Flux.jl/src/layers/normalise.jl

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istraining() = false
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@adjoint istraining() = true, _ -> nothing
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_dropout_shape(s, ::Colon) = size(s)
_dropout_shape(s, dims) = tuple((i dims ? 1 : si for (i, si) enumerate(size(s)))...)
_dropout_kernel(y::T, p, q) where {T} = y > p ? T(1 / q) : T(0)
dropout(x, p; dims = :) = x
@adjoint function dropout(x, p; dims = :)
y = rand!(similar(x, _dropout_shape(x, dims)))
y .= _dropout_kernel.(y, p, 1 - p)
return x .* y, Δ -> (Δ .* y, nothing)
end
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"""
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Dropout(p, dims = :)
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A Dropout layer. For each input, either sets that input to `0` (with probability
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`p`) or scales it by `1/(1-p)`. The `dims` argument is to specified the unbroadcasted
dimensions, i.e. `dims=1` does dropout along columns and `dims=2` along rows. This is
used as a regularisation, i.e. it reduces overfitting during training. see also [`dropout`](@ref).
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Does nothing to the input once in [`testmode!`](@ref).
"""
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mutable struct Dropout{F,D}
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p::F
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dims::D
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end
function Dropout(p; dims = :)
@assert 0 p 1
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Dropout{typeof(p),typeof(dims)}(p, dims)
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end
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(a::Dropout)(x) = dropout(x, a.p; dims = a.dims)
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function Base.show(io::IO, d::Dropout)
print(io, "Dropout(", d.p)
d.dims != (:) && print(io, ", dims = $(repr(d.dims))")
print(io, ")")
end
"""
AlphaDropout(p)
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A dropout layer. It is used in Self-Normalizing Neural Networks.
(https://papers.nips.cc/paper/6698-self-normalizing-neural-networks.pdf)
The AlphaDropout layer ensures that mean and variance of activations remains the same as before.
"""
mutable struct AlphaDropout{F}
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p::F
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function AlphaDropout(p)
@assert 0 p 1
new{typeof(p)}(p)
end
end
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alphadropout(x, p) = x
_alphadropout_kernel(x, noise, p, α1) = noise > (1 - p) ? x : α1
@adjoint function alphadropout(x, p)
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λ = eltype(x)(1.0507009873554804934193349852946)
α = eltype(x)(1.6732632423543772848170429916717)
α1 = eltype(x)(-λ*α)
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noise = randn(eltype(x), size(x))
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x .= _alphadropout_kernel.(x, noise, p, α1)
A = (p + p * (1 - p) * α1 ^ 2) ^ 0.5
B = -A * α1 * (1 - p)
x = @. A * x + B
return x, Δ -> (Δ .* A.* noise, nothing)
end
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(a::AlphaDropout)(x) = alphadropout(x, a.p)
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"""
LayerNorm(h::Integer)
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A [normalisation layer](https://arxiv.org/pdf/1607.06450.pdf) designed to be
used with recurrent hidden states of size `h`. Normalises the mean/stddev of
each input before applying a per-neuron gain/bias.
"""
struct LayerNorm{T}
diag::Diagonal{T}
end
LayerNorm(h::Integer) =
LayerNorm(Diagonal(h))
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@treelike LayerNorm
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(a::LayerNorm)(x) = a.diag(normalise(x))
function Base.show(io::IO, l::LayerNorm)
print(io, "LayerNorm(", length(l.diag.α), ")")
end
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"""
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BatchNorm(channels::Integer, σ = identity;
initβ = zeros, initγ = ones,
ϵ = 1e-8, momentum = .1)
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Batch Normalization layer. The `channels` input should be the size of the
channel dimension in your data (see below).
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Given an array with `N` dimensions, call the `N-1`th the channel dimension. (For
a batch of feature vectors this is just the data dimension, for `WHCN` images
it's the usual channel dimension.)
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`BatchNorm` computes the mean and variance for each each `W×H×1×N` slice and
shifts them to have a new mean and variance (corresponding to the learnable,
per-channel `bias` and `scale` parameters).
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See [Batch Normalization: Accelerating Deep Network Training by Reducing
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Internal Covariate Shift](https://arxiv.org/pdf/1502.03167.pdf).
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Example:
```julia
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m = Chain(
Dense(28^2, 64),
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BatchNorm(64, relu),
Dense(64, 10),
BatchNorm(10),
softmax)
```
"""
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mutable struct BatchNorm{F,V,W,N}
λ::F # activation function
β::V # bias
γ::V # scale
μ::W # moving mean
σ²::W # moving std
ϵ::N
momentum::N
end
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BatchNorm(chs::Integer, λ = identity;
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initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i), ϵ = 1f-5, momentum = 0.1f0) =
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BatchNorm(λ, initβ(chs), initγ(chs),
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zeros(chs), ones(chs), ϵ, momentum)
function (BN::BatchNorm)(x)
size(x, ndims(x)-1) == length(BN.β) ||
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error("BatchNorm expected $(length(BN.β)) channels, got $(size(x, ndims(x)-1))")
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dims = length(size(x))
channels = size(x, dims-1)
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affine_shape = ntuple(i->i == ndims(x) - 1 ? size(x, i) : 1, ndims(x))
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m = div(prod(size(x)), channels)
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γ = reshape(BN.γ, affine_shape...)
