diff --git a/Project.toml b/Project.toml
index 32486a3d4..c763a8824 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "KernelFunctions"
 uuid = "ec8451be-7e33-11e9-00cf-bbf324bd1392"
-version = "0.10.54"
+version = "0.10.55"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/chainrules.jl b/src/chainrules.jl
index dde352f8c..3b52860dd 100644
--- a/src/chainrules.jl
+++ b/src/chainrules.jl
@@ -2,7 +2,10 @@
 
 # Note that this is type piracy as the derivative should be NaN for x == y.
 function ChainRulesCore.frule(
-    (_, Δx, Δy), d::Distances.Euclidean, x::AbstractVector, y::AbstractVector
+    (_, Δx, Δy)::Tuple{<:Any,<:Any,<:Any},
+    d::Distances.Euclidean,
+    x::AbstractVector,
+    y::AbstractVector,
 )
     Δ = x - y
     D = sqrt(sum(abs2, Δ))
diff --git a/src/kernels/overloads.jl b/src/kernels/overloads.jl
index b3ba76c7f..3285c3dd4 100644
--- a/src/kernels/overloads.jl
+++ b/src/kernels/overloads.jl
@@ -18,5 +18,13 @@ for (M, op, T) in (
 
         $M.$op(ks::$T, k::Kernel) = $T(ks.kernels..., k)
         $M.$op(ks::$T{<:AbstractVector{<:Kernel}}, k::Kernel) = $T(vcat(ks.kernels, k))
+
+        # Fix method ambiguity issues
+        function $M.$op(ks1::$T, ks2::$T{<:AbstractVector{<:Kernel}})
+            return $T(vcat(collect(ks1.kernels), ks2.kernels))
+        end
+        function $M.$op(ks1::$T{<:AbstractVector{<:Kernel}}, ks2::$T)
+            return $T(vcat(ks1.kernels, collect(ks2.kernels)))
+        end
     end
 end
diff --git a/src/transform/chaintransform.jl b/src/transform/chaintransform.jl
index 9129fb84b..208b1f689 100644
--- a/src/transform/chaintransform.jl
+++ b/src/transform/chaintransform.jl
@@ -34,8 +34,11 @@ function ChainTransform(v, θ::AbstractVector)
 end
 
 Base.:∘(t₁::Transform, t₂::Transform) = ChainTransform((t₂, t₁))
-Base.:∘(t::Transform, tc::ChainTransform) = ChainTransform(tuple(tc.transforms..., t))
-Base.:∘(tc::ChainTransform, t::Transform) = ChainTransform(tuple(t, tc.transforms...))
+Base.:∘(t::Transform, tc::ChainTransform) = ChainTransform((tc.transforms..., t))
+Base.:∘(tc::ChainTransform, t::Transform) = ChainTransform((t, tc.transforms...))
+function Base.:∘(tc1::ChainTransform, tc2::ChainTransform)
+    return ChainTransform((tc2.transforms..., tc1.transforms...))
+end
 
 (t::ChainTransform)(x) = foldl((x, t) -> t(x), t.transforms; init=x)
 
diff --git a/src/transform/transform.jl b/src/transform/transform.jl
index c7da2729d..795a3498f 100644
--- a/src/transform/transform.jl
+++ b/src/transform/transform.jl
@@ -8,8 +8,21 @@ abstract type Transform end
 # We introduce our own _map for Transform so that we can work around
 # https://github.com/FluxML/Zygote.jl/issues/646 and define our own pullback
 # (see zygoterules.jl)
-Base.map(t::Transform, x::AbstractVector) = _map(t, x)
-_map(t::Transform, x::AbstractVector) = t.(x)
+Base.map(t::Transform, x::ColVecs) = _map(t, x)
+Base.map(t::Transform, x::RowVecs) = _map(t, x)
+
+# Fallback
+# No separate methods for `x::ColVecs` and `x::RowVecs` to avoid method ambiguities
+function _map(t::Transform, x::AbstractVector)
+    # Avoid stackoverflow
+    if x isa RowVecs
+        return map(t, eachrow(x.X))
+    elseif x isa ColVecs
+        return map(t, eachcol(x.X))
+    else
+        return map(t, x)
+    end
+end
 
 """
     IdentityTransform()
@@ -19,6 +32,9 @@ Transformation that returns exactly the input.
 struct IdentityTransform <: Transform end
 
 (t::IdentityTransform)(x) = x
+
+# More efficient implementation than `map(IdentityTransform(), x)`
+# Introduces, however, discrepancy between `map` and `_map`
 _map(::IdentityTransform, x::AbstractVector) = x
 
