API reference

# SteerableConvolutions.SteerableConvolutions — Module.

Steerable convolutional layers.

Exports

The following symbols are exported by SteerableConvolutions:

• AbstractFiniteGroup

• AbstractGroup

• AbstractRepresentation

• CyclicGroup

• DihedralGroup

• Element

• FiberField

• GSpace

• Irrep

• IrrepType

• R2Conv

• Representation

• RotationGroup

• basis

• directsum

• elements

• frequencies

• istrivial

• regular_representation

• ⊕

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# SteerableConvolutions.AbstractFiniteGroup — Type.

abstract type AbstractFiniteGroup <: AbstractGroup

Abstract finite group.

Fields

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# SteerableConvolutions.AbstractGroup — Type.

abstract type AbstractGroup

Abstract group.

Fields

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# SteerableConvolutions.AbstractRepresentation — Type.

abstract type AbstractRepresentation

Abstract group representation.

A linear representation

$$\rho :G\to \mathrm{GL}({\mathbb{R}}^d)$$

maps group elements $g$ to invertible matrices $\rho (g)$ of size $d\times d$. The representation must be such that

$$\rho (gh)=\rho (g)\rho (h)\mathrm{\forall }(g,h)\in G^2.$$

Fields

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# SteerableConvolutions.CyclicGroup — Type.

struct CyclicGroup <: AbstractFiniteGroup

Cyclic group $C_N$ of order $N$.

Example

julia> G = CyclicGroup(8)
CyclicGroup(8)

julia> one(G)
CyclicGroup(8)(0)

julia> g, h = G(1), G(2)
(CyclicGroup(8)(1), CyclicGroup(8)(2))

julia> inv(g)
CyclicGroup(8)(7)

julia> g * h
CyclicGroup(8)(3)

Fields

• N: Number of rotations in the group.

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# SteerableConvolutions.DihedralGroup — Type.

struct DihedralGroup <: AbstractFiniteGroup

Dihedral group $D_N$.

Example

julia> G = DihedralGroup(8)
DihedralGroup(8)

julia> one(G)
DihedralGroup(8)(false, 0)

julia> g, h = G(false, 5), G(true, 3)
(DihedralGroup(8)(false, 5), DihedralGroup(8)(true, 3))

julia> inv(g)
DihedralGroup(8)(false, 3)

julia> g * h
DihedralGroup(8)(true, 0)

Fields

• N: Number of rotations in the group.

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# SteerableConvolutions.Element — Type.

struct Element{G, N}

Group element. Group elements can be multiplied with *. To build group elements, call group(n) instead of Element(group, n).

Fields

• group: Group to which the element belongs.

• n: Group element content.

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# SteerableConvolutions.FiberField — Type.

struct FiberField{F, R, A}

Fiber field.

Fields

• gspace: Field type.

• representation: Representation.

• x: Field content.

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# SteerableConvolutions.GSpace — Type.

struct GSpace{G}

GSpace.

Fields

• group: Group.

• dim: Dimension of base space.

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# SteerableConvolutions.Irrep — Type.

struct Irrep{G, F} <: AbstractRepresentation

Irreducible group representation ("irrep").

Fields

• group: Group.

• freq: Irrep frequency.

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# SteerableConvolutions.R2Conv — Type.

struct R2Conv{G, RI, RO, IW, IB, C} <: LuxCore.AbstractExplicitLayer

Steerable convolutional layer on ${\mathbb{R}}^2$.

Fields

• gspace

• ρ_in

• ρ_out

• c_in

• c_out

• init_weight

• init_bias

• conv

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# SteerableConvolutions.Representation — Type.

struct Representation{F, A} <: AbstractRepresentation

General group representation. It is stored as a direct sum of irreps with a change of basis matrix.

Fields

• frequencies: List of irrep frequencies by order of appearance in direct sum.

• basis: Change of basis matrix.

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# SteerableConvolutions.RotationGroup — Type.

struct RotationGroup <: AbstractGroup

Rotation group in the plane.

Fields

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# SteerableConvolutions.:⊕ — Function.

Alias for directsum.

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# SteerableConvolutions.basis — Function.

Get change of basis matrix for block-diagonal representation decomposition.

Methods

basis(ψ)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:98.

basis(ρ)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:101.

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# SteerableConvolutions.directsum — Function.

Direct sum of matrices or representations.

Methods

directsum(x)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:105.

directsum(r)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:116.

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# SteerableConvolutions.elements — Function.

Get elements of a finite group.

Methods

elements(group)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:225.

elements(group)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:284.

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# SteerableConvolutions.frequencies — Function.

Get irrep frequencies used to block-diagonalize a representation.

Methods

frequencies(ψ)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:97.

frequencies(ρ)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:100.

frequencies(group)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:247.

frequencies(group)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:301.

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# SteerableConvolutions.istrivial — Function.

istrivial(::Irrep)

Return true if the irrep is trivial.

Methods

istrivial(ψ)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:248.

istrivial(ψ)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:306.

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# SteerableConvolutions.regular_representation — Method.

regular_representation(
    group
) -> Representation{_A, Matrix{Float64}} where _A

Get the regular representation of a group.

Methods

regular_representation(group)

defined at /home/runner/work/SteerableConvolutions.jl/SteerableConvolutions.jl/src/group.jl:137.

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# SteerableConvolutions.IrrepType — Module.

Irrep type.

Exports

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