SwePub
Sök i LIBRIS databas

  Extended search

id:"swepub:oai:research.chalmers.se:95ed9969-976e-43a3-9b2e-eb68080b8434"
 

Search: id:"swepub:oai:research.chalmers.se:95ed9969-976e-43a3-9b2e-eb68080b8434" > Geometric deep lear...

  • 1 of 1
  • Previous record
  • Next record
  •    To hitlist

Geometric deep learning and equivariant neural networks

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
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
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
show more...
Linander, Hampus, 1985 (author)
Gothenburg University,Göteborgs universitet,Institutionen för fysik (GU),Department of Physics (GU),Department of Physics, Gothenburg University, Gothenburg, Sweden
Ohlsson, Fredrik (author)
Umeå universitet,Institutionen för matematik och matematisk statistik
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
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
show less...
 (creator_code:org_t)
Springer Nature, 2023
2023
English.
In: Artificial Intelligence Review. - : Springer Nature. - 1573-7462 .- 0269-2821. ; 56:12, s. 14605-14662
  • Journal article (peer-reviewed)
Abstract Subject headings
Close  
  • 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)

Find in a library

To the university's database

  • 1 of 1
  • Previous record
  • Next record
  •    To hitlist

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.

 
pil uppåt Close

Copy and save the link in order to return to this view