 ### TODO Maybe defining adjoints could help but so far it's not working
diff --git a/src/utils.jl b/src/utils.jl
index bb805b15f..0942fa5f7 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -101,10 +101,10 @@ _to_colvecs(x::AbstractVector{<:Real}) = ColVecs(reshape(x, 1, :))
 
 pairwise(d::PreMetric, x::ColVecs) = Distances_pairwise(d, x.X; dims=2)
 pairwise(d::PreMetric, x::ColVecs, y::ColVecs) = Distances_pairwise(d, x.X, y.X; dims=2)
-function pairwise(d::PreMetric, x::AbstractVector, y::ColVecs)
+function pairwise(d::PreMetric, x::AbstractVector{<:AbstractVector{<:Real}}, y::ColVecs)
     return Distances_pairwise(d, reduce(hcat, x), y.X; dims=2)
 end
-function pairwise(d::PreMetric, x::ColVecs, y::AbstractVector)
+function pairwise(d::PreMetric, x::ColVecs, y::AbstractVector{<:AbstractVector{<:Real}})
     return Distances_pairwise(d, x.X, reduce(hcat, y); dims=2)
 end
 function pairwise!(out::AbstractMatrix, d::PreMetric, x::ColVecs)
@@ -172,10 +172,10 @@ dim(x::RowVecs) = size(x.X, 2)
 
 pairwise(d::PreMetric, x::RowVecs) = Distances_pairwise(d, x.X; dims=1)
 pairwise(d::PreMetric, x::RowVecs, y::RowVecs) = Distances_pairwise(d, x.X, y.X; dims=1)
-function pairwise(d::PreMetric, x::AbstractVector, y::RowVecs)
+function pairwise(d::PreMetric, x::AbstractVector{<:AbstractVector{<:Real}}, y::RowVecs)
     return Distances_pairwise(d, permutedims(reduce(hcat, x)), y.X; dims=1)
 end
-function pairwise(d::PreMetric, x::RowVecs, y::AbstractVector)
+function pairwise(d::PreMetric, x::RowVecs, y::AbstractVector{<:AbstractVector{<:Real}})
     return Distances_pairwise(d, x.X, permutedims(reduce(hcat, y)); dims=1)
 end
 function pairwise!(out::AbstractMatrix, d::PreMetric, x::RowVecs)
diff --git a/test/kernels/kernelproduct.jl b/test/kernels/kernelproduct.jl
index b2cdea042..94e816ade 100644
--- a/test/kernels/kernelproduct.jl
+++ b/test/kernels/kernelproduct.jl
@@ -3,6 +3,12 @@
     k2 = SqExponentialKernel()
     k = KernelProduct(k1, k2)
     @test k == KernelProduct([k1, k2]) == KernelProduct((k1, k2))
+    for (_k1, _k2) in Iterators.product(
+        (k1, KernelProduct((k1,)), KernelProduct([k1])),
+        (k2, KernelProduct((k2,)), KernelProduct([k2])),
+    )
+        @test k == _k1 * _k2
+    end
     @test length(k) == 2
     @test string(k) == (
         "Product of 2 kernels:\n\tLinear Kernel (c = 0.0)\n\tSquared " *
diff --git a/test/kernels/kernelsum.jl b/test/kernels/kernelsum.jl
index cfe239717..4b6f30f94 100644
--- a/test/kernels/kernelsum.jl
+++ b/test/kernels/kernelsum.jl
@@ -3,6 +3,11 @@
     k2 = SqExponentialKernel()
     k = KernelSum(k1, k2)
     @test k == KernelSum([k1, k2]) == KernelSum((k1, k2))
+    for (_k1, _k2) in Iterators.product(
+        (k1, KernelSum((k1,)), KernelSum([k1])), (k2, KernelSum((k2,)), KernelSum([k2]))
+    )
+        @test k == _k1 + _k2
+    end
     @test length(k) == 2
     @test repr(k) == (
         "Sum of 2 kernels:\n" *
diff --git a/test/kernels/kerneltensorproduct.jl b/test/kernels/kerneltensorproduct.jl
index d181b89ac..a59c972ee 100644
--- a/test/kernels/kerneltensorproduct.jl
+++ b/test/kernels/kerneltensorproduct.jl
@@ -13,6 +13,12 @@
 
     @test kernel1 == kernel2
     @test kernel1.kernels === (k1, k2) === KernelTensorProduct((k1, k2)).kernels
+    for (_k1, _k2) in Iterators.product(
+        (k1, KernelTensorProduct((k1,)), KernelTensorProduct([k1])),
+        (k2, KernelTensorProduct((k2,)), KernelTensorProduct([k2])),
+    )
+        @test kernel1 == _k1 ⊗ _k2
+    end
     @test length(kernel1) == length(kernel2) == 2
     @test string(kernel1) == (
         "Tensor product of 2 kernels:\n" *
diff --git a/test/runtests.jl b/test/runtests.jl
index f486ddd2a..caf43cb91 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -149,7 +149,10 @@ include("test_utils.jl")
     if GROUP == "" || GROUP == "Others"
         include("utils.jl")
 
-        @test isempty(detect_unbound_args(KernelFunctions))
+        @testset "general" begin
+            @test isempty(detect_unbound_args(KernelFunctions))
+            @test isempty(detect_ambiguities(KernelFunctions))
+        end
 
         @testset "distances" begin
             include("distances/pairwise.jl")
diff --git a/test/transform/chaintransform.jl b/test/transform/chaintransform.jl
index dad6f563d..8d7442e05 100644
--- a/test/transform/chaintransform.jl
+++ b/test/transform/chaintransform.jl
@@ -12,6 +12,7 @@
     # Check composition constructors.
     @test (tf ∘ ChainTransform([tp])).transforms == (tp, tf)
     @test (ChainTransform([tf]) ∘ tp).transforms == (tp, tf)
+    @test (ChainTransform([tf]) ∘ ChainTransform([tp])).transforms == (tp, tf)
 
     # Verify correctness.
     x = ColVecs(randn(rng, 2, 3))