processing elements (PEs) with tensor units.…

We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…

We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions which are accessible by samples. Our algorithm is based on the saddle point…

Mixture of Experts (MoE) models have emerged as the de facto architecture for scaling up language models without significantly increasing the computational cost. Recent MoE models demonstrate a clear trend towards high expert granularity…

Optimizing deep learning algorithms currently requires slow, manual derivation, potentially leaving much performance untapped. Methods like FlashAttention have achieved a x6 performance improvement over native PyTorch by avoiding…

Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…

An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide…

Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…

Slot attention is a powerful method for object-centric modeling in images and videos. However, its set-equivariance limits its ability to handle videos with a dynamic number of objects because it cannot break ties. To overcome this…

To find deterministic solutions to the transient $S_N$ neutron transport equation, iterative schemes are typically used to treat the scattering (and fission) source terms. We explore the one-cell inversion iteration scheme to do this on the…

While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…

Mixture-of-Experts (MoE) architectures power the majority of frontier large language models, but their inference is bottlenecked by irregular memory access patterns and expert routing overhead. Existing optimized MoE kernels (Megablocks,…

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…

The use of optimal transport (OT) distances, and in particular entropic-regularised OT distances, is an increasingly popular evaluation metric in many areas of machine learning and data science. Their use has largely been driven by the…

Attention, as a core layer of the ubiquitous Transformer architecture, is the bottleneck for large language models and long-context applications. While FlashAttention-3 optimized attention for Hopper GPUs through asynchronous execution and…

Diffusion Transformers (DiTs) have gained increasing adoption in high-quality image and video generation. As demand for higher-resolution images and longer videos increases, single-GPU inference becomes inefficient due to increased latency…

Scaling algorithms for entropic transport-type problems have become a very popular numerical method, encompassing Wasserstein barycenters, multi-marginal problems, gradient flows and unbalanced transport. However, a standard implementation…

Sparse Mixture-of-Experts (SMoE) has gained prominence as a scalable and computationally efficient architecture, enabling significant growth in model capacity without incurring additional inference costs. However, existing SMoE models often…

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…