diff --git a/src/transformers/models/ctrl/modeling_ctrl.py b/src/transformers/models/ctrl/modeling_ctrl.py
index f03046928ca4..6eac103ac8ff 100644
--- a/src/transformers/models/ctrl/modeling_ctrl.py
+++ b/src/transformers/models/ctrl/modeling_ctrl.py
@@ -15,7 +15,7 @@
 # limitations under the License.
 """ PyTorch CTRL model."""
 
-from typing import Tuple
+from typing import Optional, Tuple, Union
 
 import numpy as np
 import torch
@@ -359,18 +359,18 @@ def _prune_heads(self, heads_to_prune):
     )
     def forward(
         self,
-        input_ids=None,
-        past_key_values=None,
-        attention_mask=None,
-        token_type_ids=None,
-        position_ids=None,
-        head_mask=None,
-        inputs_embeds=None,
-        use_cache=None,
-        output_attentions=None,
-        output_hidden_states=None,
-        return_dict=None,
-    ):
+        input_ids: Optional[torch.LongTensor] = None,
+        past_key_values: Optional[Tuple[Tuple[torch.FloatTensor]]] = None,
+        attention_mask: Optional[torch.FloatTensor] = None,
+        token_type_ids: Optional[torch.LongTensor] = None,
+        position_ids: Optional[torch.LongTensor] = None,
+        head_mask: Optional[torch.FloatTensor] = None,
+        inputs_embeds: Optional[torch.FloatTensor] = None,
+        use_cache: Optional[bool] = None,
+        output_attentions: Optional[bool] = None,
+        output_hidden_states: Optional[bool] = None,
+        return_dict: Optional[bool] = None,
+    ) -> Union[Tuple[torch.Tensor], BaseModelOutputWithPast]:
 
         output_attentions = output_attentions if output_attentions is not None else self.config.output_attentions
         use_cache = use_cache if use_cache is not None else self.config.use_cache
@@ -521,19 +521,19 @@ def prepare_inputs_for_generation(self, input_ids, past=None, use_cache=None, **
     )
     def forward(
         self,
-        input_ids=None,
-        past_key_values=None,
-        attention_mask=None,
-        token_type_ids=None,
-        position_ids=None,
-        head_mask=None,
-        inputs_embeds=None,
-        labels=None,
-        use_cache=None,
-        output_attentions=None,
-        output_hidden_states=None,
-        return_dict=None,
-    ):
+        input_ids: Optional[torch.LongTensor] = None,
+        past_key_values: Optional[Tuple[Tuple[torch.FloatTensor]]] = None,
+        attention_mask: Optional[torch.FloatTensor] = None,
+        token_type_ids: Optional[torch.LongTensor] = None,
+        position_ids: torch.LongTensor = None,
+        head_mask: torch.FloatTensor = None,
+        inputs_embeds: torch.FloatTensor = None,
+        labels: Optional[torch.LongTensor] = None,
+        use_cache: Optional[bool] = None,
+        output_attentions: Optional[bool] = None,
+        output_hidden_states: Optional[bool] = None,
+        return_dict: Optional[bool] = None,
+    ) -> Union[Tuple[torch.Tensor], CausalLMOutputWithPast]:
         r"""
         labels (`torch.LongTensor` of shape `(batch_size, sequence_length)`, *optional*):
             Labels for language modeling. Note that the labels **are shifted** inside the model, i.e. you can set
@@ -625,19 +625,19 @@ def __init__(self, config):
     )
     def forward(
         self,
-        input_ids=None,
-        past_key_values=None,
-        attention_mask=None,
-        token_type_ids=None,
-        position_ids=None,
-        head_mask=None,
-        inputs_embeds=None,
-        labels=None,
-        use_cache=None,
-        output_attentions=None,
-        output_hidden_states=None,
-        return_dict=None,
-    ):
+        input_ids: Optional[torch.LongTensor] = None,
+        past_key_values: Optional[Tuple[Tuple[torch.FloatTensor]]] = None,
+        attention_mask: Optional[torch.FloatTensor] = None,
+        token_type_ids: Optional[torch.LongTensor] = None,
+        position_ids: Optional[torch.LongTensor] = None,
+        head_mask: Optional[torch.FloatTensor] = None,
+        inputs_embeds: Optional[torch.FloatTensor] = None,
+        labels: Optional[torch.LongTensor] = None,
+        use_cache: Optional[bool] = None,
+        output_attentions: Optional[bool] = None,
+        output_hidden_states: Optional[bool] = None,
+        return_dict: Optional[bool] = None,
+    ) -> Union[Tuple[torch.Tensor], SequenceClassifierOutput]:
         r"""
         labels (`torch.LongTensor` of shape `(batch_size,)`, *optional*):
             Labels for computing the sequence classification/regression loss. Indices should be in `[0, ...,