diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 5c5a952a..7c3b18cc 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -53,27 +53,3 @@ jobs:
           file: lcov.info
         continue-on-error: ${{ matrix.julia-version == 'nightly' }}
 
-  docs:
-    name: Documentation
-    runs-on: ubuntu-latest
-    steps:
-      - uses: actions/checkout@v3
-      - uses: julia-actions/setup-julia@v1
-        with:
-          version: '1.6'
-      - run: |
-          julia --project=docs -e '
-            using Pkg
-            Pkg.develop(PackageSpec(path=pwd()))
-            Pkg.instantiate()'
-      - run: |
-          julia --color=yes --project=docs/ -e '
-            using Optimisers
-            using Documenter
-            using Documenter: doctest
-            DocMeta.setdocmeta!(Optimisers, :DocTestSetup, :(using Optimisers); recursive = true)
-            doctest(Optimisers)'
-      - run: julia --project=docs docs/make.jl
-        env:
-          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
-          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }}
diff --git a/.github/workflows/dependabot.yml b/.github/workflows/dependabot.yml
new file mode 100644
index 00000000..700707ce
--- /dev/null
+++ b/.github/workflows/dependabot.yml
@@ -0,0 +1,7 @@
+# https://docs.github.com/github/administering-a-repository/configuration-options-for-dependency-updates
+version: 2
+updates:
+  - package-ecosystem: "github-actions"
+    directory: "/" # Location of package manifests
+    schedule:
+      interval: "weekly"
diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml
new file mode 100644
index 00000000..efb91902
--- /dev/null
+++ b/.github/workflows/documentation.yml
@@ -0,0 +1,28 @@
+name: Documentation
+
+on:
+  push:
+    branches:
+      - master # update to match your development branch (master, main, dev, trunk, ...)
+    tags: '*'
+  pull_request:
+
+jobs:
+  build:
+    permissions:
+      contents: write
+      statuses: write
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v1
+        with:
+          version: '1.10'
+      - uses: julia-actions/cache@v1
+      - name: Install dependencies
+        run: julia --project=docs/ -e 'using Pkg; Pkg.develop(PackageSpec(path=pwd())); Pkg.instantiate()'
+      - name: Build and deploy
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }} # If authenticating with GitHub Actions token
+          DOCUMENTER_KEY: ${{ secrets.DOCUMENTER_KEY }} # If authenticating with SSH deploy key
+        run: julia --project=docs/ docs/make.jl
diff --git a/Project.toml b/Project.toml
index 7422f28c..4920eaa9 100644
--- a/Project.toml
+++ b/Project.toml
@@ -12,7 +12,7 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [compat]
 ChainRulesCore = "1"
-Functors = "0.4"
+Functors = "0.4.9"
 Statistics = "1"
 Zygote = "0.6.40"
 julia = "1.6"
diff --git a/docs/.DS_Store b/docs/.DS_Store
index e1455310..3836d25d 100644
Binary files a/docs/.DS_Store and b/docs/.DS_Store differ
diff --git a/docs/Project.toml b/docs/Project.toml
index 47d2b7c1..31e718a6 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,5 +1,6 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Functors = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
+Optimisers = "3bd65402-5787-11e9-1adc-39752487f4e2"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
diff --git a/docs/make.jl b/docs/make.jl
index 47d64137..55594e8c 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,8 +1,9 @@
 using Documenter, Optimisers, Zygote, StaticArrays, Functors
 
-DocMeta.setdocmeta!(Optimisers, :DocTestSetup, :(using Optimisers); recursive = true)
+DocMeta.setdocmeta!(Optimisers, :DocTestSetup, :(using Optimisers, Functors); recursive = true)
+DocMeta.setdocmeta!(Functors, :DocTestSetup, :(using Functors); recursive = true)
 
-makedocs(modules = [Optimisers],
+makedocs(modules = [Optimisers, Functors],
          doctest = false,
          sitename = "Optimisers.jl",
          pages = ["Home" => "index.md",
@@ -13,6 +14,7 @@ makedocs(modules = [Optimisers],
              assets = ["assets/flux.css"],
              prettyurls = get(ENV, "CI", nothing) == "true"
          ),
+         checkdocs = :none, # don't check that Functors' docstrings are all reported here
 )
 
 deploydocs(
diff --git a/docs/src/api.md b/docs/src/api.md
index 5c203492..378bf72a 100644
--- a/docs/src/api.md
+++ b/docs/src/api.md
@@ -1,3 +1,6 @@
+```@meta
+CollapsedDocStrings = true
+```
 
 ## Optimisation Rules
 
@@ -72,3 +75,14 @@ Optimisers.@lazy
 Optimisers.adjust(::AbstractRule, ::Real)
 Optimisers.@def
 ```
+
+## KeyPath
+
+A `KeyPath` is a sequence of keys that can be used to access a value within a nested structure.
