diff --git a/torchmetrics/classification/__init__.py b/torchmetrics/classification/__init__.py
index 36ebd20781b..023b1ed59e5 100644
--- a/torchmetrics/classification/__init__.py
+++ b/torchmetrics/classification/__init__.py
@@ -24,7 +24,7 @@
 from torchmetrics.classification.hamming_distance import HammingDistance  # noqa: F401
 from torchmetrics.classification.hinge import Hinge  # noqa: F401
 from torchmetrics.classification.iou import IoU  # noqa: F401
-from torchmetrics.classification.kldivergence import KLDivergence  # noqa: F401
+from torchmetrics.classification.kl_divergence import KLDivergence  # noqa: F401
 from torchmetrics.classification.matthews_corrcoef import MatthewsCorrcoef  # noqa: F401
 from torchmetrics.classification.precision_recall import Precision, Recall  # noqa: F401
 from torchmetrics.classification.precision_recall_curve import PrecisionRecallCurve  # noqa: F401
diff --git a/torchmetrics/classification/kldivergence.py b/torchmetrics/classification/kl_divergence.py
similarity index 95%
rename from torchmetrics/classification/kldivergence.py
rename to torchmetrics/classification/kl_divergence.py
index 08bec92962a..c8935d60ae2 100644
--- a/torchmetrics/classification/kldivergence.py
+++ b/torchmetrics/classification/kl_divergence.py
@@ -11,12 +11,12 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Callable, List, Optional, Union
+from typing import Any, Callable, Optional
 
 import torch
 from torch import Tensor
 
-from torchmetrics.functional.classification.kldivergence import _kld_compute, _kld_update
+from torchmetrics.functional.classification.kl_divergence import _kld_compute, _kld_update
 from torchmetrics.metric import Metric
 from torchmetrics.utilities.data import dim_zero_cat
 
@@ -60,6 +60,8 @@ class KLDivergence(Metric):
         >>> kldivergence(p, q)
         tensor(0.0853)
     """
+    # canot be used because if scripting
+    # measures: Union[List[Tensor], Tensor]
     total: Tensor
 
     def __init__(
diff --git a/torchmetrics/classification/stat_scores.py b/torchmetrics/classification/stat_scores.py
index 5a1ec84bc6f..87dab7927ca 100644
--- a/torchmetrics/classification/stat_scores.py
+++ b/torchmetrics/classification/stat_scores.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Any, Callable, Optional, Tuple, Union, List
+from typing import Any, Callable, Optional, Tuple
 
 import torch
 from torch import Tensor
@@ -130,6 +130,12 @@ class StatScores(Metric):
 
     """
 
+    # canot be used because if scripting
+    # tp: Union[Tensor, List[Tensor]]
+    # fp: Union[Tensor, List[Tensor]]
+    # tn: Union[Tensor, List[Tensor]]
+    # fn: Union[Tensor, List[Tensor]]
+
     def __init__(
         self,
         threshold: float = 0.5,
diff --git a/torchmetrics/functional/__init__.py b/torchmetrics/functional/__init__.py
index 8074ebab775..631ef7e4246 100644
--- a/torchmetrics/functional/__init__.py
+++ b/torchmetrics/functional/__init__.py
@@ -25,7 +25,7 @@
 from torchmetrics.functional.classification.hamming_distance import hamming_distance  # noqa: F401
 from torchmetrics.functional.classification.hinge import hinge  # noqa: F401
 from torchmetrics.functional.classification.iou import iou  # noqa: F401
-from torchmetrics.functional.classification.kldivergence import kldivergence  # noqa: F401
+from torchmetrics.functional.classification.kl_divergence import kldivergence  # noqa: F401
 from torchmetrics.functional.classification.matthews_corrcoef import matthews_corrcoef  # noqa: F401
 from torchmetrics.functional.classification.precision_recall import precision, precision_recall, recall  # noqa: F401
 from torchmetrics.functional.classification.precision_recall_curve import precision_recall_curve  # noqa: F401
diff --git a/torchmetrics/functional/classification/__init__.py b/torchmetrics/functional/classification/__init__.py
index 205f67b8b67..d8319601f23 100644
--- a/torchmetrics/functional/classification/__init__.py
+++ b/torchmetrics/functional/classification/__init__.py
@@ -22,7 +22,7 @@
 from torchmetrics.functional.classification.hamming_distance import hamming_distance  # noqa: F401
 from torchmetrics.functional.classification.hinge import hinge  # noqa: F401
 from torchmetrics.functional.classification.iou import iou  # noqa: F401
-from torchmetrics.functional.classification.kldivergence import kldivergence  # noqa: F401
+from torchmetrics.functional.classification.kl_divergence import kldivergence  # noqa: F401
 from torchmetrics.functional.classification.matthews_corrcoef import matthews_corrcoef  # noqa: F401
 from torchmetrics.functional.classification.precision_recall import precision, precision_recall, recall  # noqa: F401
 from torchmetrics.functional.classification.precision_recall_curve import precision_recall_curve  # noqa: F401
diff --git a/torchmetrics/functional/classification/kldivergence.py b/torchmetrics/functional/classification/kl_divergence.py
similarity index 100%
rename from torchmetrics/functional/classification/kldivergence.py
rename to torchmetrics/functional/classification/kl_divergence.py