17 citations · 58 across the 11 of their papers we have counts for
13 papers
Certifying Robustness via Topological Representations
Jens Agerberg, Andrea Guidolin, Andrea Martinelli +3
We propose a neural network architecture that can learn discriminative geometric representations of data from persistence diagrams, common descriptors of Topological Data Analysis.…
Identifying latent distances with Finslerian geometry
Alison Pouplin, David Eklund, Carl Henrik Ek +1
Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be…
Computing geometric feature sizes for algebraic manifolds
Sandra Di Rocco, Parker B. Edwards, David Eklund +2
We introduce numerical algebraic geometry methods for computing lower bounds on the reach, local feature size, and the weak feature size of the real part of an equidimensional and…
Sampling and homology via bottlenecks
Sandra Di Rocco, David Eklund, Oliver Gäfvert
In this paper we present an efficient algorithm to produce a provably dense sample of a smooth compact variety. The procedure is partly based on computing of…
Variational Autoencoders with Riemannian Brownian Motion Priors
Dimitris Kalatzis, David Eklund, Georgios Arvanitidis +1
Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean. This assumption naturally leads to the commo…
Expected path length on random manifolds
David Eklund, Søren Hauberg
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provi…