+It is defined in Functors.jl and re-exported by Optimisers.jl here for convenience.
+
+```@docs
+Functors.KeyPath
+Functors.haskeypath
+Functors.getkeypath
+```
diff --git a/src/Optimisers.jl b/src/Optimisers.jl
index 3cc98808..2e115c40 100644
--- a/src/Optimisers.jl
+++ b/src/Optimisers.jl
@@ -1,11 +1,15 @@
 module Optimisers
 
-using Functors: functor, fmap, isleaf, @functor, fmapstructure, children, AbstractWalk
+using Functors: functor, fmap, fmap_with_path, 
+                KeyPath, haskeypath, getkeypath,
+                isleaf, @functor, fmapstructure, children, AbstractWalk
 using LinearAlgebra
 
 include("interface.jl")
 export AbstractRule
 
+include("utils.jl")
+
 include("adjust.jl")
 
 include("destructure.jl")
@@ -13,6 +17,7 @@ export destructure
 
 include("trainables.jl")
 export trainables
+export KeyPath, haskeypath, getkeypath # from Functors.jl
 
 include("rules.jl")
 export Descent, Adam, Momentum, Nesterov, Rprop, RMSProp,
diff --git a/src/destructure.jl b/src/destructure.jl
index f9950a92..a6284522 100644
--- a/src/destructure.jl
+++ b/src/destructure.jl
@@ -78,7 +78,7 @@ end
 
 struct TrainableStructWalk <: AbstractWalk end
 
-(::TrainableStructWalk)(recurse, x) = map(recurse, _trainable(x))
+(::TrainableStructWalk)(recurse, x) = mapvalue(recurse, _trainable(x))
 
 _vec(x::Number) = LinRange(x,x,1)
 _vec(x::AbstractArray) = vec(x)
diff --git a/src/interface.jl b/src/interface.jl
index aa5447c0..ac9b90bc 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -45,7 +45,7 @@ function _setup(rule, x; cache)
       cache[x] = ℓ
     end
   else
-    valuemap(xᵢ -> _setup(rule, xᵢ; cache), _trainable(x))
+    mapvalue(xᵢ -> _setup(rule, xᵢ; cache), _trainable(x))
   end
 end
 
@@ -82,7 +82,7 @@ function _update!(tree, x; grads, params)
   haskey(params, (tree,x)) && return params[(tree,x)]
   isbits(tree) && return x  # means () is not cached, and also (((),),)
   x′, re = functor(x)
-  x′′ = re(valuemap((tᵢ, xᵢ) -> _update!(tᵢ, xᵢ; grads, params), tree, x′))
+  x′′ = re(mapvalue((tᵢ, xᵢ) -> _update!(tᵢ, xᵢ; grads, params), tree, x′))
   if ismutable(x′′)
     params[(tree,x)] = x′′
   else  # no ties to preserve between immutable structs, right?
@@ -115,7 +115,7 @@ function _grads!(dict::IdDict, tree, x, x̄s...)
   # functor(typeof(tree), base(x̄)), for things like Transpose
   x̄s′ = map(x̄ -> functor(typeof(x), base(x̄))[1], x̄s)
   x′, _ = functor(typeof(x), x)
-  valueforeach((tᵢ, xᵢ, x̄sᵢ...) -> _grads!(dict, tᵢ, xᵢ, x̄sᵢ...), tree, x′, x̄s′...)
