istraining() = false @adjoint istraining() = true, _ -> nothing _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 """ Dropout(p, dims = :) A Dropout layer. For each input, either sets that input to `0` (with probability `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). Does nothing to the input once in [`testmode!`](@ref). """ mutable struct Dropout{F,D} p::F dims::D end function Dropout(p; dims = :) @assert 0 ≤ p ≤ 1 Dropout{typeof(p),typeof(dims)}(p, dims) end (a::Dropout)(x) = dropout(x, a.p; dims = a.dims) 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) 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} p::F function AlphaDropout(p) @assert 0 ≤ p ≤ 1 new{typeof(p)}(p) end end alphadropout(x, p) = x _alphadropout_kernel(x, noise, p, α1) = noise > (1 - p) ? x : α1 @adjoint function alphadropout(x, p) λ = eltype(x)(1.0507009873554804934193349852946) α = eltype(x)(1.6732632423543772848170429916717) α1 = eltype(x)(-λ*α) noise = randn(eltype(x), size(x)) 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 (a::AlphaDropout)(x) = alphadropout(x, a.p) """ LayerNorm(h::Integer) 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)) @treelike LayerNorm (a::LayerNorm)(x) = a.diag(normalise(x)) function Base.show(io::IO, l::LayerNorm) print(io, "LayerNorm(", length(l.diag.α), ")") end """ BatchNorm(channels::Integer, σ = identity; initβ = zeros, initγ = ones, ϵ = 1e-8, momentum = .1) Batch 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.) `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). See [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://arxiv.org/pdf/1502.03167.pdf). Example: ```julia m = Chain( Dense(28^2, 64), BatchNorm(64, relu), Dense(64, 10), BatchNorm(10), softmax) ``` """ 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 BatchNorm(chs::Integer, λ = identity; initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i), ϵ = 1f-5, momentum = 0.1f0) = BatchNorm(λ, initβ(chs), initγ(chs), zeros(chs), ones(chs), ϵ, momentum) function (BN::BatchNorm)(x) size(x, ndims(x)-1) == length(BN.β) || error("BatchNorm expected $(length(BN.β)) channels, got $(size(x, ndims(x)-1))") dims = length(size(x)) channels = size(x, dims-1) affine_shape = ntuple(i->i == ndims(x) - 1 ? size(x, i) : 1, ndims(x)) m = div(prod(size(x)), channels) γ = reshape(BN.γ, affine_shape...) β = reshape(BN.β, affine_shape...) if !istraining() μ = reshape(BN.μ, affine_shape...) σ² = reshape(BN.σ², affine_shape...) ϵ = BN.ϵ else T = eltype(x) axes = [1:dims-2; dims] # axes to reduce along (all but channels axis) μ = mean(x, dims = axes) σ² = sum((x .- μ) .^ 2, dims = axes) ./ m ϵ = convert(T, BN.ϵ) # update moving mean/std mtm = BN.momentum S = eltype(BN.μ) BN.μ = (1 - mtm) .* BN.μ .+ mtm .* S.(reshape(μ, :)) BN.σ² = (1 - mtm) .* BN.σ² .+ (mtm * m / (m - 1)) .* S.(reshape(σ², :)) end let λ = BN.λ x̂ = (x .- μ) ./ sqrt.(σ² .+ ϵ) λ.(γ .* x̂ .+ β) end end children(BN::BatchNorm) = (BN.λ, BN.β, BN.γ, BN.μ, BN.σ², BN.ϵ, BN.momentum) mapchildren(f, BN::BatchNorm) = # e.g. mapchildren(cu, BN) BatchNorm(BN.λ, f(BN.β), f(BN.γ), f(BN.μ), f(BN.σ²), BN.ϵ, BN.momentum) function Base.show(io::IO, l::BatchNorm) print(io, "BatchNorm($(join(size(l.β), ", "))") (l.λ == identity) || print(io, ", λ = $(l.λ)") print(io, ")") end """ 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...) 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) = InstanceNorm(λ, initβ(chs), initγ(chs), zeros(chs), ones(chs), ϵ, momentum) function (in::InstanceNorm)(x) size(x, ndims(x)-1) == length(in.β) || error("InstanceNorm expected $(length(in.