Horizontal Flows and Manifold Stochastics in Geometric Deep Learning

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Standard

Horizontal Flows and Manifold Stochastics in Geometric Deep Learning. / Sommer, Stefan; Bronstein, Alex M.

I: IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Sommer, S & Bronstein, AM 2020, 'Horizontal Flows and Manifold Stochastics in Geometric Deep Learning', IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/TPAMI.2020.2994507

APA

Sommer, S., & Bronstein, A. M. (2020). Horizontal Flows and Manifold Stochastics in Geometric Deep Learning. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/TPAMI.2020.2994507

Vancouver

Sommer S, Bronstein AM. Horizontal Flows and Manifold Stochastics in Geometric Deep Learning. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2020. https://doi.org/10.1109/TPAMI.2020.2994507

Author

Sommer, Stefan ; Bronstein, Alex M. / Horizontal Flows and Manifold Stochastics in Geometric Deep Learning. I: IEEE Transactions on Pattern Analysis and Machine Intelligence. 2020.

Bibtex

@article{9f52150e88fd4abbb12c82076b33ee70,
title = "Horizontal Flows and Manifold Stochastics in Geometric Deep Learning",
abstract = "We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted Brownian motion maximum likelihood mean. Both methods are inspired by stochastics on manifolds and geometric statistics, and provide examples of how stochastic methods -- here horizontal frame bundle flows and non-linear bridge sampling schemes, can be used in geometric deep learning. We outline the theoretical foundation of the two methods, discuss their relation to Euclidean deep networks and existing methodology in geometric deep learning, and establish important properties of the proposed constructions.",
author = "Stefan Sommer and Bronstein, {Alex M.}",
year = "2020",
doi = "10.1109/TPAMI.2020.2994507",
language = "English",
journal = "I E E E Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
publisher = "Institute of Electrical and Electronics Engineers",

}

RIS

TY - JOUR

T1 - Horizontal Flows and Manifold Stochastics in Geometric Deep Learning

AU - Sommer, Stefan

AU - Bronstein, Alex M.

PY - 2020

Y1 - 2020

N2 - We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted Brownian motion maximum likelihood mean. Both methods are inspired by stochastics on manifolds and geometric statistics, and provide examples of how stochastic methods -- here horizontal frame bundle flows and non-linear bridge sampling schemes, can be used in geometric deep learning. We outline the theoretical foundation of the two methods, discuss their relation to Euclidean deep networks and existing methodology in geometric deep learning, and establish important properties of the proposed constructions.

AB - We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted Brownian motion maximum likelihood mean. Both methods are inspired by stochastics on manifolds and geometric statistics, and provide examples of how stochastic methods -- here horizontal frame bundle flows and non-linear bridge sampling schemes, can be used in geometric deep learning. We outline the theoretical foundation of the two methods, discuss their relation to Euclidean deep networks and existing methodology in geometric deep learning, and establish important properties of the proposed constructions.

U2 - 10.1109/TPAMI.2020.2994507

DO - 10.1109/TPAMI.2020.2994507

M3 - Journal article

C2 - 32406826

JO - I E E E Transactions on Pattern Analysis and Machine Intelligence

JF - I E E E Transactions on Pattern Analysis and Machine Intelligence

SN - 0162-8828

ER -

ID: 243465291