+  foreachvalue((tᵢ, xᵢ, x̄sᵢ...) -> _grads!(dict, tᵢ, xᵢ, x̄sᵢ...), tree, x′, x̄s′...)
 end
 
 # default all rules to first order calls
@@ -172,7 +172,7 @@ _trainable(x) = _trainable(functor(x)[1], trainable(x))
 _trainable(ch::NamedTuple, tr::NamedTuple) = merge(map(_ -> nothing, ch), tr)
 _trainable(ch::Tuple{Vararg{Any,N}}, tr::Tuple{Vararg{Any,N}}) where N = tr
 _trainable(ch::AbstractArray, tr::AbstractArray) = tr
-_trainable(ch::Dict, tr::Dict) = merge(valuemap(_ -> nothing, ch), tr)
+_trainable(ch::Dict, tr::Dict) = merge(mapvalue(_ -> nothing, ch), tr)
 
 function _trainable(ch::NamedTuple, tr::Tuple)  # for old Flux-style no-names tuple
   @warn "trainable(x) should now return a NamedTuple with the field names, not a Tuple" maxlog=3
@@ -180,14 +180,6 @@ function _trainable(ch::NamedTuple, tr::Tuple)  # for old Flux-style no-names tu
 end
 
 
-valuemap(f, x...) = map(f, x...)
-valuemap(f, x::Dict, ys...) = Dict(k => f(v, (get(y, k, nothing) for y in ys)...) for (k,v) in x)
-valueforeach(f, x...) = foreach(f, x...)
-valueforeach(f, x::Dict, ys...) = foreach(pairs(x)) do (k, v)
-  f(v, (get(y, k, nothing) for y in ys)...)
-end
-
-
 ###
 ### rule definition helpers
 ###
diff --git a/src/trainables.jl b/src/trainables.jl
index 625c5659..370de0f6 100644
--- a/src/trainables.jl
+++ b/src/trainables.jl
@@ -1,12 +1,17 @@
 
 """
-    trainables(x)
+    trainables(x, path = false)
 
-Return a list over all the trainable parameters in `x`, that is all the numerical
+Return an iterable over all the trainable parameters in `x`, that is all the numerical
 arrays (see [`isnumeric`](@ref Optimisers.isnumeric)) which are reachable through [`trainable`](@ref Optimisers.trainable).
 
 Parameters appearing multiple times in the model (tied weights) will be present only once in the output.
 
+If `path = false`, the output is a list of numerical arrays.
+
+If `path = true`, the output is a list of `(KeyPath, AbstractArray)` pairs, where [`KeyPath`](@ref) is a type
+representing the path to the array in the original structure.
+
 See also [`destructure`](@ref) for a similar operation that returns a single flat vector instead.
