diff --git a/Project.toml b/Project.toml
index 7f34fa4..c85cb0d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,12 +1,13 @@
 name = "MLDataDevices"
 uuid = "7e8f7934-dd98-4c1a-8fe8-92b47a384d40"
 authors = ["Avik Pal <avikpal@mit.edu> and contributors"]
-version = "1.4.0"
+version = "1.4.1"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Preferences = "21216c6a-2e73-6563-6e65-726566657250"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
@@ -53,6 +54,7 @@ Compat = "4.15"
 FillArrays = "1"
 Functors = "0.4.8"
 GPUArrays = "10, 11"
+LinearAlgebra = "1.10"
 MLUtils = "0.4.4"
 Metal = "1"
 Preferences = "1.4"
diff --git a/src/MLDataDevices.jl b/src/MLDataDevices.jl
index 108d8bf..c837887 100644
--- a/src/MLDataDevices.jl
+++ b/src/MLDataDevices.jl
@@ -5,6 +5,7 @@ using Functors: Functors, fleaves
 using Preferences: @delete_preferences!, @load_preference, @set_preferences!
 using Random: AbstractRNG, Random
 using Compat: @compat
+using LinearAlgebra: Transpose, Adjoint
 
 abstract type AbstractDevice <: Function end
 abstract type AbstractCPUDevice <: AbstractDevice end
diff --git a/src/public.jl b/src/public.jl
index 281980e..104a424 100644
--- a/src/public.jl
+++ b/src/public.jl
@@ -397,3 +397,6 @@ data movement if `isleaf(x::T) == true`.
 If `MLDataDevices.isleaf(x::T)` is not defined, then it will fall back to `Functors.isleaf(x)`.
 """
 isleaf(x) = Functors.isleaf(x)
+
+isleaf(::AbstractArray{T}) where {T} = isbitstype(T)
+isleaf(::Union{Transpose, Adjoint, PermutedDimsArray}) = false
diff --git a/test/misc_tests.jl b/test/misc_tests.jl
index 942c2ff..9bec386 100644
--- a/test/misc_tests.jl
+++ b/test/misc_tests.jl
@@ -160,21 +160,50 @@ end
 end
 
 @testset "isleaf" begin
-    # Functors.isleaf fallback
-    @test MLDataDevices.isleaf(rand(2))
-    @test !MLDataDevices.isleaf((rand(2),))
+    @testset "basics" begin
+        # Functors.isleaf fallback
+        @test MLDataDevices.isleaf(rand(2))
+        @test !MLDataDevices.isleaf((rand(2),))
+
+        struct Tleaf
+            x::Any
+        end
+        Functors.@functor Tleaf
+        MLDataDevices.isleaf(::Tleaf) = true
+        Adapt.adapt_structure(dev::CPUDevice, t::Tleaf) = Tleaf(2 .* dev(t.x))
+
+        cpu = cpu_device()
+        t = Tleaf(ones(2))
+        y = cpu(t)
+        @test y.x == 2 .* ones(2)
+        y = cpu([(t,)])
+        @test y[1][1].x == 2 .* ones(2)
+    end
+
+    @testset "shared parameters" begin
+        # from  
+        x = rand(1)
+        m = (; a=x, b=x')
+        count = Ref(0)
+        mcopy = Functors.fmap(m; exclude=MLDataDevices.isleaf) do x
+            count[] += 1
+            return copy(x)
+        end
+        @test count[] == 1
+        @test mcopy.a === mcopy.b'
+    end
 
-    struct Tleaf
-        x::Any
+    @testset "bitstypes and wrapped types" begin
+        struct BitsType
+            x::Int32
+            y::Float64
+        end
+
+        for x in [1.0, 'a', BitsType(1, 2.0)]
+            @test MLDataDevices.isleaf([x])
+            @test !MLDataDevices.isleaf([x]')
+            @test !MLDataDevices.isleaf(transpose([x]))
+            @test !MLDataDevices.isleaf(PermutedDimsArray([x;;], (1, 2)))
+        end
     end
-    Functors.@functor Tleaf
-    MLDataDevices.isleaf(::Tleaf) = true
-    Adapt.adapt_structure(dev::CPUDevice, t::Tleaf) = Tleaf(2 .* dev(t.x))
-
-    cpu = cpu_device()
-    t = Tleaf(ones(2))
-    y = cpu(t)
-    @test y.x == 2 .* ones(2)
-    y = cpu([(t,)])
-    @test y[1][1].x == 2 .* ones(2)
 end