β = reshape(BN.β, affine_shape...)
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if !istraining()
μ = reshape(BN.μ, affine_shape...)
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σ² = reshape(BN.σ², affine_shape...)
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ϵ = BN.ϵ
else
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T = eltype(x)
axes = [1:dims-2; dims] # axes to reduce along (all but channels axis)
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μ = mean(x, dims = axes)
σ² = sum((x .- μ) .^ 2, dims = axes) ./ m
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ϵ = convert(T, BN.ϵ)
# update moving mean/std
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mtm = BN.momentum
S = eltype(BN.μ)
BN.μ = (1 - mtm) .* BN.μ .+ mtm .* S.(reshape(μ, :))
BN.σ² = (1 - mtm) .* BN.σ² .+ (mtm * m / (m - 1)) .* S.(reshape(σ², :))
end
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let λ = BN.λ
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= (x .- μ) ./ sqrt.(σ² .+ ϵ)
λ.(γ .* .+ β)
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end
end
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children(BN::BatchNorm) =
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(BN.λ, BN.β, BN.γ, BN.μ, BN.σ², BN.ϵ, BN.momentum)
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mapchildren(f, BN::BatchNorm) = # e.g. mapchildren(cu, BN)
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BatchNorm(BN.λ, f(BN.β), f(BN.γ), f(BN.μ), f(BN.σ²), BN.ϵ, BN.momentum)
function Base.show(io::IO, l::BatchNorm)
print(io, "BatchNorm($(join(size(l.β), ", "))")
(l.λ == identity) || print(io, ", λ = $(l.λ)")
print(io, ")")
end
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"""
InstanceNorm(channels::Integer, σ = identity;
initβ = zeros, initγ = ones,
ϵ = 1e-8, momentum = .1)
Instance Normalization layer. The `channels` input should be the size of the
channel dimension in your data (see below).
Given an array with `N` dimensions, call the `N-1`th the channel dimension. (For
a batch of feature vectors this is just the data dimension, for `WHCN` images
it's the usual channel dimension.)
`InstanceNorm` computes the mean and variance for each each `W×H×1×1` slice and
shifts them to have a new mean and variance (corresponding to the learnable,
per-channel `bias` and `scale` parameters).
See [Instance Normalization: The Missing Ingredient for Fast Stylization](https://arxiv.org/abs/1607.08022).
Example:
```julia
m = Chain(
Dense(28^2, 64),
InstanceNorm(64, relu),
Dense(64, 10),
InstanceNorm(10),
softmax)
```
"""
expand_inst = (x, as) -> reshape(repeat(x, outer=[1, as[length(as)]]), as...)
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mutable struct InstanceNorm{F,V,W,N}
λ::F # activation function
β::V # bias
γ::V # scale
μ::W # moving mean
σ²::W # moving std
ϵ::N
momentum::N
end
InstanceNorm(chs::Integer, λ = identity;
initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i), ϵ = 1f-5, momentum = 0.1f0) =
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InstanceNorm(λ, initβ(chs), initγ(chs),
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zeros(chs), ones(chs), ϵ, momentum)
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function (in::InstanceNorm)(x)
size(x, ndims(x)-1) == length(in.β) ||
error("InstanceNorm expected $(length(in.β)) channels, got $(size(x, ndims(x)-1))")
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ndims(x) > 2 ||
error("InstanceNorm requires at least 3 dimensions. With 2 dimensions an array of zeros would be returned")
# these are repeated later on depending on the batch size
dims = length(size(x))
c = size(x, dims-1)
bs = size(x, dims)
affine_shape = ntuple(i->i == ndims(x) - 1 || i == ndims(x) ? size(x, i) : 1, ndims(x))
m = div(prod(size(x)), c*bs)
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γ, β = expand_inst(in.γ, affine_shape), expand_inst(in.β, affine_shape)
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if !istraining()
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μ = expand_inst(in.μ, affine_shape)
σ² = expand_inst(in.σ², affine_shape)
ϵ = in.ϵ
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else
T = eltype(x)
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ϵ = convert(T, in.ϵ)
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axes = 1:dims-2 # axes to reduce along (all but channels and batch size axes)
μ = mean(x, dims = axes)
σ² = mean((x .- μ) .^ 2, dims = axes)
S = eltype(in.μ)
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# update moving mean/std
mtm = in.momentum
in.μ = dropdims(mean(repeat((1 - mtm) .* in.μ, outer=[1, bs]) .+ mtm .* S.(reshape(μ, (c, bs))), dims = 2), dims=2)
in.σ² = dropdims(mean((repeat((1 - mtm) .* in.σ², outer=[1, bs]) .+ (mtm * m / (m - 1)) .* S.(reshape(σ², (c, bs)))), dims = 2), dims=2)
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end
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let λ = in.λ
= (x .- μ) ./ sqrt.(σ² .+ ϵ)
λ.(γ .* .+ β)
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end
end
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children(in::InstanceNorm) =
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(in.λ, in.β, in.γ, in.μ, in.σ², in.ϵ, in.momentum)
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mapchildren(f, in::InstanceNorm) = # e.g. mapchildren(cu, in)
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InstanceNorm(in.λ, f(in.β), f(in.γ), f(in.μ), f(in.σ²), in.ϵ, in.momentum)
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function Base.show(io::IO, l::InstanceNorm)
print(io, "InstanceNorm($(join(size(l.β), ", "))")
(l.λ == identity) || print(io, ", λ = $(l.λ)")
print(io, ")")
end
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"""
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Group Normalization.
