Related papers: Hierarchical Optimal Transport for Document Repres…
Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. There is a recent graph…
With the growing focus on semantic searches and interpretations, an increasing number of standardized vocabularies and ontologies are being designed and used to describe data. We investigate the querying of objects described by a…
In this paper, we develop a neural summarization model which can effectively process multiple input documents and distill Transformer architecture with the ability to encode documents in a hierarchical manner. We represent cross-document…
This paper is devoted to variational problems on the set of probability measures which involve optimal transport between unequal dimensional spaces. In particular, we study the minimization of a functional consisting of the sum of a term…
The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
Document alignment aims to identify pairs of documents in two distinct languages that are of comparable content or translations of each other. Such aligned data can be used for a variety of NLP tasks from training cross-lingual…
We introduce a new class of objectives for optimal transport computations of datasets in high-dimensional Euclidean spaces. The new objectives are parametrized by $\rho \geq 1$, and provide a metric space $\mathcal{R}_{\rho}(\cdot, \cdot)$…
Text classification algorithms investigate the intricate relationships between words or phrases and attempt to deduce the document's interpretation. In the last few years, these algorithms have progressed tremendously. Transformer…
We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…
Readability assessment aims to evaluate the reading difficulty of a text. In recent years, while deep learning technology has been gradually applied to readability assessment, most approaches fail to consider either the length of the text…
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…
Recent works on word representations mostly rely on predictive models. Distributed word representations (aka word embeddings) are trained to optimally predict the contexts in which the corresponding words tend to appear. Such models have…
Feature modeling of different modalities is a basic problem in current research of cross-modal information retrieval. Existing models typically project texts and images into one embedding space, in which semantically similar information…
This paper focuses on the Monge-Kantorovich formulation of the optimal transport problem and the associated $L^2$ Wasserstein distance. We use the $L^2$ Wasserstein distance in the Nearest Neighbour (NN) machine learning architecture to…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
Hypernym discovery is the problem of finding terms that have is-a relationship with a given term. We introduce a new context type, and a relatedness measure to differentiate hypernyms from other types of semantic relationships. Our Document…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…