 
 # Examples
@@ -33,11 +38,36 @@ julia> trainables(x)
  2-element Vector{AbstractArray}:
  [1.0, 2.0]
  [3.0]
+```
+
+```jldoctest
+julia> x = (a = [1.0,2.0], b = (Dict("c" => [3.0, 4.0], "d" => 5.0), [6.0,7.0]));
+
+julia> for (kp, y) in trainables(x, path = true)
+           println(kp, " => ", y)
+       end
+KeyPath(:a,) => [1.0, 2.0]
+KeyPath(:b, 1, "c") => [3.0, 4.0]
+KeyPath(:b, 2) => [6.0, 7.0]
+
+julia> getkeypath(x, KeyPath(:b, 1, "c"))
+2-element Vector{Float64}:
+ 3.0
+ 4.0
+```
 """
-function trainables(x)
+function trainables(x; path = false)
+    if path
+        return _trainables_with_path(x)
+    else
+        return _trainables(x)
+    end
+end
+
+
+function _trainables(x)
     arrays = AbstractArray[]
-    exclude(x) = Optimisers.isnumeric(x)
-    fmap(x; exclude, walk = Optimisers.TrainableStructWalk()) do y
+    fmap(x; exclude = isnumeric, walk = TrainableStructWalk()) do y
         push!(arrays, y)
         return y
     end
@@ -45,15 +75,50 @@ function trainables(x)
 end
 
 function ∇trainables(x, Δ)
-    exclude(x) = Optimisers.isnumeric(x)
     i = 0
-    return fmapstructure(x; exclude, walk = TrainableStructWalk()) do _
+    return fmapstructure(x; exclude = isnumeric, walk = TrainableStructWalk()) do _
                 return Δ[i+=1]
            end
 end
 
-function ChainRulesCore.rrule(::typeof(trainables), x)
+function ChainRulesCore.rrule(::typeof(_trainables), x)
     y = trainables(x)
     trainables_back(Δ) = (NoTangent(), ∇trainables(x, unthunk(Δ)))
     return y, trainables_back
 end
+
+function _trainables_with_path(x)
+    named_params = []
+    exclude(kp, x) = isnumeric(x)
+    fmap_with_path(x; exclude, walk = TrainableStructWalkWithPath()) do kp, y
+        push!(named_params, (kp, y))
+        return y
+    end
+    return named_params
+end
+
+struct TrainableStructWalkWithPath <: AbstractWalk end
+
+function (::TrainableStructWalkWithPath)(recurse, kp::KeyPath, x)
+    x_children = trainable(x)
+    kps = mapkey(c -> KeyPath(kp, c), x_children)
+    return mapvalue(recurse, kps, x_children)
+end
+
+function ChainRulesCore.rrule(::typeof(_trainables_with_path), x)
+    y = _trainables_with_path(x)
+    trainables_with_path_back(Δ) = (NoTangent(), ∇trainables_with_path(x, unthunk(Δ)))
+    return y, trainables_with_path_back
+end
+
+function ∇trainables_with_path(x, Δ)
+    i = 0
+    return fmapstructure(x; exclude = isnumeric, walk = TrainableStructWalk()) do _
+                Δi = Δ[i+=1]
+                if isnothing(Δi)
+                    return nothing
+                else
+                    return Δi[2]
+                end
+           end
+end
diff --git a/src/utils.jl b/src/utils.jl
new file mode 100644
index 00000000..7c6c95be
--- /dev/null
+++ b/src/utils.jl
@@ -0,0 +1,15 @@
+
+mapvalue(f, x...) = map(f, x...)
+mapvalue(f, x::Dict, ys...) = Dict(k => f(v, (get(y, k, nothing) for y in ys)...) for (k,v) in x)
+
+mapkey(f, x::NamedTuple{Ks}) where Ks = NamedTuple{Ks}(map(f, Ks))
+mapkey(f, x::Dict) = Dict(k => f(k) for k in keys(x))
+mapkey(f, x::Tuple) = ntuple(i -> f(i), length(x))
+mapkey(f, x::AbstractArray) = [f(i) for i=1:length(x)]
+
+foreachvalue(f, x...) = foreach(f, x...)
+
+foreachvalue(f, x::Dict, ys...) = foreach(pairs(x)) do (k, v)
+  f(v, (get(y, k, nothing) for y in ys)...)
