15 citations · 45 across the 17 of their papers we have counts for
22 papers
Topological degree as a discrete diagnostic for disentanglement, with applications to the VAE
Mahefa Ratsisetraina Ravelonanosy, Vlado Menkovski, Jacobus W. Portegies
We investigate the ability of Diffusion Variational Autoencoder (VAE) with unit sphere as latent space to capture topological and geometrical structure and disen…
Neural Langevin Dynamics: towards interpretable Neural Stochastic Differential Equations
Simon M. Koop, Mark A. Peletier, Jacobus W. Portegies +1
Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be har…
Small time asymptotics of the entropy of the heat kernel on a Riemannian manifold
Vlado Menkovski, Jacobus W. Portegies, Mahefa Ratsisetraina Ravelonanosy
We give an asymptotic expansion of the relative entropy between the heat kernel of a compact Riemannian manifold and the normalized Riemannian volume for small val…
Semicontinuity of capacity under pointed intrinsic flat convergence
Jeffrey L. Jauregui, Raquel Perales, Jacobus W. Portegies
The concept of the capacity of a compact set in generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multip…
Universal Approximation in Dropout Neural Networks
Oxana A. Manita, Mark A. Peletier, Jacobus W. Portegies +2
We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random -valued f…
A Metric for Linear Symmetry-Based Disentanglement
Luis A. Pérez Rey, Loek Tonnaer, Vlado Menkovski +2
The definition of Linear Symmetry-Based Disentanglement (LSBD) proposed by (Higgins et al., 2018) outlines the properties that should characterize a disentangled representation tha…
The homotopy significant spectrum compared to the Krasnoselskii spectrum
S. J. Fokma, J. W. Portegies
How to generalize the concept of eigenvalues of quadratic forms to eigenvalues of arbitrary, even, homogeneous continuous functionals, if stability of the set of eigenvalues under…
Arrow Contraction and Expansion in Tropical Diagrams
Rostislav Matveev, Jacobus W. Portegies
Arrow contraction applied to a tropical diagram of probability spaces is a modification of the diagram, replacing one of the morphisms by an isomorphims, while preserving other par…
Conditioning in tropical probability theory
Rostislav Matveev, Jacobus W. Portegies
We define a natural operation of conditioning of tropical diagrams of probability spaces and show that it is Lipschitz continuous with respect to the asymptotic entropy distance.
Tropical probability theory and an application to the entropic cone
Rostislav Matveev, Jacobus W. Portegies
In a series of articles, we have been developing a theory of tropical diagrams of probability spaces, expecting it to be useful for information optimization problems in information…
Tropical diagrams of probability spaces
Rostislav Matveev, Jacobus W. Portegies
After endowing the space of diagrams of probability spaces with an entropy distance, we study its large-scale geometry by identifying the asymptotic cone as a closed convex cone in…
Embedding of spaces in via eigenfunctions
Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies +1
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results by Bérard, Bé…
Continuity of nonlinear eigenvalues in spaces with respect to measured Gromov-Hausdorff convergence
Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies
In this note we prove in the nonlinear setting of spaces the stability of the Krasnoselskii spectrum of the Laplace operator under measured Gromov-Hausdorff con…
Tropical Limits of Probability Spaces, Part I: The Intrinsic Kolmogorov-Sinai Distance and the Asymptotic Equipartition Property for Configurations
Rostislav Matveev, Jacobus W. Portegies
The entropy of a finite probability space measures the observable cardinality of large independent products of the probability space. If two probability spaces…
On the regular representation of measures
Jürgen Jost, Rostislav Matveev, Jacobus W. Portegies +1
We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class . The conditio…
Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci curvature bounded below
Rostislav Matveev, Jacobus W. Portegies
We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature uniformly bounded from below and diameter uniformly bounded above…
Semicontinuity of eigenvalues under intrinsic flat convergence
Jacobus W. Portegies
We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integrati…
Embeddings of Riemannian manifolds with heat kernels and eigenfunctions
Jacobus W. Portegies
We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from heat kernels at a certain time from a finite number of points. Both this time an…
Properties of the Intrinsic Flat Distance
J. Portegies, C. Sormani
Here we explore a variety of properties of intrinsic flat convergence. We introduce the sliced filling volume and interval sliced filling volume and explore the relationship betwee…
Semicontinuity of Eigenvalues under Flat Convergence in Euclidean Space
Jacobus W Portegies
Recall that Federer-Fleming defined the notion of flat convergence of submanifolds of Euclidean space to solve the Plateau problem. Here we prove the upper semicontinuity of Neuman…
Efimov Trimers in a Harmonic Potential
Jacobus Portegies, Servaas Kokkelmans
We study the Efimov effect in a harmonic oscillator in the hyperspherical formulation, and show how a reduced model allows for a description that is a generalization of the Efimov…
Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows
Jacobus W. Portegies, Mark A. Peletier
We develop a gradient-flow framework based on the Wasserstein metric for a parabolic moving-boundary problem that models crystal dissolution and precipitation. In doing so we deriv…