diff --git a/Project.toml b/Project.toml
index 47ee0d086..c15432dd7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.37"
+version = "0.10.38"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
@@ -19,7 +19,6 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
 TensorCore = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
-ZygoteRules = "700de1a5-db45-46bc-99cf-38207098b444"
 
 [compat]
 ChainRulesCore = "1"
@@ -34,5 +33,4 @@ Requires = "1.0.1"
 SpecialFunctions = "0.8, 0.9, 0.10, 1, 2"
 StatsBase = "0.32, 0.33"
 TensorCore = "0.1"
-ZygoteRules = "0.2"
 julia = "1.3"
diff --git a/src/KernelFunctions.jl b/src/KernelFunctions.jl
index 0211340e6..39a4a1385 100644
--- a/src/KernelFunctions.jl
+++ b/src/KernelFunctions.jl
@@ -60,7 +60,6 @@ using IrrationalConstants: logtwo, twoπ, invsqrt2
 using LogExpFunctions: softplus
 using StatsBase
 using TensorCore
-using ZygoteRules: ZygoteRules, AContext, literal_getproperty, literal_getfield
 
 # Hack to work around Zygote type inference problems.
 const Distances_pairwise = Distances.pairwise
@@ -122,7 +121,6 @@ include("mokernels/intrinsiccoregion.jl")
 include("mokernels/lmm.jl")
 
 include("chainrules.jl")
-include("zygoterules.jl")
 
 include("test_utils.jl")
 
diff --git a/src/kernels/transformedkernel.jl b/src/kernels/transformedkernel.jl
index 88e719ef1..87fab6493 100644
--- a/src/kernels/transformedkernel.jl
+++ b/src/kernels/transformedkernel.jl
@@ -82,37 +82,37 @@ end
 # Kernel matrix operations
 
 function kernelmatrix_diag!(K::AbstractVector, κ::TransformedKernel, x::AbstractVector)
-    return kernelmatrix_diag!(K, κ.kernel, _map(κ.transform, x))
+    return kernelmatrix_diag!(K, κ.kernel, map(κ.transform, x))
 end
 
 function kernelmatrix_diag!(
     K::AbstractVector, κ::TransformedKernel, x::AbstractVector, y::AbstractVector
 )
-    return kernelmatrix_diag!(K, κ.kernel, _map(κ.transform, x), _map(κ.transform, y))
+    return kernelmatrix_diag!(K, κ.kernel, map(κ.transform, x), map(κ.transform, y))
 end
 
 function kernelmatrix!(K::AbstractMatrix, κ::TransformedKernel, x::AbstractVector)
-    return kernelmatrix!(K, κ.kernel, _map(κ.transform, x))
+    return kernelmatrix!(K, κ.kernel, map(κ.transform, x))
 end
 
 function kernelmatrix!(
     K::AbstractMatrix, κ::TransformedKernel, x::AbstractVector, y::AbstractVector
 )
-    return kernelmatrix!(K, κ.kernel, _map(κ.transform, x), _map(κ.transform, y))
+    return kernelmatrix!(K, κ.kernel, map(κ.transform, x), map(κ.transform, y))
 end
 
 function kernelmatrix_diag(κ::TransformedKernel, x::AbstractVector)
-    return kernelmatrix_diag(κ.kernel, _map(κ.transform, x))
+    return kernelmatrix_diag(κ.kernel, map(κ.transform, x))
 end
 
 function kernelmatrix_diag(κ::TransformedKernel, x::AbstractVector, y::AbstractVector)
-    return kernelmatrix_diag(κ.kernel, _map(κ.transform, x), _map(κ.transform, y))
+    return kernelmatrix_diag(κ.kernel, map(κ.transform, x), map(κ.transform, y))
 end
 
 function kernelmatrix(κ::TransformedKernel, x::AbstractVector)
-    return kernelmatrix(κ.kernel, _map(κ.transform, x))
+    return kernelmatrix(κ.kernel, map(κ.transform, x))
 end
 
 function kernelmatrix(κ::TransformedKernel, x::AbstractVector, y::AbstractVector)
-    return kernelmatrix(κ.kernel, _map(κ.transform, x), _map(κ.transform, y))
+    return kernelmatrix(κ.kernel, map(κ.transform, x), map(κ.transform, y))
 end
diff --git a/src/transform/ardtransform.jl b/src/transform/ardtransform.jl
index 726d940ad..ff1ac3027 100644
--- a/src/transform/ardtransform.jl
+++ b/src/transform/ardtransform.jl
@@ -35,9 +35,9 @@ dim(t::ARDTransform) = length(t.v)
 (t::ARDTransform)(x::Real) = only(t.v) * x
 (t::ARDTransform)(x) = t.v .* x
 