+end
+
diff --git a/test/trainables.jl b/test/trainables.jl
index d4b93ce8..e1aa0115 100644
--- a/test/trainables.jl
+++ b/test/trainables.jl
@@ -14,102 +14,128 @@ mat = Float32[4 6; 5 7]
 m9 = (a = m1, b = mat, c = [mat, m1])
 
 @testset "trainables" begin
-  ps = trainables(m1)
-  @test ps isa Vector
-  @test length(ps) == 1
-  @test ps[1] == m1
-
-  ps = trainables(m2)
-  @test ps isa Vector
-  @test length(ps) == 2
-  @test ps[1] == m2[1]
-  @test ps[2] == m2[2]
-
-  ps = trainables(m3)
-  @test length(ps) == 2
-  @test ps[1] == 1:3
-  @test ps[2] == 4:6
-
-  ps = trainables(m4)
-  @test length(ps) == 2
-  @test ps[1] == 1:3
-  @test ps[2] == 4:6
-  
-  ps = trainables(m5)
-  @test length(ps) == 3
-  @test ps[1] == 1:3
-  @test ps[2] == 4:6
-  @test ps[3] == 4:6
-
-  ps = trainables(m6)
-  @test length(ps) == 2
-  @test ps[1] == 1:3
-  @test ps[2] == ComplexF64[4.0 + 1.0im]
-
-  ps = trainables(m7)
-  @test length(ps) == 1
-  @test ps[1] == [1.0, 2.0, 3.0]
-
-  ps = trainables(m8)
-  @test length(ps) == 3
-  @test ps[1] == 1:3
-  @test ps[2] == [4.0]
-  @test ps[3] == [5.0]
-
-  ps = trainables(m9)
-  @test length(ps) == 2
-  @test ps[1] == 1:3
-  @test ps[2] == mat
+    ps = trainables(m1)
+    @test ps isa Vector
+    @test length(ps) == 1
+    @test ps[1] == m1
+
+    ps = trainables(m2)
+    @test ps isa Vector
+    @test length(ps) == 2
+    @test ps[1] == m2[1]
+    @test ps[2] == m2[2]
+
+    ps = trainables(m3)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == 4:6
+
+    ps = trainables(m4)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == 4:6
+    
+    ps = trainables(m5)
+    @test length(ps) == 3
+    @test ps[1] == 1:3
+    @test ps[2] == 4:6
+    @test ps[3] == 4:6
+
+    ps = trainables(m6)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == ComplexF64[4.0 + 1.0im]
+
+    ps = trainables(m7)
+    @test length(ps) == 1
+    @test ps[1] == [1.0, 2.0, 3.0]
+
+    ps = trainables(m8)
+    @test length(ps) == 3
+    @test ps[1] == 1:3
+    @test ps[2] == [4.0]
+    @test ps[3] == [5.0]
+
+    ps = trainables(m9)
+    @test length(ps) == 2
+    @test ps[1] == 1:3
+    @test ps[2] == mat
 end
 
 @testset "gradient" begin
-  loss(m) = sum([sum(abs2, p) for p in trainables(m)])
-  g = gradient(loss, m1)[1]
-  @test g == [2.0, 4.0, 6.0]
-
-  g = gradient(loss, m2)[1]
-  @test g == ([2.0, 4.0, 6.0], [8.0, 10.0, 12.0])
-
-  g = gradient(loss, m3)[1]
-  @test g.x == [2.0, 4.0, 6.0]
-  @test g.y === nothing
-  @test g.z == [8.0, 10.0, 12.0]
-
-  g = gradient(loss, m4)[1]
-  @test g == (x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0], z = [8.0, 10.0, 12.0])
-  g.x === g.y # shared gradient for shared weights
-
-  g = gradient(loss, m5)[1]
-  @test g == (a = ((x = [2.0, 4.0, 6.0], y = nothing, z = [8.0, 10.0, 12.0]), nothing), b = ([2.0, 4.0, 6.0], nothing), c = ((x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0], z = [8.0, 10.0, 12.0]), nothing))
-  
-  g = gradient(loss, m6)[1]
-  @test g == (a = [2.0, 4.0, 6.0], b = ComplexF64[8.0 + 2.0im], c = [2.0, 4.0, 6.0])
-  
-  g = gradient(loss, m7)[1]
-  @test g == (a = (nothing, [2.0, 4.0, 6.0]), b = nothing, c = nothing)
