Related papers: Hierarchical Multi-Marginal Optimal Transport for …
Fluid-flow devices with low dissipation, but high contact area, are of importance in many applications. A well-known strategy to design such devices is multi-scale topology optimization (MTO), where optimal microstructures are designed…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
Transferring linguistic knowledge from a pretrained language model (PLM) to acoustic feature learning has proven effective in enhancing end-to-end automatic speech recognition (E2E-ASR). However, aligning representations between linguistic…
Optimal transport is a machine learning problem with applications including distribution comparison, feature selection, and generative adversarial networks. In this paper, we propose feature-robust optimal transport (FROT) for…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map.…
Cross-modal matching, a fundamental task in bridging vision and language, has recently garnered substantial research interest. Despite the development of numerous methods aimed at quantifying the semantic relatedness between image-text…
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
Multimodal Attributed Graphs (MAGs) have been widely adopted for modeling complex systems by integrating multi-modal information, such as text and images, on nodes. However, we identify a discrepancy between the implicit semantic structure…
Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of…
Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…
This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the…
Network alignment aims to find regions of topological or functional similarities between networks. In computational biology, it can be used to transfer biological knowledge from a well-studied species to a poorly-studied species between…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…
Survival prediction is a complicated ordinal regression task that aims to predict the ranking risk of death, which generally benefits from the integration of histology and genomic data. Despite the progress in joint learning from pathology…