Contents
What is Equivariant neural network?
Equivariant Neural Network Definition. Given a group on a homogeneous space , a G-covariant neural network is linear map ψ : f ( X ) → f ′ ( X ) that has the property[KT18]: (13.5) If , the is a G-equivariant neural network. If g = g ′ = e , the identity, then is a G-invariant neural network.
What does permutation invariant mean?
A state of a collection of identical registers is said to be permutation invariant if it is unchanged under arbitrary permutations of the contents of the registers.
What is permutation invariance in deep learning?
A function f of a vector argument x=(x1,…, xn) is permutation invariant if the value of f do not change if we permute the components of x, that is, for instance, when n=3: f((x1,x2,x3))=f((x2,x1,x3))=f((x3,x1,x2)) and so on.
What is spherical CNN?
We propose a definition for the spherical cross-correlation that is both expressive and rotation-equivariant. The spherical correlation satisfies a generalized Fourier theorem, which allows us to compute it efficiently using a generalized (non-commutative) Fast Fourier Transform (FFT) algorithm.
What is CNN Equivariance?
Translational Equivariance or just equivariance is a very important property of the convolutional neural networks where the position of the object in the image should not be fixed in order for it to be detected by the CNN. This simply means that if the input changes, the output also changes.
How are feature maps in G-CNNs equivariant?
Depending on the specific implementation used, feature maps in G-CNNs are equivariant under newly imposed symmetry transformations. Specifically, they designed G-convolutions that were able to learn features that equivary under 90-degree rotations and mirror reflections besides being equivariant under shifts only.
Which is the best paper for equivariant neural network?
Paper list for equivariant neural network. Work-in-progress. Feel free to suggest relevant papers in the following format.
How to create an equivariant network in phase space?
Note: general framework for constructing equivariant normalizing flows on euclidean spaces. Instantiation for particle systems/point clouds = simultanoues SE (3) and permutation equivariance. Note: general framework for constructing equivariant normalizing flows in phase space utilizing Hamiltonian dynamics.
How are group convolutional networks equivariant under symmetry transformations?
Besides translations, G-CNNs exploit other realistic symmetries of the sampling lattice as well. The working horses are the group convolutions, or G-convolutions, that again increase the degree of weight sharing. Depending on the specific implementation used, feature maps in G-CNNs are equivariant under newly imposed symmetry transformations.