Related papers: Alpha shapes and optimal transport on the sphere

The Squared-Gradient approximation to the Modified-Core Van der Waals density functional theory model is developed. A simple, explicit expression for the SGA coefficient involving only the bulk equation of state and the interaction…

An equation of Monge-Amp\`ere type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport…

The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…

Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…

This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and…

Transport-based density estimation methods are receiving growing interest because of their ability to efficiently generate samples from the approximated density. We further invertigate the sequential transport maps framework proposed from…

We develop a semi-discrete optimal transport scheme for the compressible semi-geostrophic equations, a system that plays an important role in modelling large-scale atmospheric dynamics and frontogenesis. Unlike the incompressible case, the…

Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…

Tabular data, widely used in industries like healthcare, finance, and transportation, presents unique challenges for deep learning due to its heterogeneous nature and lack of spatial structure. This survey reviews the evolution of deep…

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In…

In this article we investigate the effects of conformal transformations on kernel functions used in Support Vector Machines. Our focus lies in the task of text document categorization, which involves assigning each document to a particular…

Recently, the fundamental problem of unsupervised domain adaptation (UDA) on 3D point clouds has been motivated by a wide variety of applications in robotics, virtual reality, and scene understanding, to name a few. The point cloud data…

We present a new multiscale algorithm for solving regularized Optimal Transport problems on the GPU, with a linear memory footprint. Relying on Sinkhorn divergences which are convex, smooth and positive definite loss functions, this method…

We develop a new method based on Caffarelli's contraction theorem in optimal transport to obtain sharp and uniform modulus of continuity estimates for $\beta$-Dyson Brownian motions with $\beta \geq 2$. Our method extends to a large class…

Fusion is a technique for merging multiple independently-trained neural networks in order to combine their capabilities. Past attempts have been restricted to the case of fully-connected, convolutional, and residual networks. This paper…

This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies…

Deep neural networks are typically trained in a single shot for a specific task and data distribution, but in real world settings both the task and the domain of application can change. The problem becomes even more challenging in dense…

State-of-the-art data stream mining has long drawn from ensembles of the Very Fast Decision Tree, a seminal algorithm honored with the 2015 KDD Test-of-Time Award. However, the emergence of large tabular models, i.e., transformers designed…

Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a…

We describe a new model for image propagation through open air in the presence of changes in the index of refraction (e.g. due to turbulence) using the theory of optimal transport. We describe the relationship between photon density, or…