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Gradients for prod, cumsum, cumprod #524

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Gradients for prod, cumsum, cumprod #524

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75 changes: 68 additions & 7 deletions src/tracker/lib/array.jl
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Expand Up @@ -279,15 +279,76 @@ Base.sum(f::Union{Function,Type},xs::TrackedArray) = sum(f.(xs))
@grad sum(xs; dims = :) = sum(data(xs), dims = dims),
Δ -> (zero(xs) .+ Δ, )

Base.prod(xs::TrackedArray, dim) = track(prod, xs, dim)
Base.prod(xs::TrackedArray) = track(prod, xs)
Base.prod(xs::TrackedArray; dims=:) = track(prod, xs; dims=dims)
Base.prod(f::Union{Function, Type}, xs::TrackedArray) = prod(f.(xs))

@grad prod(xs) = prod(data(xs)), Δ -> (prod(xs) ./ xs .* Δ,)
@grad prod(xs, dim) = prod(data(xs), dims = dim),
Δ -> (nobacksies(:sum,
reshape(.*(circshift.([reshape(data(xs), length(xs))], 1:length(xs)-1)...), size(xs)) .* Δ),
nothing)
@grad prod(xs; dims=:) = _prod(xs.data, prod(xs.data, dims=dims), dims)
_prod(xd, p, ::Colon) = p, Δ -> (nobacksies(:prod, ∇prod(xd, p, data(Δ)) ),)
_prod(xd, p, dims) = count(iszero, p) == 0 ?
(p, Δ -> (nobacksies(:prod, p ./ xd .* data(Δ) ),)) :
(p, Δ -> (nobacksies(:prod, mapslices(∇prod, xd; dims=dims) .* data(Δ)),))

function ∇prod(x, p=prod(x), Δ=1)
numzero = count(iszero, x)
if numzero == 0
∇ = p ./ x .* Δ
elseif numzero > 1
∇ = zero(x)
else
∇ = ∇prod_one(x, Δ)
end
end
function ∇prod_one(x::Array, Δ)
zloc = findfirst(iszero, x)
∇ = copy(x)
∇[zloc] = 1
nonzero = prod(∇) * Δ
∇ .= 0
∇[zloc] = nonzero
∇
end
∇prod_one(x::AbstractArray, Δ) = ForwardDiff.gradient(y -> prod(y) * Δ, x)

Base.cumsum(xs::TrackedArray; dims=1) = track(cumsum, xs; dims=dims)

@grad cumsum(xs; dims=1) = _cumsum(xs.data, dims)
_cumsum(xd::Array, d) = cumsum(xd; dims=d), Δ -> (reverse(cumsum(reverse(Δ,dims=d),dims=d),dims=d),)
_cumsum(xd::AbstractArray, d) = cumsum(xd; dims=d), Δ -> (mapslices(reverse∘cumsum∘reverse,Δ, dims=d),)

Base.cumprod(xs::TrackedArray; dims=nothing) = track(cumprod, xs; dims=dims)

@grad cumprod(xs; dims=nothing) = _cumprod(xs.data, dims)
_cumprod(xd, ::Nothing, p = cumprod(xd)) = p, Δ -> (nobacksies(:cumprod, ∇cumprod(xd, p, data(Δ)) ),)
_cumprod(xd, d, p = cumprod(xd, dims=d)) = p, Δ -> (nobacksies(:cumprod, ∇cumprod_d(xd, Val(d), p, data(Δ)) ),)

function ∇cumprod(x::Vector, p, Δ)
len = length(x)
z = something(findfirst(iszero, x), len+1)
∇ = zero(x)
@inbounds for i=1:z-1
ixi = 1/x[i]
for k=i:z-1
∇[i] += p[k] * Δ[k] * ixi
end
end
@inbounds if z != len+1
pk = z==1 ? one(p[1]) : p[z-1] # will be prod(x[j] for j=1:k if j!=z)
∇[z] += pk * Δ[z]
for k=(z+1):len
pk *= x[k]
∇[z] += pk * Δ[k]
end
end
∇
end
∇cumprod(x::AbstractVector, p, Δ) = vec(Δ' * ForwardDiff.jacobian(cumprod, x))
@noinline function ∇cumprod_d(x::AbstractArray{T,N}, ::Val{d}, p, Δ) where {T,N,d}
∇ = similar(x)
for i in Iterators.product(ntuple(k -> k==d ? Ref(:) : axes(x,k), Val(N))...)
copyto!(view(∇,i...), ∇cumprod(x[i...], p[i...], Δ[i...]))
end
∇ # roughly mapslices(∇cumprod, x,p,Δ; dims=d) if that existed
end

Base.findfirst(xs::TrackedArray, args...) = findfirst(xs.data, args...)

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23 changes: 23 additions & 0 deletions test/tracker.jl
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Expand Up @@ -17,12 +17,35 @@ gradtest(f, dims...) = gradtest(f, rand.(Float64, dims)...)
@test gradtest((x, W, b) -> logσ.(W*x .+ b), (5,3), (2,5), 2)
@test gradtest((w, x) -> w'*x, randn(Float64,10, 2), randn(Float64,10))
@test gradtest((w, x) -> w*x', randn(Float64,5,5), randn(Float64,5,5))

@test gradtest(x -> sum(x, dims = (2, 3)), (3,4,5))
@test gradtest(x -> sum(x, dims = 1), randn(Float64,2,3))
@test gradtest(x -> sum(x, dims = [1,2]), randn(Float64,2,3))
@test gradtest(x -> sum(x), randn(Float64,2,3))

@test gradtest(x -> prod(x, dims=(2, 3)), (3,4,5))
@test gradtest(x -> prod(x, dims=1), (3,4,5))
@test gradtest(x -> prod(x, dims=1), (3,))
@test gradtest(x -> prod(x), (3,4,5))
@test gradtest(x -> prod(x), (3,))

rzero(dims...) = (x = rand(dims...); x[2]=0; x)
@test gradtest(x -> prod(x, dims=(2, 3)), rzero(3,4,5))
@test gradtest(x -> prod(x, dims=1), rzero(3,4,5))
@test gradtest(x -> prod(x, dims=1), rzero(3,))
@test gradtest(x -> prod(x), rzero(3,4,5))
@test gradtest(x -> prod(x), rzero(3,))

@test gradtest(x -> cumsum(x, dims=2), (3,4,5))
@test gradtest(x -> cumsum(x, dims=1), (3,))
@test gradtest(x -> cumsum(x), (3,))

@test gradtest(x -> cumprod(x, dims=2), (3,4,5))
@test gradtest(x -> cumprod(x, dims=1), (3,))
@test gradtest(x -> cumprod(x), (3,))
@test gradtest(x -> cumprod(x, dims=2), rzero(3,4,5))
@test gradtest(x -> cumprod(x, dims=1), rzero(3,))
@test gradtest(x -> cumprod(x), rzero(3,))

@test gradtest(x -> softmax(x).*(1:3), 3)
@test gradtest(x -> softmax(x).*(1:3), (3,5))
Expand Down