Horizontal Flows and Manifold Stochastics in Geometric Deep Learning
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Horizontal Flows and Manifold Stochastics in Geometric Deep Learning. / Sommer, Stefan; Bronstein, Alex M.
I: IEEE Transactions on Pattern Analysis and Machine Intelligence, Bind 44, Nr. 2, 2021, s. 811 - 822.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Horizontal Flows and Manifold Stochastics in Geometric Deep Learning
AU - Sommer, Stefan
AU - Bronstein, Alex M.
PY - 2021
Y1 - 2021
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 diffusion 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 diffusion 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
VL - 44
SP - 811
EP - 822
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
SN - 0162-8828
IS - 2
ER -
ID: 243465291