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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)

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