[WIP] Fix AD issues with various kernels

src/basekernels/maha.jl

@@ -3,7 +3,7 @@
 
 Mahalanobis distance-based kernel given by
 ```math
- κ(x,y) = exp(-r^2), r^2 = maha(x,P,y) = (x-y)'*inv(P)*(x-y)
+ κ(x,y) = exp(-r^2), r^2 = maha(x,P,y) = (x-y)'* P *(x-y)
 ```
 where the matrix P is the metric.
 

src/basekernels/matern.jl

@@ -5,7 +5,9 @@ The matern kernel is a Mercer kernel given by the formula:
 ```
  κ(x,y) = 2^{1-ν}/Γ(ν)*(√(2ν)‖x-y‖)^ν K_ν(√(2ν)‖x-y‖)
 ```
-For `ν=n+1/2, n=0,1,2,...` it can be simplified and you should instead use [`ExponentialKernel`](@ref) for `n=0`, [`Matern32Kernel`](@ref), for `n=1`, [`Matern52Kernel`](@ref) for `n=2` and [`SqExponentialKernel`](@ref) for `n=∞`.
+For `ν=n+1/2, n=0,1,2,...` it can be simplified and you should instead use 
+[`ExponentialKernel`](@ref) for `n=0`, [`Matern32Kernel`](@ref), for `n=1`, 
+[`Matern52Kernel`](@ref) for `n=2` and [`SqExponentialKernel`](@ref) for `n=∞`.
 """
 struct MaternKernel{Tν<:Real} <: SimpleKernel
  ν::Vector{Tν}

src/basekernels/nn.jl

@@ -23,4 +23,32 @@ function (κ::NeuralNetworkKernel)(x, y)
  return asin(dot(x, y) / sqrt((1 + sum(abs2, x)) * (1 + sum(abs2, y))))
 end
 
+function kernelmatrix(::NeuralNetworkKernel, x::ColVecs, y::ColVecs)
+ validate_inputs(x, y)
+ X_2 = sum(x.X .* x.X; dims=1)
+ Y_2 = sum(y.X .* y.X; dims=1)
+ XY = x.X' * y.X
+ return asin.(XY ./ sqrt.((X_2 .+ 1)' * (Y_2 .+ 1)))
+end
+
+function kernelmatrix(::NeuralNetworkKernel, x::ColVecs)
+ X_2_1 = sum(x.X .* x.X; dims=1) .+ 1
+ XX = x.X' * x.X
+ return asin.(XX ./ sqrt.(X_2_1' * X_2_1))
+end
+
+function kernelmatrix(::NeuralNetworkKernel, x::RowVecs, y::RowVecs)
+ validate_inputs(x, y)
+ X_2 = sum(x.X .* x.X; dims=2)
+ Y_2 = sum(y.X .* y.X; dims=2)
+ XY = x.X * y.X'
+ return asin.(XY ./ sqrt.((X_2 .+ 1)' * (Y_2 .+ 1)))
+end
+
+function kernelmatrix(::NeuralNetworkKernel, x::RowVecs)
+ X_2_1 = sum(x.X .* x.X; dims=2) .+ 1
+ XX = x.X * x.X'
+ return asin.(XX ./ sqrt.(X_2_1' * X_2_1))
+end
+
 Base.show(io::IO, κ::NeuralNetworkKernel) = print(io, "Neural Network Kernel")

src/zygote_adjoints.jl

@@ -62,19 +62,19 @@ end
 @adjoint function ColVecs(X::AbstractMatrix)
  back(Δ::NamedTuple) = (Δ.X,)
  back(Δ::AbstractMatrix) = (Δ,)
- function back(Δ::AbstractVector{<:AbstractVector{<:Real}})
+ function ColVecs_pullback(Δ::AbstractVector{<:AbstractVector{<:Real}})
  throw(error("In slow method"))
  end
- return ColVecs(X), back
+ return ColVecs(X), ColVecs_pullback
 end
 
 @adjoint function RowVecs(X::AbstractMatrix)
  back(Δ::NamedTuple) = (Δ.X,)
  back(Δ::AbstractMatrix) = (Δ,)
- function back(Δ::AbstractVector{<:AbstractVector{<:Real}})
+ function RowVecs_pullback(Δ::AbstractVector{<:AbstractVector{<:Real}})
  throw(error("In slow method"))
  end
- return RowVecs(X), back
+ return RowVecs(X), RowVecs_pullback
 end
 
