Related papers: Hierarchical Optimal Transport for Document Repres…
In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal…
Recent advances in social and mobile technology have enabled an abundance of digital traces (in the form of mobile check-ins, association of mobile devices to specific WiFi hotspots, etc.) revealing the physical presence history of diverse…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…
Scheduling problems are often tackled independently, and rarely solved by leveraging the commonalities across problems. Lack of awareness of this inter-task similarity could impede the search efficacy. A quantifiable relationship between…
We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a…
Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
A major computational burden, while performing document clustering, is the calculation of similarity measure between a pair of documents. Similarity measure is a function that assigns a real number between 0 and 1 to a pair of documents,…
Existing image-text matching approaches typically infer the similarity of an image-text pair by capturing and aggregating the affinities between the text and each independent object of the image. However, they ignore the connections between…
The optimal transport problem studies how to transport one measure to another in the most cost-effective way and has wide range of applications from economics to machine learning. In this paper, we introduce and study an information…
The word mover's distance (WMD) is a popular semantic similarity metric for two texts. This position paper studies several possible extensions of WMD. We experiment with the frequency of words in the corpus as a weighting factor and the…
This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to…
This paper presents a light-weight, high-quality texture synthesis algorithm that easily generalizes to other applications such as style transfer and texture mixing. We represent texture features through the deep neural activation vectors…
Recent work exhibited that distributed word representations are good at capturing linguistic regularities in language. This allows vector-oriented reasoning based on simple linear algebra between words. Since many different methods have…
Optimal transport has been used to define bijective nonlinear transforms and different transport-related metrics for discriminating data and signals. Here we briefly describe the advances in this topic with the main applications and…
We present a novel divide-and-conquer method for the neural summarization of long documents. Our method exploits the discourse structure of the document and uses sentence similarity to split the problem into an ensemble of smaller…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…