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Geometric deep lear...
Geometric deep learning and equivariant neural networks
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- Gerken, Jan, 1991 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Algebra och geometri,Department of Mathematical Sciences, Algebra and Geometry,Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Gothenburg, Sweden; Machine Learning Group, Berlin Institute of Technology (TU Berlin), Berlin, Germany; Berlin Institute for the Foundations of Learning and Data (BIFOLD), Berlin, Germany
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- Aronsson, Jimmy, 1992 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Algebra och geometri,Department of Mathematical Sciences, Algebra and Geometry,Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Gothenburg, Sweden
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- Carlsson, Oscar, 1996 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, Algebra och geometri,Department of Mathematical Sciences, Algebra and Geometry,Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Gothenburg, Sweden
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- Linander, Hampus, 1985 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för fysik (GU),Department of Physics (GU),Department of Physics, Gothenburg University, Gothenburg, Sweden
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- Ohlsson, Fredrik (author)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Petersson, Christoffer, 1979 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Gothenburg, Sweden; Zenseact, Gothenburg, Sweden
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- Persson, Daniel, 1978 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Department of Mathematical Sciences, Chalmers University of Technology & University of Gothenburg, Gothenburg, Sweden
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(creator_code:org_t)
- Springer Nature, 2023
- 2023
- English.
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In: Artificial Intelligence Review. - : Springer Nature. - 1573-7462 .- 0269-2821. ; 56:12, s. 14605-14662
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Abstract
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- We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds M using principal bundles with structure group K and equivariant maps between sections of associated vector bundles. We also discuss group equivariant neural networks for homogeneous spaces M= G/ K , which are instead equivariant with respect to the global symmetry G on M . Group equivariant layers can be interpreted as intertwiners between induced representations of G, and we show their relation to gauge equivariant convolutional layers. We analyze several applications of this formalism, including semantic segmentation and object detection networks. We also discuss the case of spherical networks in great detail, corresponding to the case M= S2= SO (3) / SO (2) . Here we emphasize the use of Fourier analysis involving Wigner matrices, spherical harmonics and Clebsch–Gordan coefficients for G= SO (3) , illustrating the power of representation theory for deep learning.
Subject headings
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Bioinformatik (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Bioinformatics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Data- och informationsvetenskap -- Datavetenskap (hsv//swe)
- NATURAL SCIENCES -- Computer and Information Sciences -- Computer Sciences (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Publication and Content Type
- art (subject category)
- ref (subject category)
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- By the author/editor
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Gerken, Jan, 199 ...
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Aronsson, Jimmy, ...
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Carlsson, Oscar, ...
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Linander, Hampus ...
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Ohlsson, Fredrik
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Petersson, Chris ...
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Persson, Daniel, ...
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- About the subject
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Mathematics
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and Geometry
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Computer and Inf ...
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and Bioinformatics
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Mathematics
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and Probability Theo ...
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Mathematics
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and Mathematical Ana ...
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Computer and Inf ...
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and Computer Science ...
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- NATURAL SCIENCES
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NATURAL SCIENCES
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and Mathematics
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and Computational Ma ...
- Articles in the publication
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Artificial Intel ...
- By the university
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Chalmers University of Technology
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University of Gothenburg
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Umeå University