Related papers: LBONet: Supervised Spectral Descriptors for Shape …

This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…

Spectral methods are widely used in geometry processing of 3D models. They rely on the projection of the mesh geometry on the basis defined by the eigenvectors of the graph Laplacian operator, becoming computationally prohibitive as the…

Accurate identification of complex terrain characteristics, such as soil composition and coefficient of friction, is essential for model-based planning and control of mobile robots in off-road environments. Spectral signatures leverage…

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…

We study the estimation of quadratic Sobolev-type integral functionals of an unknown density on the unit sphere. The functional is defined through fractional powers of the Laplace--Beltrami operator and provides a global measure of…

Due to the growing ubiquity of unlabeled data, learning with unlabeled data is attracting increasing attention in machine learning. In this paper, we propose a novel semi-supervised kernel learning method which can seamlessly combine…

The problem of determining the domain of the closure of the Laplace-Beltrami operator on a 2D almost-Riemannian manifold is considered. Using tools from theory of Lie groupoids natural domains of perturbations of the Laplace-Beltrami…

We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely…

Spreading of liquid droplets on solid substrates constitutes a classic multiphysics problem with widespread applications ranging from inkjet printing, spray cooling, to biomedical microfluidic systems. Yet, accurate computational fluid…

We present a novel method for computing correspondences across 3D shapes using unsupervised learning. Our method computes a non-linear transformation of given descriptor functions, while optimizing for global structural properties of the…

The rapid growth of image data has led to the development of advanced image processing and computer vision techniques, which are crucial in various applications such as image classification, image segmentation, and pattern recognition.…

We propose two deep learning models that fully automate shape parameterization for aerodynamic shape optimization. Both models are optimized to parameterize via deep geometric learning to embed human prior knowledge into learned geometric…

Deep networks for image classification often rely more on texture information than object shape. While efforts have been made to make deep-models shape-aware, it is often difficult to make such models simple, interpretable, or rooted in…

Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…

Training loss and throughput can hide distinct internal representation in language-model training. To examine these hidden mechanics, we use spectral measurements as practical and operational diagnostics. Using a controlled family of…

In this paper, we present a spectral graph wavelet approach for shape analysis of carpal bones of human wrist. We apply a metric called global spectral graph wavelet signature for representation of cortical surface of the carpal bone based…

Supernet training of LLMs is of great interest in industrial applications as it confers the ability to produce a palette of smaller models at constant cost, regardless of the number of models (of different size / latency) produced. We…

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in…

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…

We present a novel deep convolutional network pipeline, LO-Net, for real-time lidar odometry estimation. Unlike most existing lidar odometry (LO) estimations that go through individually designed feature selection, feature matching, and…