-_map(t::ARDTransform, x::AbstractVector{<:Real}) = t.v' .* x
-_map(t::ARDTransform, x::ColVecs) = ColVecs(t.v .* x.X)
-_map(t::ARDTransform, x::RowVecs) = RowVecs(t.v' .* x.X)
+Base.map(t::ARDTransform, x::AbstractVector{<:Real}) = t.v' .* x
+Base.map(t::ARDTransform, x::ColVecs) = ColVecs(t.v .* x.X)
+Base.map(t::ARDTransform, x::RowVecs) = RowVecs(t.v' .* x.X)
 
 Base.isequal(t::ARDTransform, t2::ARDTransform) = isequal(t.v, t2.v)
 
diff --git a/src/transform/chaintransform.jl b/src/transform/chaintransform.jl
index bd4627b19..9fa0e4570 100644
--- a/src/transform/chaintransform.jl
+++ b/src/transform/chaintransform.jl
@@ -39,7 +39,7 @@ Base.:∘(tc::ChainTransform, t::Transform) = ChainTransform(vcat(t, tc.transfor
 
 (t::ChainTransform)(x) = foldl((x, t) -> t(x), t.transforms; init=x)
 
-function _map(t::ChainTransform, x::AbstractVector)
+function Base.map(t::ChainTransform, x::AbstractVector)
     return foldl((x, t) -> map(t, x), t.transforms; init=x)
 end
 
diff --git a/src/transform/functiontransform.jl b/src/transform/functiontransform.jl
index 53dc0b28d..df53d2991 100644
--- a/src/transform/functiontransform.jl
+++ b/src/transform/functiontransform.jl
@@ -23,16 +23,16 @@ end
 
 (t::FunctionTransform)(x) = t.f(x)
 
-_map(t::FunctionTransform, x::AbstractVector{<:Real}) = map(t.f, x)
+Base.map(t::FunctionTransform, x::AbstractVector{<:Real}) = map(t.f, x)
 
-function _map(t::FunctionTransform, x::ColVecs)
+function Base.map(t::FunctionTransform, x::ColVecs)
     vals = map(axes(x.X, 2)) do i
         t.f(view(x.X, :, i))
     end
     return ColVecs(reduce(hcat, vals))
 end
 
-function _map(t::FunctionTransform, x::RowVecs)
+function Base.map(t::FunctionTransform, x::RowVecs)
     vals = map(axes(x.X, 1)) do i
         t.f(view(x.X, i, :))
     end
diff --git a/src/transform/lineartransform.jl b/src/transform/lineartransform.jl
index b61ba6a94..52ac39740 100644
--- a/src/transform/lineartransform.jl
+++ b/src/transform/lineartransform.jl
@@ -34,9 +34,9 @@ end
 (t::LinearTransform)(x::Real) = vec(t.A * x)
 (t::LinearTransform)(x::AbstractVector{<:Real}) = t.A * x
 
-_map(t::LinearTransform, x::AbstractVector{<:Real}) = ColVecs(t.A * collect(x'))
-_map(t::LinearTransform, x::ColVecs) = ColVecs(t.A * x.X)
-_map(t::LinearTransform, x::RowVecs) = RowVecs(x.X * t.A')
+Base.map(t::LinearTransform, x::AbstractVector{<:Real}) = ColVecs(t.A * collect(x'))
+Base.map(t::LinearTransform, x::ColVecs) = ColVecs(t.A * x.X)
+Base.map(t::LinearTransform, x::RowVecs) = RowVecs(x.X * t.A')
 
 function Base.show(io::IO, t::LinearTransform)
     return print(io::IO, "Linear transform (size(A) = ", size(t.A), ")")
diff --git a/src/transform/periodic_transform.jl b/src/transform/periodic_transform.jl
index 098262309..53dc435bf 100644
--- a/src/transform/periodic_transform.jl
+++ b/src/transform/periodic_transform.jl
@@ -27,7 +27,7 @@ dim(t::PeriodicTransform) = 2
 
 (t::PeriodicTransform)(x::Real) = [sinpi(2 * only(t.f) * x), cospi(2 * only(t.f) * x)]
 
-function _map(t::PeriodicTransform, x::AbstractVector{<:Real})
+function Base.map(t::PeriodicTransform, x::AbstractVector{<:Real})
     return RowVecs(hcat(sinpi.((2 * only(t.f)) .* x), cospi.((2 * only(t.f)) .* x)))
 end
 
diff --git a/src/transform/scaletransform.jl b/src/transform/scaletransform.jl
index 18923fcc4..c6c62d982 100644
--- a/src/transform/scaletransform.jl
+++ b/src/transform/scaletransform.jl
@@ -26,9 +26,9 @@ set!(t::ScaleTransform, ρ::Real) = t.s .= [ρ]
 
