diff --git a/ext/TensorOperationsChainRulesCoreExt.jl b/ext/TensorOperationsChainRulesCoreExt.jl
index 3d7fbd4..a838917 100644
--- a/ext/TensorOperationsChainRulesCoreExt.jl
+++ b/ext/TensorOperationsChainRulesCoreExt.jl
@@ -18,6 +18,8 @@ trivtuple(N) = ntuple(identity, N)
 @non_differentiable TensorOperations.tensorcontract_structure(args...)
 @non_differentiable TensorOperations.tensorcontract_type(args...)
 @non_differentiable TensorOperations.tensoralloc_contract(args...)
+@non_differentiable TensorOperations.promote_contract(args...)
+@non_differentiable TensorOperations.promote_add(args...)
 
 # Cannot free intermediate tensors when using AD
 # Thus we change the forward passes: `istemp=false` and `tensorfree!` is a no-op
@@ -38,11 +40,11 @@ function ChainRulesCore.rrule(
     return output, tensoralloc_pullback
 end
 
-# TODO: possibly use the non-inplace functions, to avoid depending on Base.copy
 function ChainRulesCore.rrule(::typeof(tensorscalar), C)
+    projectC = ProjectTo(C)
     function tensorscalar_pullback(Δc)
-        ΔC = TensorOperations.tensoralloc(typeof(C), TensorOperations.tensorstructure(C))
-        return NoTangent(), fill!(ΔC, unthunk(Δc))
+        _Δc = unthunk(Δc)
+        return NoTangent(), projectC(_Δc)
     end
     return tensorscalar(C), tensorscalar_pullback
 end
@@ -95,7 +97,7 @@ function _rrule_tensoradd!(C, A, pA, conjA, α, β, ba)
             ipA = invperm(linearize(pA))
             _dA = zerovector(A, VectorInterface.promote_add(ΔC, α))
             _dA = tensoradd!(_dA, ΔC, (ipA, ()), conjA, conjA ? α : conj(α), Zero(), ba...)
-            return projectA(_dA)
+            projectA(_dA)
         end
         dα = @thunk let
             _dα = tensorscalar(
@@ -105,7 +107,7 @@ function _rrule_tensoradd!(C, A, pA, conjA, α, β, ba)
                     ((), ()), One(), ba...
                 )
             )
-            return projectα(_dα)
+            projectα(_dα)
         end
         dβ = @thunk let
             # TODO: consider using `inner`
@@ -116,7 +118,7 @@ function _rrule_tensoradd!(C, A, pA, conjA, α, β, ba)
                     ((), ()), One(), ba...
                 )
             )
-            return projectβ(_dβ)
+            projectβ(_dβ)
         end
         dba = map(_ -> NoTangent(), ba)
         return NoTangent(), dC, dA, NoTangent(), NoTangent(), dα, dβ, dba...
@@ -194,7 +196,7 @@ function _rrule_tensorcontract!(C, A, pA, conjA, B, pB, conjB, pAB, α, β, ba)
                 ipA,
                 conjA ? α : conj(α), Zero(), ba...
             )
-            return projectA(_dA)
+            projectA(_dA)
         end
         dB = @thunk let
             ipB = (invperm(linearize(pB)), ())
@@ -208,7 +210,7 @@ function _rrule_tensorcontract!(C, A, pA, conjA, B, pB, conjB, pAB, α, β, ba)
                 ipB,
                 conjB ? α : conj(α), Zero(), ba...
             )
-            return projectB(_dB)
+            projectB(_dB)
         end
         dα = @thunk let
             C_αβ = tensorcontract(A, pA, conjA, B, pB, conjB, pAB, One(), ba...)
@@ -220,7 +222,7 @@ function _rrule_tensorcontract!(C, A, pA, conjA, B, pB, conjB, pAB, α, β, ba)
                     ((), ()), One(), ba...
                 )
             )
-            return projectα(_dα)
+            projectα(_dα)
         end
         dβ = @thunk let
             # TODO: consider using `inner`
@@ -231,7 +233,7 @@ function _rrule_tensorcontract!(C, A, pA, conjA, B, pB, conjB, pAB, α, β, ba)
                     ((), ()), One(), ba...
                 )
             )
-            return projectβ(_dβ)
+            projectβ(_dβ)
         end
         dba = map(_ -> NoTangent(), ba)
         return NoTangent(), dC,
@@ -283,7 +285,7 @@ function _rrule_tensortrace!(C, A, p, q, conjA, α, β, ba)
         dA = @thunk let
             ip = invperm((linearize(p)..., q[1]..., q[2]...))
             Es = map(q[1], q[2]) do i1, i2
-                return one(
+                one(
                     TensorOperations.tensoralloc_add(
                         scalartype(A), A, ((i1,), (i2,)), conjA
                     )
@@ -297,7 +299,7 @@ function _rrule_tensortrace!(C, A, p, q, conjA, α, β, ba)
                 (ip, ()),
                 conjA ? α : conj(α), Zero(), ba...
             )
-            return projectA(_dA)
+            projectA(_dA)
         end
         dα = @thunk let
             C_αβ = tensortrace(A, p, q, false, One(), ba...)
@@ -309,7 +311,7 @@ function _rrule_tensortrace!(C, A, p, q, conjA, α, β, ba)
                     ((), ()), One(), ba...
                 )
             )
-            return projectα(_dα)
+            projectα(_dα)
         end
         dβ = @thunk let
             _dβ = tensorscalar(
@@ -319,7 +321,7 @@ function _rrule_tensortrace!(C, A, p, q, conjA, α, β, ba)
                     ((), ()), One(), ba...
                 )
             )
-            return projectβ(_dβ)
+            projectβ(_dβ)
         end
         dba = map(_ -> NoTangent(), ba)
         return NoTangent(), dC, dA, NoTangent(), NoTangent(), NoTangent(), dα, dβ, dba...