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Equivariant map
About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.
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TL;DR: It is concluded that although the free parameters of the invariant/equivarint models are exponentially fewer than the one of the usual models, the invarian/equivariant models can approximate the invariants/Equivariant functions to arbitrary accuracy.
Abstract: In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$. Especially, for a given $G$-invariant/equivariant function, we construct its universal approximator by deep neural network whose layers equip $G$-actions and each affine transformations are $G$-equivariant/invariant. Due to representation theory, we can show that this approximator has exponentially fewer free parameters than usual models.
53 citations
TL;DR: In this paper, an affine equivariant estimator of multivariate location was proposed, which combines a high breakdown point and a bounded influence function with high asymptotic efficiency.
Abstract: We propose an affine equivariant estimator of multivariate location that combines a high breakdown point and a bounded influence function with high asymptotic efficiency. This proposal is basically a location $M$-estimator based on the observations obtained after scaling with an affine equivariant high breakdown covariance estimator. The resulting location estimator will inherit the breakdown point of the initial covariance estimator and within the location-covariance model only the $M$-estimator will determine the type of influence function and the asymptotic behaviour. We prove consistency and asymptotic normality and obtain the breakdown point and the influence function.
53 citations
TL;DR: In this paper, a class of helical geodesic equivariant immersions of orderd(⩾3), which are neither Kaehler nor totally real, are constructed in complex projective spaces.
Abstract: This paper consists of two parts. One is to construct a class of helical geodesic equivariant immersions of orderd(⩾3), which are neither Kaehler nor totally real immersions, into complex projective spaces. The other is to show the basic results about a helix in complex space forms.
52 citations
TL;DR: In this article, a categorization of the Chern character is proposed, which refines earlier work of Toen and Vezzosi and of Ganter and Kapranov, and shows that the secondary Chern character factors through secondary K-theory.
52 citations