 (t::ScaleTransform)(x) = only(t.s) * x
 
-_map(t::ScaleTransform, x::AbstractVector{<:Real}) = only(t.s) .* x
-_map(t::ScaleTransform, x::ColVecs) = ColVecs(only(t.s) .* x.X)
-_map(t::ScaleTransform, x::RowVecs) = RowVecs(only(t.s) .* x.X)
+Base.map(t::ScaleTransform, x::AbstractVector{<:Real}) = only(t.s) .* x
+Base.map(t::ScaleTransform, x::ColVecs) = ColVecs(only(t.s) .* x.X)
+Base.map(t::ScaleTransform, x::RowVecs) = RowVecs(only(t.s) .* x.X)
 
 Base.isequal(t::ScaleTransform, t2::ScaleTransform) = isequal(only(t.s), only(t2.s))
 
diff --git a/src/transform/selecttransform.jl b/src/transform/selecttransform.jl
index 9c83daedc..9ccb6f9b8 100644
--- a/src/transform/selecttransform.jl
+++ b/src/transform/selecttransform.jl
@@ -25,8 +25,8 @@ duplicate(t::SelectTransform, θ) = t
 _maybe_unwrap(x) = x
 _maybe_unwrap(x::AbstractArray{<:Any,0}) = x[]
 
-_map(t::SelectTransform, x::ColVecs) = _wrap(view(x.X, t.select, :), ColVecs)
-_map(t::SelectTransform, x::RowVecs) = _wrap(view(x.X, :, t.select), RowVecs)
+Base.map(t::SelectTransform, x::ColVecs) = _wrap(view(x.X, t.select, :), ColVecs)
+Base.map(t::SelectTransform, x::RowVecs) = _wrap(view(x.X, :, t.select), RowVecs)
 
 _wrap(x::AbstractVector{<:Real}, ::Any) = x
 _wrap(X::AbstractMatrix{<:Real}, ::Type{T}) where {T} = T(X)
diff --git a/src/transform/transform.jl b/src/transform/transform.jl
index 40ce8c058..53ed7ed3f 100644
--- a/src/transform/transform.jl
+++ b/src/transform/transform.jl
@@ -5,8 +5,7 @@ Abstract type defining a transformation of the input.
 """
 abstract type Transform end
 
-Base.map(t::Transform, x::AbstractVector) = _map(t, x)
-_map(t::Transform, x::AbstractVector) = t.(x)
+Base.map(t::Transform, x::AbstractVector) = t.(x)
 
 """
     IdentityTransform()
@@ -16,7 +15,7 @@ Transformation that returns exactly the input.
 struct IdentityTransform <: Transform end
 
 (t::IdentityTransform)(x) = x
-_map(::IdentityTransform, x::AbstractVector) = x
+Base.map(::IdentityTransform, x::AbstractVector) = x
 
 ### TODO Maybe defining adjoints could help but so far it's not working
 
diff --git a/src/zygoterules.jl b/src/zygoterules.jl
deleted file mode 100644
index e405a4946..000000000
--- a/src/zygoterules.jl
+++ /dev/null
@@ -1,13 +0,0 @@
-ZygoteRules.@adjoint function Base.map(t::Transform, X::ColVecs)
-    return ZygoteRules.pullback(_map, t, X)
-end
-
-ZygoteRules.@adjoint function Base.map(t::Transform, X::RowVecs)
-    return ZygoteRules.pullback(_map, t, X)
-end
-
-function ZygoteRules._pullback(
-    cx::AContext, ::typeof(literal_getproperty), x::ColVecs, ::Val{f}
-) where {f}
-    return ZygoteRules._pullback(cx, literal_getfield, x, Val{f}())
-end
diff --git a/test/runtests.jl b/test/runtests.jl
index a1f5c395a..30ee3d71d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -168,7 +168,6 @@ include("test_utils.jl")
 
         include("generic.jl")
         include("chainrules.jl")
-        include("zygoterules.jl")
 
         @testset "doctests" begin
             DocMeta.setdocmeta!(
diff --git a/test/transform/selecttransform.jl b/test/transform/selecttransform.jl
index c9888443c..1f10976ae 100644
--- a/test/transform/selecttransform.jl
+++ b/test/transform/selecttransform.jl
@@ -117,7 +117,7 @@
             ("ColVecs", ColVecs(randn(5, 10))),
             ("RowVecs", RowVecs(randn(11, 4))),
         ]
-            @test KernelFunctions._map(t, x) isa AbstractVector{Float64}
+            @test map(t, x) isa AbstractVector{Float64}
         end
     end
 end
diff --git a/test/zygoterules.jl b/test/zygoterules.jl
deleted file mode 100644
index dc3bb98fe..000000000
--- a/test/zygoterules.jl
+++ /dev/null
@@ -1 +0,0 @@
-@testset "zygoterules" begin end