Fast Approximate Geodesics for Deep Generative Models

Chen, Nutan; Ferroni, Francesco; Klushyn, Alexej; Paraschos, Alexandros; Bayer, Justin; Smagt, Patrick van der

doi:10.1007/978-3-030-30484-3_45

Cited by 38 publications

(77 citation statements)

References 25 publications

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“…Note that geodesics do generally not follow a closed-form expression in these models, and numerical approximations are in order. This can be done by direct minimization of curve length [38,22], A * search [9], integration of the associated ODE [2], or various heuristics [8].…”

Section: Variational Autoencoders As Riemannian Manifoldsmentioning

confidence: 99%

Learning Riemannian Manifolds for Geodesic Motion Skills

Beik-Mohammadi

Hauberg²,

Arvanitidis

et al. 2021

Robotics: Science and Systems XVII

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For robots to work alongside humans and perform in unstructured environments, they must learn new motion skills and adapt them to unseen situations on the fly. This demands learning models that capture relevant motion patterns, while offering enough flexibility to adapt the encoded skills to new requirements, such as dynamic obstacle avoidance. We introduce a Riemannian manifold perspective on this problem, and propose to learn a Riemannian manifold from human demonstrations on which geodesics are natural motion skills. We realize this with a variational autoencoder (VAE) over the space of position and orientations of the robot end-effector. Geodesic motion skills let a robot plan movements from and to arbitrary points on the data manifold. They also provide a straightforward method to avoid obstacles by redefining the ambient metric in an online fashion. Moreover, geodesics naturally exploit the manifold resulting from multiple-mode tasks to design motions that were not explicitly demonstrated previously. We test our learning framework using a 7-DoF robotic manipulator, where the robot satisfactorily learns and reproduces realistic skills featuring elaborated motion patterns, avoids previously-unseen obstacles, and generates novel movements in multiple-mode settings.

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Section: Variational Autoencoders As Riemannian Manifoldsmentioning

confidence: 99%

Learning Riemannian Manifolds for Geodesic Motion Skills

Beik-Mohammadi

Hauberg²,

Arvanitidis

et al. 2021

Robotics: Science and Systems XVII

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show abstract

“…Autoencoders [Rumelhart et al, 1986] and generative adversarial networks [Goodfellow et al, 2014] are two prominent examples. Our work is not applicable to this setting, and a series of papers have investigated such deterministic decoders [Shao et al, 2018, Chen et al, 2018a, Laine, 2018. As demonstrated in Sec.…”

Section: Related Workmentioning

confidence: 99%

Pulling back information geometry

Arvanitidis¹,

Miguel²,

Alison³

et al. 2021

Preprint

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Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its simple reparametrization allows us to interpret the generating process as a random projection of a deterministic manifold. Consequently, this approach breaks down when applied to decoders that are not as easily reparametrized. We here propose to use the Fisher-Rao metric associated with the space of decoder distributions as a reference metric, which we pull back to the latent space. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions for which the previous theory was not applicable, opening the door to 'black box' latent geometries. * Equal contribution.Preprint. Under review.

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“…In lieu of implementing a structured geometric prior, some techniques incorporate natural data structure into a latent space by computing geodesic paths between points using an estimated Riemannian metric (Arvanitidis, Hansen, and Hauberg 2017;Chen et al 2017;Shao, Kumar, and Thomas Fletcher 2018). Similar to our main aims, these techniques identify situations in which linear paths are not effective for representing transformations and aim to estimate more accurate nonlinear manifold paths between points.…”

Section: Nonlinear Structure In Encoded Networkmentioning

confidence: 99%

“…We train on walking sequences 1-16 from subject 35. Walking data from this subject is abundant and this subject has been widely used for gait analysis (Chen et al 2017;Taylor, Hinton, and Roweis 2007).…”

Section: Gait Sequencesmentioning

confidence: 99%

Representing Closed Transformation Paths in Encoded Network Latent Space

Connor

Rozell

2020

AAAI

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Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the Euclidean structure of the latent space may be a poor match for the underlying latent structure in the data. In this work, we incorporate a generative manifold model into the latent space of an autoencoder in order to learn the low-dimensional manifold structure from the data and adapt the latent space to accommodate this structure. In particular, we focus on applications in which the data has closed transformation paths which extend from a starting point and return to nearly the same point. Through experiments on data with natural closed transformation paths, we show that this model introduces the ability to learn the latent dynamics of complex systems, generate transformation paths, and classify samples that belong on the same transformation path.

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Fast Approximate Geodesics for Deep Generative Models

Cited by 38 publications

References 25 publications

Learning Riemannian Manifolds for Geodesic Motion Skills

Learning Riemannian Manifolds for Geodesic Motion Skills

Pulling back information geometry

Representing Closed Transformation Paths in Encoded Network Latent Space

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