 @adjoint function Base.map(t::Transform, X::ColVecs)
@@ -84,3 +84,58 @@ end
 @adjoint function Base.map(t::Transform, X::RowVecs)
  pullback(_map, t, X)
 end
+
+@adjoint function (dist::Distances.SqMahalanobis)(a, b)
+ function SqMahalanobis_pullback(Δ::Real)
+ B_Bᵀ = dist.qmat + transpose(dist.qmat)
+ a_b = a - b
+ δa = (B_Bᵀ * a_b) * Δ
+ return (qmat = (a_b * a_b') * Δ,), δa, -δa 
+ end
+ return evaluate(dist, a, b), SqMahalanobis_pullback
+end
+
+
+@adjoint function Distances.pairwise(
+ dist::SqMahalanobis, 
+ a::AbstractMatrix, 
+ b::AbstractMatrix;
+ dims::Union{Nothing,Integer}=nothing
+)
+ function pairwise_pullback(Δ::AbstractMatrix)
+ B_Bᵀ = dist.qmat + transpose(dist.qmat)
+ a_b = map(
+ x -> (first(last(x)) - last(last(x)))*first(x), 
+ zip(
+ Δ,
+ Iterators.product(eachslice(a, dims=dims), eachslice(b, dims=dims))
+ )
+ )
+ δa = reduce(hcat, sum(map(x -> B_Bᵀ*x, a_b), dims=2))
+ δB = sum(map(x -> x*transpose(x), a_b))
+ return (qmat=δB,), δa, -δa
+ end
+ return Distances.pairwise(dist, a, b, dims=dims), pairwise_pullback
+end
+
+@adjoint function Distances.pairwise(
+ dist::SqMahalanobis, 
+ a::AbstractMatrix;
+ dims::Union{Nothing,Integer}=nothing
+)
+ function pairwise_pullback(Δ::AbstractMatrix)
+ B_Bᵀ = dist.qmat + transpose(dist.qmat)
+ a_a = map(
+ x -> (first(last(x)) - last(last(x)))*first(x), 
+ zip(
+ Δ,
+ Iterators.product(eachslice(a, dims=dims), eachslice(a, dims=dims))
+ )
+ )
+ δa = reduce(hcat, sum(map(x -> B_Bᵀ*x, a_a), dims=2))
+ δB = sum(map(x -> x*transpose(x), a_a))
+ return (qmat=δB,), δa
+ end
+ return Distances.pairwise(dist, a, b, dims=dims), pairwise_pullback
+end
+

test/basekernels/exponential.jl

@@ -38,8 +38,7 @@
  @test metric(GammaExponentialKernel(γ=2.0)) == SqEuclidean()
  @test repr(k) == "Gamma Exponential Kernel (γ = $(γ))"
  @test KernelFunctions.iskroncompatible(k) == true
- test_ADs(γ -> GammaExponentialKernel(gamma=first(γ)), [γ], ADs = [:ForwardDiff, :ReverseDiff])
- @test_broken "Zygote gradient given γ"
+ test_ADs(γ -> GammaExponentialKernel(gamma=first(γ)), [γ])
  test_params(k, ([γ],))
  #Coherence :
  @test GammaExponentialKernel(γ=1.0)(v1,v2) ≈ SqExponentialKernel()(v1,v2)

test/basekernels/fbm.jl

@@ -22,8 +22,7 @@
  @test kernelmatrix(k, x1*ones(1,1), x2*ones(1,1))[1] ≈ k(x1, x2) atol=1e-5
 
  @test repr(k) == "Fractional Brownian Motion Kernel (h = $(h))"
- test_ADs(FBMKernel, ADs = [:ReverseDiff])
- @test_broken "Tests failing for kernelmatrix(k, x) for ForwardDiff and Zygote"
-
+ test_ADs(FBMKernel, ADs = [:ReverseDiff, :Zygote])
+ @test_broken "Tests failing for kernelmatrix(k, x) for ForwardDiff"
  test_params(k, ([h],))
 end

test/basekernels/gabor.jl

@@ -17,7 +17,6 @@
  @test k.ell ≈ 1.0 atol=1e-5
  @test k.p ≈ 1.0 atol=1e-5
  @test repr(k) == "Gabor Kernel (ell = 1.0, p = 1.0)"
- #test_ADs(x -> GaborKernel(ell = x[1], p = x[2]), [ell, p])#, ADs = [:ForwardDiff, :ReverseDiff])
- @test_broken "Tests failing for Zygote on differentiating through ell and p"
+ test_ADs(x -> GaborKernel(ell = x[1], p = x[2]), [ell, p], ADs = [:Zygote])
  # Tests are also failing randomly for ForwardDiff and ReverseDiff but randomly
 end

test/basekernels/maha.jl

@@ -4,14 +4,39 @@
  v1 = rand(rng, 3)
  v2 = rand(rng, 3)
 
