[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.
 
@@ -20,4 +20,8 @@ kappa(κ::MahalanobisKernel, d::T) where {T<:Real} = exp(-d)
 
 metric(κ::MahalanobisKernel) = SqMahalanobis(κ.P)
 
+function dot_perslice(A::AbstractMatrix, B::AbstractMatrix; dims=2)
+    return reshape(sum(A .* B, dims=3-dims), :)
+end
+
 Base.show(io::IO, κ::MahalanobisKernel) = print(io, "Mahalanobis Kernel (size(P) = ", size(κ.P), ")")

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

@@ -84,3 +84,13 @@ end
 @adjoint function Base.map(t::Transform, X::RowVecs)
     pullback(_map, t, X)
 end
+
+@adjoint function (dist::Distances.SqMahalanobis)(a, b)
+    function back(Δ::Real)
+        B_B_inv = dist.qmat + transpose(dist.qmat)
+        a_b = a - b
+        δa = B_B_inv * a_b
+        return (qmat = a_b * a_b',), δa, -δa 
+    end
+  return evaluate(dist::SqMahalanobis, a, b), back
+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])
         #Coherence :
         @test GammaExponentialKernel(γ=1.0)(v1,v2) ≈ SqExponentialKernel()(v1,v2)
         @test GammaExponentialKernel(γ=0.5)(v1,v2) ≈ ExponentialKernel()(v1,v2)

test/basekernels/fbm.jl

@@ -22,6 +22,6 @@
     @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"
 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

@@ -11,6 +11,6 @@
     @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)
+    test_ADs(P -> MahalanobisKernel(P), P, ADs=[:Zygote])
     @test_broken "Nothing passes (problem with Mahalanobis distance in Distances)"
 end

test/basekernels/nn.jl

@@ -43,6 +43,5 @@
     @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