Timezone: »
Identifying latent distances with Finslerian geometry
Alison Pouplin · David Eklund · Carl Henrik Ek · Søren Hauberg
Event URL: https://openreview.net/forum?id=9nE8VxXCMZ- »
Riemannian geometry has been shown useful to explore the latent space of models of high dimensional data. This latent space is learnt via a stochastic smooth mapping, and a deterministic approximation of the metric is required. Yet, this approximation is ad-hoc and doesn't lead to interpretable quantities, such as the curve length. Here, we are defining a new metric as the expectation of the stochastic length induced by this smooth mapping. We show that this norm is a Finsler metric. We compare this Finsler metric with the previously studied expected Riemannian metric, and we show that in high dimensions, these metrics converge to each other.
Author Information
Alison Pouplin (Technical University of Denmark)
David Eklund
Carl Henrik Ek (University of Cambridge)
Søren Hauberg (Technical University of Denmark)
More from the Same Authors
-
2021 : A kernel for continuously relaxed, discrete Bayesian optimization of protein sequences »
Yevgen Zainchkovskyy · Simon Bartels · Søren Hauberg · Jes Frellsen · Wouter Boomsma -
2021 Meetup: Copenhagen, Denmark »
Søren Hauberg -
2022 : Probabilistic thermal stability prediction through sparsity promoting transformer representation »
Yevgen Zainchkovskyy · Jesper Ferkinghoff-Borg · Anja Bennett · Thomas Egebjerg · Nikolai Lorenzen · Per Greisen · Søren Hauberg · Carsten Stahlhut -
2022 : Optimal Latent Transport »
Hrittik Roy · Søren Hauberg -
2022 Poster: Revisiting Active Sets for Gaussian Process Decoders »
Pablo Moreno-Muñoz · Cilie Feldager · Søren Hauberg -
2022 Poster: Laplacian Autoencoders for Learning Stochastic Representations »
Marco Miani · Frederik Warburg · Pablo Moreno-Muñoz · Nicki Skafte · Søren Hauberg -
2021 Poster: Bounds all around: training energy-based models with bidirectional bounds »
Cong Geng · Jia Wang · Zhiyong Gao · Jes Frellsen · Søren Hauberg -
2020 : Isometric Gaussian Process Latent Variable Model »
Martin Jørgensen · Søren Hauberg -
2020 : Invited Talk 3: Reparametrization invariance in representation learning »
Søren Hauberg -
2019 Poster: Reliable training and estimation of variance networks »
Nicki Skafte · Martin Jørgensen · Søren Hauberg -
2019 Poster: Explicit Disentanglement of Appearance and Perspective in Generative Models »
Nicki Skafte · Søren Hauberg -
2016 Poster: A Locally Adaptive Normal Distribution »
Georgios Arvanitidis · Lars K Hansen · Søren Hauberg