相关论文: SWIFT: Scalable Wasserstein Factorization for Spar…
The clustering problem, and more generally, latent factor discovery --or latent space inference-- is formulated in terms of the Wasserstein barycenter problem from optimal transport. The objective proposed is the maximization of the…
Best-of-N sampling is a powerful method for improving Large Language Model (LLM) performance, but it is often limited by its dependence on massive, text-based reward models. These models are not only computationally expensive but also…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
The sliced Wasserstein distance (SW) reduces optimal transport on $\mathbb{R}^d$ to a sum of one-dimensional projections, and thanks to this efficiency, it is widely used in geometry, generative modeling, and registration tasks. Recent work…
The performance of unsupervised methods such as clustering depends on the choice of distance metric between features, or ground metric. Commonly, ground metrics are decided with heuristics or learned via supervised algorithms. However,…
Tensors are multi-way arrays, and the Candecomp/Parafac (CP) tensor factorization has found application in many different domains. The CP model is typically fit using a least squares objective function, which is a maximum likelihood…
The benefits of most large language models come with steep and often hidden economic and environmental costs due to their resource usage inefficiency during deployment. Model quantization improves energy and memory efficiency through…
We consider tensor factorizations based on sparse measurements of the components of relatively high rank tensors. The measurements are designed in a way that the underlying graph of interactions is a random graph. The setup will be useful…
With the tremendous success of large transformer models in natural language understanding, down-sizing them for cost-effective deployments has become critical. Recent studies have explored the low-rank weight factorization techniques which…
Given a high-dimensional large-scale tensor, how can we decompose it into latent factors? Can we process it on commodity computers with limited memory? These questions are closely related to recommender systems, which have modeled rating…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Due to the sparse connectivity of superconducting quantum computers, qubit communication via SWAP gates accounts for the vast majority of overhead in quantum programs. We introduce a method for improving the speed and reliability of SWAPs…
We propose a transfer principle to study the adapted 2-Wasserstein distance between stochastic processes. First, we obtain an explicit formula for the distance between real-valued mean-square continuous Gaussian processes by introducing the…
We present a tensor train (TT) based algorithm designed for sampling from a target distribution and employ TT approximation to capture the high-dimensional probability density evolution of overdamped Langevin dynamics. This involves…
We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over $\mathbb{R}^d$ into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on…
Sliced optimal transport (SOT), or sliced Wasserstein (SW) distance, is widely recognized for its statistical and computational scalability. In this work, we further enhance computational scalability by proposing the first method for…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Obtaining solutions to Optimal Transportation (OT) problems is typically intractable when the marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d.…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…