scatter rrules

fix tests fix test case add test cases for scatter fix rrule for scatter! fix ∇scatter_src! for max/min simplify pullback function name fix bug unify interfaces
FluxML · Apr 8, 2021 · a4e9f88 · a4e9f88
1 parent 6905ca7
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diff --git a/src/scatter.jl b/src/scatter.jl
@@ -145,3 +145,93 @@ function scatter(op::typeof(mean),
     fill!(dst, Base.reduce_empty(+, FT))
     scatter!(op, dst, src, idx)
 end
+
+## Gradients
+
+opname(::typeof(+)) = :add
+opname(::typeof(-)) = :sub
+opname(::typeof(*)) = :mul
+opname(::typeof(/)) = :div
+
+
+∇scatter_dst!(op, Δ, dst, y) = Δ
+
+function ∇scatter_dst!(op::Union{typeof(max),typeof(min)}, Δ, dst, y)
+    mask_y = (dst .== op.(dst, y))
+    mask_y .* Δ
+end
+
+modify_src(::typeof(+), X) = X
+modify_src(::typeof(-), X) = -X
+modify_src(::typeof(*), X, Y) = X
+modify_src(::typeof(/), X, Y) = -X ./ Y.^2
+
+∇src_init!(Δ, idx) = gather(Δ, idx)
+∇src_init!(Δ, dst, idx) = gather(dst, idx) .* ∇src_init!(Δ, idx)
+∇src_init(Δ, idx) = gather(Δ, idx)
+
+∇scatter_src!(op::Union{typeof(+),typeof(-)}, Δ, dst, src, idx) = modify_src(op, ∇src_init!(Δ, idx))
+∇scatter_src(op::Union{typeof(+),typeof(-)}, Δ, dst, src, idx) = modify_src(op, ∇src_init(Δ, idx))
+
+function ∇scatter_src!(op::Union{typeof(*),typeof(/)}, Δ, dst,
+                       src::AbstractArray{Tsrc,Nsrc}, 
+                       idx::AbstractArray{Tidx,Nidx}) where {Tsrc,Tidx,Nsrc,Nidx}
+    dims = Nsrc - Nidx
+    Δsrc = modify_src(op, ∇src_init!(Δ, dst, idx), src)
+    rev_idx = reverse_indices(idx)
+    for k = CartesianIndices(idx)
+        inds = filter(x -> x != k, rev_idx[idx[k]])
+        for i = CartesianIndices(axes(src)[1:dims])
+            Δsrc[i, k] *= prod(j -> src[i, j], inds)
+        end
+    end
+    Δsrc
+end
+
+function ∇scatter_src(op::Union{typeof(*),typeof(/)}, Δ, dst,
+                      src::AbstractArray{Tsrc,Nsrc}, 
+                      idx::AbstractArray{Tidx,Nidx}) where {Tsrc,Tidx,Nsrc,Nidx}
+    dims = Nsrc - Nidx
+    Δsrc = modify_src(op, ∇src_init(Δ, idx), src)
+    rev_idx = reverse_indices(idx)
+    for k = CartesianIndices(idx)
+        inds = filter(x -> x != k, rev_idx[idx[k]])
+        for i = CartesianIndices(axes(src)[1:dims])
+            Δsrc[i, k] = op(Δsrc[i, k], prod(j -> src[i, j], inds))
+        end
+    end
+    Δsrc
+end
+
+∇scatter_src!(op::Union{typeof(max),typeof(min)}, Δ, dst, src, idx) = (src .== op.(src, gather(dst, idx))) .* ∇src_init!(Δ, idx)
+∇scatter_src(op::Union{typeof(max),typeof(min)}, Δ, dst, src, idx) = (src .== op.(src, gather(dst, idx))) .* ∇src_init(Δ, idx)
+
+∇scatter_src!(::typeof(mean), Δ, idx, dims) = divide_by_counts!(∇src_init!(Δ, idx), idx, dims)
+∇scatter_src(::typeof(mean), Δ, idx, dims) = divide_by_counts!(∇src_init(Δ, idx), idx, dims)
+
+
+function rrule(::typeof(scatter!), op, dst::AbstractArray, src::AbstractArray, idx::AbstractArray, dims)
+    y = scatter!(op, copy(dst), src, idx, dims)
+    scatter!_pullback(Δ) = (NO_FIELDS, NO_FIELDS, ∇scatter_dst!(op, Δ, dst, y), ∇scatter_src!(op, Δ, dst, src, idx), DoesNotExist(), DoesNotExist())
+    y, scatter!_pullback
+end
+
+function rrule(::typeof(scatter), op, src::AbstractArray, idx::AbstractArray)
+    y = scatter(op, src, idx)
