Further simplify rules

Author: Simone Carlo Surace

src/rulesets/LinearAlgebra/dense.jl

@@ -416,7 +416,7 @@ end
 function rrule(::typeof(kron), x::AbstractMatrix{<:Number}, y::AbstractVector{<:Number})
     function kron_pullback(z̄)
         dz = reshape(unthunk(z̄), length(y), size(x)...)
-        x̄ = @thunk Ref(y') .* eachslice(dz; dims = (2, 3))
+        x̄ = @thunk conj.(dot.(eachslice(dz; dims = (2, 3)), Ref(y)))
         ȳ = @thunk conj.(dot.(eachslice(dz; dims = 1), Ref(x)))
         return NoTangent(), x̄, ȳ
     end
@@ -427,7 +427,7 @@ function rrule(::typeof(kron), x::AbstractVector{<:Number}, y::AbstractMatrix{<:
     function kron_pullback(z̄)
         dz = reshape(unthunk(z̄), size(y, 1), length(x), size(y, 2))
         x̄ = @thunk conj.(dot.(eachslice(dz; dims = 2), Ref(y)))
-        ȳ = @thunk Ref(x') .* eachslice(dz; dims = (1, 3))
+        ȳ = @thunk conj.(dot.(eachslice(dz; dims = (1, 3)), Ref(x)))
         return NoTangent(), x̄, ȳ
     end
     return kron(x, y), kron_pullback
@@ -437,7 +437,7 @@ function rrule(::typeof(kron), x::AbstractMatrix{<:Number}, y::AbstractMatrix{<:
     function kron_pullback(z̄)
         dz = reshape(unthunk(z̄), size(y, 1), size(x, 1), size(y, 2), size(x, 2))
         x̄ = @thunk conj.(dot.(eachslice(dz, dims = (2, 4)), Ref(y)))
-        ȳ = @thunk dot.(eachslice(conj.(dz); dims = (1, 3)), Ref(conj.(x)))
+        ȳ = @thunk conj.(dot.(eachslice(dz; dims = (1, 3)), Ref(x)))
         return NoTangent(), x̄, ȳ
     end
     return kron(x, y), kron_pullback