diff --git a/src/torchjd/autojac/_transform/diagonalize.py b/src/torchjd/autojac/_transform/diagonalize.py
index 903b5e591..a1283ba86 100644
--- a/src/torchjd/autojac/_transform/diagonalize.py
+++ b/src/torchjd/autojac/_transform/diagonalize.py
@@ -1,5 +1,3 @@
-from typing import Iterable
-
 import torch
 from torch import Tensor
 
@@ -9,29 +7,28 @@
 
 
 class Diagonalize(Transform[Gradients, Jacobians]):
-    def __init__(self, considered: Iterable[Tensor]):
-        self.considered = OrderedSet(considered)
+    def __init__(self, key_order: OrderedSet[Tensor]):
+        self.key_order = key_order
         self.indices: list[tuple[int, int]] = []
         begin = 0
-        for tensor in self.considered:
+        for tensor in self.key_order:
             end = begin + tensor.numel()
             self.indices.append((begin, end))
             begin = end
 
     def __call__(self, tensors: Gradients) -> Jacobians:
-        flattened_considered_values = [tensors[key].reshape([-1]) for key in self.considered]
+        flattened_considered_values = [tensors[key].reshape([-1]) for key in self.key_order]
         diagonal_matrix = torch.cat(flattened_considered_values).diag()
         diagonalized_tensors = {
             key: diagonal_matrix[:, begin:end].reshape((-1,) + key.shape)
-            for (begin, end), key in zip(self.indices, self.considered)
+            for (begin, end), key in zip(self.indices, self.key_order)
         }
         return Jacobians(diagonalized_tensors)
 
     def check_keys(self, input_keys: set[Tensor]) -> set[Tensor]:
-        considered = set(self.considered)
-        if not considered == input_keys:
+        if not set(self.key_order) == input_keys:
             raise RequirementError(
-                f"The input_keys must match the considered keys. Found input_keys {input_keys} and"
-                f"considered keys {considered}."
+                f"The input_keys must match the key_order. Found input_keys {input_keys} and"
+                f"key_order {self.key_order}."
             )
-        return considered
+        return input_keys
diff --git a/src/torchjd/autojac/backward.py b/src/torchjd/autojac/backward.py
index 12aada35a..6478bd578 100644
--- a/src/torchjd/autojac/backward.py
+++ b/src/torchjd/autojac/backward.py
@@ -103,7 +103,7 @@ def _create_transform(
     init = Init(tensors)
 
     # Transform that turns the gradients into Jacobians.
-    diag = Diagonalize(tensors)
+    diag = Diagonalize(OrderedSet(tensors))
 
     # Transform that computes the required Jacobians.
     jac = Jac(tensors, inputs, parallel_chunk_size, retain_graph)
diff --git a/tests/unit/autojac/_transform/test_diagonalize.py b/tests/unit/autojac/_transform/test_diagonalize.py
index cf29ec05c..95986948a 100644
--- a/tests/unit/autojac/_transform/test_diagonalize.py
+++ b/tests/unit/autojac/_transform/test_diagonalize.py
@@ -2,6 +2,7 @@
 from pytest import raises
 
 from torchjd.autojac._transform import Diagonalize, Gradients, RequirementError
+from torchjd.autojac._transform.ordered_set import OrderedSet
 
 from ._dict_assertions import assert_tensor_dicts_are_close
 
@@ -13,7 +14,7 @@ def test_single_input():
     value = torch.ones_like(key)
     input = Gradients({key: value})
 
-    diag = Diagonalize([key])
+    diag = Diagonalize(OrderedSet([key]))
 
     output = diag(input)
     expected_output = {key: torch.tensor([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]])}
@@ -32,7 +33,7 @@ def test_multiple_inputs():
     value3 = torch.ones_like(key3)
     input = Gradients({key1: value1, key2: value2, key3: value3})
 
-    diag = Diagonalize([key1, key2, key3])
+    diag = Diagonalize(OrderedSet([key1, key2, key3]))
 
     output = diag(input)
     expected_output = {
@@ -88,8 +89,8 @@ def test_permute_order():
     value2 = torch.ones_like(key2)
     input = Gradients({key1: value1, key2: value2})
 
-    permuted_diag = Diagonalize([key2, key1])
-    diag = Diagonalize([key1, key2])
+    permuted_diag = Diagonalize(OrderedSet([key2, key1]))
+    diag = Diagonalize(OrderedSet([key1, key2]))
 
     permuted_output = permuted_diag(input)
     output = {key1: permuted_output[key2], key2: permuted_output[key1]}  # un-permute
@@ -106,7 +107,7 @@ def test_check_keys():
 
     key1 = torch.tensor([1.0])
     key2 = torch.tensor([1.0])
-    diag = Diagonalize([key1])
+    diag = Diagonalize(OrderedSet([key1]))
 
     output_keys = diag.check_keys({key1})
     assert output_keys == {key1}
diff --git a/tests/unit/autojac/_transform/test_interactions.py b/tests/unit/autojac/_transform/test_interactions.py
index ccebcba3d..ef5626ae5 100644
--- a/tests/unit/autojac/_transform/test_interactions.py
+++ b/tests/unit/autojac/_transform/test_interactions.py
@@ -17,6 +17,7 @@
     Stack,
     TensorDict,
 )
+from torchjd.autojac._transform.ordered_set import OrderedSet
 
 from ._dict_assertions import assert_tensor_dicts_are_close
 
@@ -35,7 +36,7 @@ def test_jac_is_stack_of_grads():
     input = Gradients({y1: torch.ones_like(y1), y2: torch.ones_like(y2)})
 
     jac = Jac(outputs=[y1, y2], inputs=[a1, a2], chunk_size=None, retain_graph=True)
-    diag = Diagonalize([y1, y2])
+    diag = Diagonalize(OrderedSet([y1, y2]))
     jac_diag = jac << diag
 
     grad1 = Grad(outputs=[y1], inputs=[a1, a2])
@@ -101,7 +102,7 @@ def test_multiple_differentiations():
 def test_str():
     """Tests that the __str__ method works correctly even for a complex transform."""
     init = Init([])
-    diag = Diagonalize([])
+    diag = Diagonalize(OrderedSet([]))
     jac = Jac([], [], chunk_size=None)
     transform = jac << diag << init