- P = rand(rng, 3, 3)
- k = MahalanobisKernel(P=P)
-
+ U = UpperTriangular(rand(rng, 3,3))
+ P = Matrix(Cholesky(U, 'U', 0))
+ @assert isposdef(P)
+ k = MahalanobisKernel(P)
+
  @test kappa(k, x) == exp(-x)
  @test k(v1, v2) ≈ exp(-sqmahalanobis(v1, v2, P))
  @test kappa(ExponentialKernel(), x) == kappa(k, x)
  @test repr(k) == "Mahalanobis Kernel (size(P) = $(size(P)))"
- # test_ADs(P -> MahalanobisKernel(P=P), P)
+
+ M1, M2 = rand(rng,3,2), rand(rng,3,2)
+ fdm = FiniteDifferences.Central(5, 1);
+
+
+ function FiniteDifferences.to_vec(dist::SqMahalanobis{Float64})
+ return vec(dist.qmat), x -> SqMahalanobis(reshape(x, size(dist.qmat)...))
+ end
+
+ function test_mahakernel(U::UpperTriangular, v1::AbstractVector, v2::AbstractVector)
+ return MahalanobisKernel(Array(U'*U))(v1, v2)
+ end
+
+ @test_broken all(j′vp(fdm, test_mahakernel, 1, U, v1, v2) .≈
+ Zygote.pullback(test_mahakernel, U, v1, v2)[2](1))
+
+ function test_sqmaha(U::UpperTriangular, v1::AbstractVector, v2::AbstractVector)
+ return SqMahalanobis(Array(U'*U))(v1, v2)
+ end
+
+ @test_broken all(j′vp(fdm, test_sqmaha, 1, U, v1, v2) .≈ 
+ Zygote.pullback(test_sqmaha, U, v1, v2)[2](1))
+
+ # test_ADs(U -> MahalanobisKernel(Array(U' * U)), U, ADs=[:Zygote])
  @test_broken "Nothing passes (problem with Mahalanobis distance in Distances)"
 
  test_params(k, (P,))

test/basekernels/nn.jl

@@ -38,11 +38,10 @@
  @test kerneldiagmatrix(k, m1) ≈ A4 atol=1e-5
 
  A5 = ones(4,4)
- @test_throws AssertionError kernelmatrix!(A5, k, m1, m2, obsdim=3)
- @test_throws AssertionError kernelmatrix!(A5, k, m1, obsdim=3)
+ @test_throws AssertionError kernelmatrix!(A5, k, m1, m2; obsdim=3)
+ @test_throws AssertionError kernelmatrix!(A5, k, m1; obsdim=3)
  @test_throws DimensionMismatch kernelmatrix!(A5, k, ones(4,3), ones(3,4))
 
  @test k([x1], [x2]) ≈ k(x1, x2) atol=1e-5
- test_ADs(NeuralNetworkKernel, ADs = [:ForwardDiff, :ReverseDiff])
- @test_broken "Zygote uncompatible with BaseKernel"
+ test_ADs(NeuralNetworkKernel)
 end

test/zygote_adjoints.jl

@@ -4,6 +4,9 @@
  x = rand(rng, 5)
  y = rand(rng, 5)
  r = rand(rng, 5)
+ Q = Matrix(Cholesky(rand(rng, 5, 5), 'U', 0))
+ @assert isposdef(Q)
+
 
  gzeucl = gradient(:Zygote, [x,y]) do xy
  evaluate(Euclidean(), xy[1], xy[2])
@@ -20,6 +23,9 @@
  gzsinus = gradient(:Zygote, [x,y]) do xy
  evaluate(KernelFunctions.Sinus(r), xy[1], xy[2])
  end
+ gzsqmaha = gradient(:Zygote, [Q,x,y]) do xy
+ evaluate(SqMahalanobis(xy[1]), xy[2], xy[3])
+ end
 
  gfeucl = gradient(:FiniteDiff, [x,y]) do xy
  evaluate(Euclidean(), xy[1], xy[2])
@@ -36,11 +42,15 @@
  gfsinus = gradient(:FiniteDiff, [x,y]) do xy
  evaluate(KernelFunctions.Sinus(r), xy[1], xy[2])
  end
+ gfsqmaha = gradient(:FiniteDiff, [Q,x,y]) do xy
+ evaluate(SqMahalanobis(xy[1]), xy[2], xy[3])
+ end
 
 
  @test all(gzeucl .≈ gfeucl)
  @test all(gzsqeucl .≈ gfsqeucl)
  @test all(gzdotprod .≈ gfdotprod)
  @test all(gzdelta .≈ gfdelta)
  @test all(gzsinus .≈ gfsinus)
+ @test all(gzsqmaha .≈ gfsqmaha)
 end