β)) channels, got $(size(x, ndims(x)-1))") ndims(x) > 2 || error("InstanceNorm requires at least 3 dimensions. With 2 dimensions an array of zeros would be returned") # these are repeated later on depending on the batch size dims = length(size(x)) c = size(x, dims-1) bs = size(x, dims) affine_shape = ntuple(i->i == ndims(x) - 1 || i == ndims(x) ? size(x, i) : 1, ndims(x)) m = div(prod(size(x)), c*bs) γ, β = expand_inst(in.γ, affine_shape), expand_inst(in.β, affine_shape) if !istraining() μ = expand_inst(in.μ, affine_shape) σ² = expand_inst(in.σ², affine_shape) ϵ = in.ϵ else T = eltype(x) ϵ = convert(T, in.ϵ) axes = 1:dims-2 # axes to reduce along (all but channels and batch size axes) μ = mean(x, dims = axes) σ² = mean((x .- μ) .^ 2, dims = axes) S = eltype(in.μ) # update moving mean/std mtm = in.momentum in.μ = dropdims(mean(repeat((1 - mtm) .* in.μ, outer=[1, bs]) .+ mtm .* S.(reshape(μ, (c, bs))), dims = 2), dims=2) in.σ² = dropdims(mean((repeat((1 - mtm) .* in.σ², outer=[1, bs]) .+ (mtm * m / (m - 1)) .* S.(reshape(σ², (c, bs)))), dims = 2), dims=2) end let λ = in.λ x̂ = (x .- μ) ./ sqrt.(σ² .+ ϵ) λ.(γ .* x̂ .+ β) end end children(in::InstanceNorm) = (in.λ, in.β, in.γ, in.μ, in.σ², in.ϵ, in.momentum) mapchildren(f, in::InstanceNorm) = # e.g. mapchildren(cu, in) InstanceNorm(in.λ, f(in.β), f(in.γ), f(in.μ), f(in.σ²), in.ϵ, in.momentum) function Base.show(io::IO, l::InstanceNorm) print(io, "InstanceNorm($(join(size(l.β), ", "))") (l.λ == identity) || print(io, ", λ = $(l.λ)") print(io, ")") end """ Group Normalization. This layer can outperform Batch-Normalization and Instance-Normalization. GroupNorm(chs::Integer, G::Integer, λ = identity; initβ = (i) -> zeros(Float32, i), initγ = (i) -> ones(Float32, i), ϵ = 1f-5, momentum = 0.1f0) ``chs`` is the number of channels, the channel dimension of your input. 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. The number of channels must be an integer multiple of the number of groups. Example: ``` m = Chain(Conv((3,3), 1=>32, leakyrelu;pad = 1), GroupNorm(32,16)) # 32 channels, 16 groups (G = 16), thus 2 channels per group used ``` 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) = GroupNorm(G, λ, initβ(chs), initγ(chs), zeros(G,1), ones(G,1), ϵ, momentum) 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 ($(size(x,ndims(x) -1)))") dims = length(size(x)) groups = gn.G channels = size(x, dims-1) batches = size(x,dims) channels_per_group = div(channels,groups) affine_shape = ntuple(i->i == ndims(x) - 1 ? size(x, i) : 1, ndims(x)) # Output reshaped to (W,H...,C/G,G,N) μ_affine_shape = ntuple(i->i == ndims(x) ? groups : 1, ndims(x) + 1) m = prod(size(x)[1:end-2]) * channels_per_group γ = reshape(gn.γ, affine_shape...) β = reshape(gn.β, affine_shape...) y = reshape(x,((size(x))[1:end-2]...,channels_per_group,groups,batches)) if !istraining() og_shape = size(x) μ = reshape(gn.μ, μ_affine_shape...) # Shape : (1,1,...C/G,G,1) σ² = reshape(gn.σ², μ_affine_shape...) # Shape : (1,1,...C/G,G,1) ϵ = gn.ϵ else T = eltype(x) og_shape = size(x) axes = [(1:ndims(y)-2)...] # axes to reduce along (all but channels axis) μ = mean(y, dims = axes) σ² = mean((y .- μ) .^ 2, dims = axes) ϵ = convert(T, gn.ϵ) # update moving mean/std mtm = gn.momentum S = eltype(gn.μ) gn.μ = mean((1 - mtm) .* gn.μ .+ mtm .* S.(reshape(μ, (groups,batches))),dims=2) gn.σ² = mean((1 - mtm) .* gn.σ² .+ (mtm * m / (m - 1)) .* S.(reshape(σ², (groups,batches))),dims=2) end let λ = gn.λ x̂ = (y .- μ) ./ sqrt.(σ² .+ ϵ) # Reshape x̂ x̂ = reshape(x̂,og_shape) λ.(γ .* x̂ .+ β) end end children(gn::GroupNorm) = (gn.λ, gn.β, gn.γ, gn.μ, gn.σ², gn.ϵ, gn.momentum) mapchildren(f, gn::GroupNorm) = # e.g. mapchildren(cu, BN) GroupNorm(gn.G,gn.λ, f(gn.β), f(gn.γ), f(gn.μ), f(gn.σ²), gn.ϵ, gn.momentum) function Base.show(io::IO, l::GroupNorm) print(io, "GroupNorm($(join(size(l.β), ", "))") (l.λ == identity) || print(io, ", λ = $(l.λ)") print(io, ")") end