+    scatter_pullback(Δ) = (NO_FIELDS, NO_FIELDS, ∇scatter_src(op, Δ, y, src, idx), DoesNotExist())
+    y, scatter_pullback
+end
+
+function rrule(::typeof(scatter!), op::typeof(mean), dst::AbstractArray, src::AbstractArray{Tsrc,Nsrc}, idx::AbstractArray{Tidx,Nidx}) where {Tsrc,Tidx,Nsrc,Nidx}
+    dims = Nsrc - Nidx
+    y = scatter!(op, copy(dst), src, idx)
+    scatter!_pullback(Δ) = (NO_FIELDS, NO_FIELDS, ∇scatter_dst!(op, Δ, dst, y), ∇scatter_src!(op, Δ, idx, dims), DoesNotExist())
+    y, scatter!_pullback
+end
+
+function rrule(::typeof(scatter), op::typeof(mean), src::AbstractArray{Tsrc,Nsrc}, idx::AbstractArray{Tidx,Nidx}) where {Tsrc,Tidx,Nsrc,Nidx}
+    dims = Nsrc - Nidx
+    y = scatter(op, src, idx)
+    scatter_pullback(Δ) = (NO_FIELDS, NO_FIELDS, ∇scatter_src(op, Δ, idx, dims), DoesNotExist())
+    y, scatter_pullback
+end
diff --git a/src/utils.jl b/src/utils.jl
@@ -16,3 +16,29 @@ maximum_dims(dims::AbstractArray{<:Integer}) = (maximum(dims), )
 function maximum_dims(dims::AbstractArray{<:Tuple})
     Tuple(maximum(xs) for xs in zip(dims...))
 end
+
+function reverse_indices(idx::Array{T}) where T
+    rev = Dict{T,Vector{CartesianIndex}}()
+    for (ind, val) = pairs(idx)
+        rev[val] = get(rev, val, CartesianIndex[])
+        push!(rev[val], ind)
+    end
+    rev
+end
+
+function count_indices(idx::AbstractArray)
+    counts = zero.(idx)
+    for i = unique(idx)
+        counts += sum(idx.==i) * (idx.==i)
+    end
+    return counts
+end
+
+function divide_by_counts!(xs, idx::AbstractArray, dims)
+    colons = Base.ntuple(_->Colon(), dims)
+    counts = count_indices(idx)
+    for i = CartesianIndices(counts)
+        view(xs, colons..., i) ./= counts[i]
+    end
+    return xs
+end
diff --git a/test/scatter.jl b/test/scatter.jl
@@ -175,3 +175,30 @@ types = [UInt8, UInt16, UInt32, UInt64, UInt128,
     idx = [1 2 3 4; 4 2 1 3; 6 7 8 9]
     @test_throws BoundsError scatter!(+, dsts[1], srcs[(1, true)], idx)
 end
+
+@testset "∇scatter" begin
+    T = Float64
+    @testset "∂dst" begin
+        for op in (+, -, max, min, *, /)
+            gradtest(xs -> scatter!(op, copy(xs), srcs[(0, true)], idxs[:int], Val(0)), T.(dsts[0]))
+            gradtest(xs -> scatter!(op, copy(xs), srcs[(1, true)], idxs[:int], Val(1)), T.(dsts[1]))
+        end
+        gradtest(xs -> scatter!(mean, copy(xs), srcs[(0, true)], idxs[:int]), T.(dsts[0]))
+        gradtest(xs -> scatter!(mean, copy(xs), srcs[(1, true)], idxs[:int]), T.(dsts[1]))
+    end
+
+    @testset "∂src" begin
+        for op in (+, -, max, min, *, /)
+            gradtest(xs -> scatter!(op, T.(dsts[0]), xs, idxs[:int], Val(0)), T.(srcs[(0, true)]))
+            gradtest(xs -> scatter!(op, T.(dsts[1]), xs, idxs[:int], Val(1)), T.(srcs[(1, true)]))
+
+            gradtest(xs -> scatter(op, xs, idxs[:int]), T.(srcs[(0, false)]))
+            gradtest(xs -> scatter(op, xs, idxs[:int]), T.(srcs[(1, false)]))
+        end
+        gradtest(xs -> scatter!(mean, T.(dsts[0]), xs, idxs[:int]), T.(srcs[(0, true)]))
+        gradtest(xs -> scatter!(mean, T.(dsts[1]), xs, idxs[:int]), T.(srcs[(1, true)]))
+
+        gradtest(xs -> scatter(mean, xs, idxs[:int]), T.(srcs[(0, false)]))
+        gradtest(xs -> scatter(mean, xs, idxs[:int]), T.(srcs[(1, false)]))
+    end
+end