Related papers: Geometry-Aware Probabilistic Circuits via Voronoi …
The Variational Autoencoder (VAE) is a powerful architecture capable of representation learning and generative modeling. When it comes to learning interpretable (disentangled) representations, VAE and its variants show unparalleled…
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…
Despite their success, modern convolutional neural networks (CNNs) exhibit fundamental limitations, including data inefficiency, poor out-of-distribution generalization, and vulnerability to adversarial perturbations. These shortcomings can…
We propose an auto-encoding network architecture for point clouds (PC) capable of extracting shape signatures without supervision. Building on this, we (i) design a loss function capable of modelling data variance on PCs which are…
Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…
Voronoi tessellations are standard in spatial planning for assigning service areas based on Euclidean proximity, underpinning regulatory frameworks like the proximity principle in waste management. However, in regions with complex…
Systems involving human-robot collaboration necessarily require that steps be taken to ensure safety of the participating human. This is usually achievable if accurate, reliable estimates of the human's pose are available. In this paper, we…
Probabilistic circuits (PCs) are a class of tractable probabilistic models that allow efficient, often linear-time, inference of queries such as marginals and most probable explanations (MPE). However, marginal MAP, which is central to many…
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations…
This paper presents a comparative analysis of algorithmic strategies for fitting tessellation models to 3D image data of materials such as polycrystals and foams. In this steadily advancing field, we review and assess optimization-based…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
Variational autoencoders (VAEs), that are built upon deep neural networks have emerged as popular generative models in computer vision. Most of the work towards improving variational autoencoders has focused mainly on making the…
This paper extends the concept of generalized polarization tensors (GPTs), which was previously defined for inclusions with homogeneous conductivities, to inhomogeneous conductivity inclusions. We begin by giving two slightly different but…
Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate…
Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…
Extracting compact, physically interpretable representations from high-dimensional scientific data is a persistent challenge due to the complex, nonlinear structures inherent in physical systems. We propose a Gaussian Mixture Variational…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linear functions on a triangulation of the domain. We define an a…
Fabrication process variations can significantly influence the performance and yield of nano-scale electronic and photonic circuits. Stochastic spectral methods have achieved great success in quantifying the impact of process variations,…
In this paper, we address the stochastic reach-avoid problem for linear systems with additive stochastic uncertainty. We seek to compute the maximum probability that the states remain in a safe set over a finite time horizon and reach a…