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Concept

Équivariance

Publications associées (8)

Leveraging topology, geometry, and symmetries for efficient Machine Learning

Michaël Defferrard

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

EPFL2022

Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties

Michele Ceriotti, Michael John Willatt, Jigyasa Nigam

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most ...

AIP Publishing2022

A Shadow Perspective on Equivariant Hochschild Homologies

Kathryn Hess Bellwald

Shadows for bicategories, defined by Ponto, provide a useful framework that generalizes classical and topological Hochschild homology. In this paper, we define Hochschild-type invariants for monoids in a symmetric monoidal, simplicial model category V, as ...

OXFORD UNIV PRESS2022

A General Theory of Equivariant CNNs on Homogeneous Spaces

Mario Geiger

We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks represent fields on a homogeneous base space, and layers are equivariant ma ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data

Mario Geiger

We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equiva ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Equivariant K-theory of GKM bundles

Silvia Sabatini

Given a fiber bundle of GKM spaces, pi: M -> B, we analyze the structure of the equivariant K-ring of M as a module over the equivariant K-ring of B by translating the fiber bundle, pi, into a fiber bundle of GKM graphs and constructing, by combinatorial t ...

Springer Netherlands2013

Multiplicative structure in equivariant cohomology

Kathryn Hess Bellwald

We introduce the notion of a strongly homotopy-comultiplicative resolution of a module coalgebra over a chain Hopf algebra, which we apply to proving a comultiplicative enrichment of a well-known theorem of Moore concerning the homology of quotient spaces ...

Elsevier2012

The group of unimodular automorphisms of a principal bundle and the Euler-Yang-Mills equations

Given a principal bundle G hooked right arrow P -> B (each being compact, connected and oriented) and a G-invariant metric h(P) on P which induces a volume form mu(P), we consider the group of all unimodular automorphisms SAut(P, mu(P)) := {phi is an eleme ...

2010

Publications associées (8)