-
-  g = gradient(loss, m8)[1]
-  @test g[1] == (x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0])
-  @test g[2] == (a = nothing, b = (x = [8.0], y = nothing), c = nothing)
-  @test g[3] == [[10.0]]
-
-  g = gradient(loss, m9)[1]
-  @test g == (a = [2.0, 4.0, 6.0], b = Float32[8.0 12.0; 10.0 14.0], c = Array[Float32[8.0 12.0; 10.0 14.0], [2.0, 4.0, 6.0]])
+    loss(m) = sum([sum(abs2, p) for p in trainables(m)])
+    g = gradient(loss, m1)[1]
+    @test g == [2.0, 4.0, 6.0]
+
+    g = gradient(loss, m2)[1]
+    @test g == ([2.0, 4.0, 6.0], [8.0, 10.0, 12.0])
+
+    g = gradient(loss, m3)[1]
+    @test g.x == [2.0, 4.0, 6.0]
+    @test g.y === nothing
+    @test g.z == [8.0, 10.0, 12.0]
+
+    g = gradient(loss, m4)[1]
+    @test g == (x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0], z = [8.0, 10.0, 12.0])
+    g.x === g.y # shared gradient for shared weights
+
+    g = gradient(loss, m5)[1]
+    @test g == (a = ((x = [2.0, 4.0, 6.0], y = nothing, z = [8.0, 10.0, 12.0]), nothing), b = ([2.0, 4.0, 6.0], nothing), c = ((x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0], z = [8.0, 10.0, 12.0]), nothing))
+    
+    g = gradient(loss, m6)[1]
+    @test g == (a = [2.0, 4.0, 6.0], b = ComplexF64[8.0 + 2.0im], c = [2.0, 4.0, 6.0])
+    
+    g = gradient(loss, m7)[1]
+    @test g == (a = (nothing, [2.0, 4.0, 6.0]), b = nothing, c = nothing)
+
+    g = gradient(loss, m8)[1]
+    @test g[1] == (x = [2.0, 4.0, 6.0], y = [2.0, 4.0, 6.0])
+    @test g[2] == (a = nothing, b = (x = [8.0], y = nothing), c = nothing)
+    @test g[3] == [[10.0]]
+
+    g = gradient(loss, m9)[1]
+    @test g == (a = [2.0, 4.0, 6.0], b = Float32[8.0 12.0; 10.0 14.0], c = Array[Float32[8.0 12.0; 10.0 14.0], [2.0, 4.0, 6.0]])
+end
+
+@testset "dict" begin
+    d = Dict(:a => rand(2), :b => ones(2))
+    ps = trainables(d)
+    @test length(ps) == 2
+    @test ps[1] == d[:a]
+    @test ps[2] == d[:b]
+
+    g = gradient(d -> sum(trainables(d)[1].^2) /2 + sum(trainables(d)[2]), d)[1]
+    @test g[:a] == d[:a]
+    @test_broken g[:b] == [1.0, 1.0]
 end
 
 @testset "second order derivatives" begin
-  struct DenseLayer
-    w
-    b
-  end
+    struct DenseLayer
+        w
+        b
+    end
+
+    Functors.@functor DenseLayer
 
-  Functors.@functor DenseLayer
+    loss(m) = sum([sum(abs2, p) for p in trainables(m)])
+
+    model = DenseLayer([1. 2.; 3. 4.], [0., 0.])
+
+    g = gradient(m -> loss(gradient(loss, m)), model)[1]
+    @test g.w == [8.0 16.0; 24.0 32.0]
+    @test g.b == [0.0, 0.0]
+end
 
-  loss(m) = sum([sum(abs2, p) for p in trainables(m)])
+@testset "trainables(x, path=true)" begin
+    loss(m) = sum(abs2, trainables(m, path=true)[1][2])
 
-  model = DenseLayer([1. 2.; 3. 4.], [0., 0.])
+    ps = trainables(m4, path=true)
+    @test length(ps) == 2
+    @test ps[1] == (KeyPath(:x,), [1.0, 2.0, 3.0])
+    @test ps[2] == (KeyPath(:z,), [4.0, 5.0, 6.0])
 
-  g = gradient(m -> loss(gradient(loss, m)), model)[1]
-  @test g.w == [8.0 16.0; 24.0 32.0]
-  @test g.b == [0.0, 0.0]
+    g = gradient(loss, m4)[1]
+    @test g.x == [2.0, 4.0, 6.0]
+    @test g.y == [2.0, 4.0, 6.0]
+    @test g.z === nothing
 end