Equivariant holomorphic maps into the Siegel disc and the metaplectic representation [PDF]
, 1997 Jean-Louis Clerc
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Equivariant neural networks and piecewise linear representation theory [PDF]
arXivEquivariant neural networks are neural networks with symmetry. Motivated by the theory of group representations, we decompose the layers of an equivariant neural network into simple representations. The nonlinear activation functions lead to interesting nonlinear equivariant maps between simple representations.
arxiv
$Sp(n)$-equivariant harmonic maps between complex projective spaces [PDF]
, 1996 Toshimasa Kobayashi
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Spaces of Maps into Classifying Spaces for Equivariant Crossed Complexes, II: The General Topological Group Case [PDF]
, 2001 Ronald Brown +3 more
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Decomposition of Equivariant Maps via Invariant Maps: Application to Universal Approximation under Symmetry [PDF]
Transactions on Machine Learning Research, 2024In this paper, we develop a theory about the relationship between invariant and equivariant maps with regard to a group $G$. We then leverage this theory in the context of deep neural networks with group symmetries in order to obtain novel insight into their mechanisms. More precisely, we establish a one-to-one relationship between equivariant maps and
arxiv
The Kernel of the Equivariant Kirwan Map and the Residue Formula [PDF]
, 2003 Lisa C. Jeffrey
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Note on equivariant maps from spheres to Stiefel manifolds
, 1974 Toshio Yoshida
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Central extensions, classical non-equivariant maps and residual symmetries [PDF]
, 2004 Francesco Toppan
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Equivariant Surgery Theory: Construction of Equivariant Normal Maps
Publications of the Research Institute for Mathematical Sciences, 1995 This procedure is one of the important ideas of equivariant surgery theory, and has enabled us to construct various exotic actions (see e.g. [BMol-2], [LaMo], [LaMoPa], [Mo 1-3], [MoU], [Pel-3], [PeR]). A method for (Step I) was presented by T. Petrie in [Pel-3], which we call the equivariant transversality construction.
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A topological model for partial equivariance in deep learning and data analysis. [PDF]
Front Artif Intell, 2023 Ferrari L +3 more
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