diff --git a/captum/_utils/common.py b/captum/_utils/common.py
index 2470ae0c1..12784bfaf 100644
--- a/captum/_utils/common.py
+++ b/captum/_utils/common.py
@@ -12,6 +12,7 @@
     Dict,
     List,
     Literal,
+    Optional,
     overload,
     Sequence,
     Tuple,
@@ -272,28 +273,9 @@ def _format_float_or_tensor_into_tuples(
     return inputs
 
 
-@overload
-def _format_additional_forward_args(additional_forward_args: None) -> None: ...
-
-
-@overload
 def _format_additional_forward_args(
-    # pyre-fixme[24]: Generic type `tuple` expects at least 1 type parameter.
-    additional_forward_args: Union[Tensor, Tuple]
-    # pyre-fixme[24]: Generic type `tuple` expects at least 1 type parameter.
-) -> Tuple: ...
-
-
-@overload
-def _format_additional_forward_args(  # type: ignore
-    # pyre-fixme[2]: Parameter annotation cannot be `Any`.
-    additional_forward_args: Any,
-    # pyre-fixme[24]: Generic type `tuple` expects at least 1 type parameter.
-) -> Union[None, Tuple]: ...
-
-
-# pyre-fixme[24]: Generic type `tuple` expects at least 1 type parameter.
-def _format_additional_forward_args(additional_forward_args: Any) -> Union[None, Tuple]:
+    additional_forward_args: Optional[object],
+) -> Union[None, Tuple[object, ...]]:
     if additional_forward_args is not None and not isinstance(
         additional_forward_args, tuple
     ):
@@ -853,8 +835,7 @@ def _register_backward_hook(
     module: Module,
     # pyre-fixme[24]: Generic type `Callable` expects 2 type parameters.
     hook: Callable,
-    # pyre-fixme[2]: Parameter annotation cannot be `Any`.
-    attr_obj: Any,
+    attr_obj: Union[object, None],
 ) -> List[torch.utils.hooks.RemovableHandle]:
     grad_out: Dict[device, Tensor] = {}
 
@@ -864,10 +845,9 @@ def forward_hook(
         out: Union[Tensor, Tuple[Tensor, ...]],
     ) -> None:
         nonlocal grad_out
-        grad_out = {}
 
-        # pyre-fixme[53]: Captured variable `grad_out` is not annotated.
         def output_tensor_hook(output_grad: Tensor) -> None:
+            nonlocal grad_out
             grad_out[output_grad.device] = output_grad
 
         if isinstance(out, tuple):
@@ -878,18 +858,19 @@ def output_tensor_hook(output_grad: Tensor) -> None:
         else:
             out.register_hook(output_tensor_hook)
 
-    # pyre-fixme[3]: Return type must be annotated.
-    # pyre-fixme[2]: Parameter must be annotated.
-    def pre_hook(module, inp):
-        # pyre-fixme[53]: Captured variable `module` is not annotated.
-        # pyre-fixme[3]: Return type must be annotated.
-        def input_tensor_hook(input_grad: Tensor):
+    def pre_hook(module: Module, inp: Union[Tensor, Tuple[Tensor, ...]]) -> Tensor:
+        def input_tensor_hook(
+            input_grad: Tensor,
+        ) -> Union[None, Tensor, Tuple[Tensor, ...]]:
+            nonlocal grad_out
+
             if len(grad_out) == 0:
-                return
+                return None
             hook_out = hook(module, input_grad, grad_out[input_grad.device])
 
             if hook_out is not None:
                 return hook_out[0] if isinstance(hook_out, tuple) else hook_out
+            return None
 
         if isinstance(inp, tuple):
             assert (