Related papers: Study of Manifold Geometry using Multiscale Non-Ne…

This research aims to develop kernel GNG, a kernelized version of the growing neural gas (GNG) algorithm, and to investigate the features of the networks generated by the kernel GNG. The GNG is an unsupervised artificial neural network that…

In this paper, we study the generalization capabilities of geometric graph neural networks (GNNs). We consider GNNs over a geometric graph constructed from a finite set of randomly sampled points over an embedded manifold with topological…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

The task of data integration for multi-omics data has emerged as a powerful strategy to unravel the complex biological underpinnings of cancer. Recent advancements in graph neural networks (GNNs) offer an effective framework to model…

Kernel fusion is a popular and effective approach for combining multiple features that characterize different aspects of data. Traditional approaches for Multiple Kernel Learning (MKL) attempt to learn the parameters for combining the…

Geometric representation learning in preserving the intrinsic geometric and topological properties for discrete non-Euclidean data is crucial in scientific applications. Previous research generally mapped non-Euclidean discrete data into…

We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge…

Unlike on images, semantic learning on 3D point clouds using a deep network is challenging due to the naturally unordered data structure. Among existing works, PointNet has achieved promising results by directly learning on point sets.…

From designing architected materials to connecting mechanical behavior across scales, computational modeling is a critical tool in solid mechanics. Recently, there has been a growing interest in using machine learning to reduce the…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…

Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…

We consider the theory of regression on a manifold using reproducing kernel Hilbert space methods. Manifold models arise in a wide variety of modern machine learning problems, and our goal is to help understand the effectiveness of various…

Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large…

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…

Neural operators are neural network-based surrogate models for approximating solution operators of parametric partial differential equations, enabling efficient many-query computations in science and engineering. Many applications,…

We propose simple yet effective improvements in point representations and local neighborhood graph construction within the general framework of graph neural networks (GNNs) for 3D point cloud processing. As a first contribution, we propose…

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper…

Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. During the past 20 years, the considerable research activity that occurred in the…