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This layer can outperform Batch-Normalization and Instance-Normalization.
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GroupNorm(chs::Integer, G::Integer, λ = identity;
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initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i),
ϵ = 1f-5, momentum = 0.1f0)
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``chs`` is the number of channels, the channel dimension of your input.
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For an array of N dimensions, the (N-1)th index is the channel dimension.
``G`` is the number of groups along which the statistics would be computed.
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The number of channels must be an integer multiple of the number of groups.
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Example:
```
m = Chain(Conv((3,3), 1=>32, leakyrelu;pad = 1),
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GroupNorm(32,16)) # 32 channels, 16 groups (G = 16), thus 2 channels per group used
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```
Link : https://arxiv.org/pdf/1803.08494.pdf
"""
mutable struct GroupNorm{F,V,W,N,T}
G::T # number of groups
λ::F # activation function
β::V # bias
γ::V # scale
μ::W # moving mean
σ²::W # moving std
ϵ::N
momentum::N
end
GroupNorm(chs::Integer, G::Integer, λ = identity;
initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i), ϵ = 1f-5, momentum = 0.1f0) =
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GroupNorm(G, λ, initβ(chs), initγ(chs),
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zeros(G,1), ones(G,1), ϵ, momentum)
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function(gn::GroupNorm)(x)
size(x,ndims(x)-1) == length(gn.β) || error("Group Norm expected $(length(gn.β)) channels, but got $(size(x,ndims(x)-1)) channels")
ndims(x) > 2 || error("Need to pass at least 3 channels for Group Norm to work")
(size(x,ndims(x) -1))%gn.G == 0 || error("The number of groups ($(gn.G)) must divide the number of channels ($(size(x,ndims(x) -1)))")
dims = length(size(x))
groups = gn.G
channels = size(x, dims-1)
batches = size(x,dims)
channels_per_group = div(channels,groups)
affine_shape = ntuple(i->i == ndims(x) - 1 ? size(x, i) : 1, ndims(x))
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# Output reshaped to (W,H...,C/G,G,N)
μ_affine_shape = ntuple(i->i == ndims(x) ? groups : 1, ndims(x) + 1)
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m = prod(size(x)[1:end-2]) * channels_per_group
γ = reshape(gn.γ, affine_shape...)
β = reshape(gn.β, affine_shape...)
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y = reshape(x,((size(x))[1:end-2]...,channels_per_group,groups,batches))
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if !istraining()
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og_shape = size(x)
μ = reshape(gn.μ, μ_affine_shape...) # Shape : (1,1,...C/G,G,1)
σ² = reshape(gn.σ², μ_affine_shape...) # Shape : (1,1,...C/G,G,1)
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ϵ = gn.ϵ
else
T = eltype(x)
og_shape = size(x)
axes = [(1:ndims(y)-2)...] # axes to reduce along (all but channels axis)
μ = mean(y, dims = axes)
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σ² = mean((y .- μ) .^ 2, dims = axes)
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ϵ = convert(T, gn.ϵ)
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# update moving mean/std
mtm = gn.momentum
S = eltype(gn.μ)
gn.μ = mean((1 - mtm) .* gn.μ .+ mtm .* S.(reshape(μ, (groups,batches))),dims=2)
gn.σ² = mean((1 - mtm) .* gn.σ² .+ (mtm * m / (m - 1)) .* S.(reshape(σ², (groups,batches))),dims=2)
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end
let λ = gn.λ
= (y .- μ) ./ sqrt.(σ² .+ ϵ)
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# Reshape x̂
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= reshape(,og_shape)
λ.(γ .* .+ β)
end
end
children(gn::GroupNorm) =
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(gn.λ, gn.β, gn.γ, gn.μ, gn.σ², gn.ϵ, gn.momentum)
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mapchildren(f, gn::GroupNorm) = # e.g. mapchildren(cu, BN)
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GroupNorm(gn.G,gn.λ, f(gn.β), f(gn.γ), f(gn.μ), f(gn.σ²), gn.ϵ, gn.momentum)
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function Base.show(io::IO, l::GroupNorm)
print(io, "GroupNorm($(join(size(l.β), ", "))")
(l.λ == identity) || print(io, ", λ = $(l.λ)")
print(io, ")")
end