diff --git a/colossalai/tensor/shape_consistency.py b/colossalai/tensor/shape_consistency.py
index 4ec5ad9e9..d5d28db0f 100644
--- a/colossalai/tensor/shape_consistency.py
+++ b/colossalai/tensor/shape_consistency.py
@@ -1,17 +1,12 @@
 import math
-import operator
 from copy import deepcopy
 from dataclasses import dataclass
-from enum import Enum
-from functools import reduce
-from typing import Dict, List, Optional, Tuple, Union
+from typing import Dict, List, Tuple
 
 import torch
-import torch.distributed as dist
-from torch.distributed import ReduceOp
 
 from colossalai.context.singleton_meta import SingletonMeta
-from colossalai.tensor.sharding_spec import ShardingSpec, ShardingSpecException, _DimSpec
+from colossalai.tensor.sharding_spec import ShardingSpec, ShardingSpecException
 from colossalai.tensor.utils import all_gather_simulator, all_to_all_simulator, shard_simulator
 
 from .comm_spec import *
@@ -28,7 +23,7 @@ class ShapeConsistencyOptions:
     pass
 
 
-def to_global(distributed_tensor: torch.Tensor, sharding_spec: ShardingSpec):
+def to_global(distributed_tensor: torch.Tensor, sharding_spec: ShardingSpec) -> torch.Tensor:
     shape_consistency_manager = ShapeConsistencyManager()
     global_sharding_spec = ShardingSpec(sharding_spec.device_mesh, sharding_spec.entire_shape, {})
     with torch.no_grad():
@@ -72,7 +67,8 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
         assert isinstance(value, bool)
         self._forward_only = value
 
-    def get_all_all_gather_spec(self, source_spec, orig_cost_dict):
+    def get_all_all_gather_spec(self, source_spec: ShardingSpec,
+                                orig_cost_dict: Dict[str, float]) -> Dict[ShardingSpec, float]:
         '''
         Get all valid sharding specs from source_spec with single all-gather operation, and
         accumulate commucation cost on origin cost which will finally be used in auto sharding solver.
@@ -80,7 +76,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
 
         Argument:
             source_spec(ShardingSpec): the ShardingSpec of the source_spec.
-            orig_cost(float): the original communication cost before this operation.
+            orig_cost(Dict[str, float]): the original communication cost before this operation.
 
         Return:
             valid_spec_dict(Dict[ShardingSpec, float]): all valid sharding specs from source_spec with single all-gather operation.
@@ -92,7 +88,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
             #     device_mesh_shape: (4, 4)
             sharding_spec = ShardingSpec(device_mesh, entire_shape, dim_partition_dict)
             shape_consistency_manager = ShapeConsistencyManager()
-            rst_dict = shape_consistency_manager.get_all_all_gather_spec(sharding_spec, 0)
+            rst_dict = shape_consistency_manager.get_all_all_gather_spec(sharding_spec, {'forward': 0, 'backward': 0, 'total': 0})
             print(rst_dict)
 
         Output:
@@ -143,7 +139,8 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
                 pass
         return valid_spec_dict
 
-    def get_all_all_to_all_spec(self, source_spec, orig_cost_dict):
+    def get_all_all_to_all_spec(self, source_spec: ShardingSpec,
+                                orig_cost_dict: Dict[str, float]) -> Dict[ShardingSpec, float]:
         '''
         Get all valid sharding specs from source_spec with single all-to-all operation, and
         accumulate commucation cost on origin cost which will finally be used in auto sharding solver.
@@ -151,7 +148,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
 
         Argument:
             source_spec(ShardingSpec): the ShardingSpec of the source_spec.
-            orig_cost(float): the original communication cost before this operation.
+            orig_cost(Dict[str, float]): the original communication cost before this operation.
 
         Return:
             valid_spec_dict(Dict[ShardingSpec, float]): all valid sharding specs from source_spec with single all-to-all operation.
@@ -163,7 +160,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
             #     device_mesh_shape: (4, 4)
             sharding_spec = ShardingSpec(device_mesh, entire_shape, dim_partition_dict)
             shape_consistency_manager = ShapeConsistencyManager()
-            rst_dict = shape_consistency_manager.get_all_all_to_all_spec(sharding_spec, 0)
+            rst_dict = shape_consistency_manager.get_all_all_to_all_spec(sharding_spec, {'forward': 0, 'backward': 0, 'total': 0})
             print(rst_dict)
 
         Output:
@@ -250,7 +247,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
 
         return valid_spec_dict
 
-    def get_all_shard_spec(self, source_spec, orig_cost_dict):
+    def get_all_shard_spec(self, source_spec: ShardingSpec, orig_cost_dict):
         '''
         Get all valid sharding specs from source_spec with single shard operation, and
         accumulate commucation cost on origin cost which will finally be used in auto sharding solver.
@@ -270,7 +267,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
             #     device_mesh_shape: (4, 4)
             sharding_spec = ShardingSpec(device_mesh, entire_shape, dim_partition_dict)
             shape_consistency_manager = ShapeConsistencyManager()
-            rst_dict = shape_consistency_manager.get_all_shard_spec(sharding_spec, 0)
+            rst_dict = shape_consistency_manager.get_all_shard_spec(sharding_spec, {'forward': 0, 'backward': 0, 'total': 0})
             print(rst_dict)
 
         Output:
@@ -331,7 +328,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
                     pass
         return valid_spec_dict
 
-    def get_all_one_step_transform_spec(self, source_spec, orig_cost_dict):
+    def get_all_one_step_transform_spec(self, source_spec: ShardingSpec, orig_cost_dict) -> Dict[ShardingSpec, float]:
         '''
         Get all valid sharding specs from source_spec with one step transform, and
         accumulate commucation cost on origin cost which will finally be used in auto sharding solver.
@@ -353,7 +350,8 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
         valid_spec_dict.update(self.get_all_shard_spec(source_spec, orig_cost_dict))
         return valid_spec_dict
 
-    def shape_consistency(self, source_spec, target_spec):
+    def shape_consistency(self, source_spec: ShardingSpec,
+                          target_spec: ShardingSpec) -> Tuple[List[ShardingSpec], List[CommSpec], float]:
         '''
         This method will find a path to transform source_spec to target_spec with
         a greedy algorithm.
@@ -459,7 +457,7 @@ class ShapeConsistencyManager(metaclass=SingletonMeta):
 
         raise RuntimeError(f"Could not find a valid transform path with in {MAX_TRANSFORM_STEPS} steps.")
 
-    def apply(self, tensor_with_sharding_spec, target_spec):
+    def apply(self, tensor_with_sharding_spec: torch.Tensor, target_spec: ShardingSpec) -> torch.Tensor:
         '''
         Apply target_spec to tensor with source sharding spec, the transform path is generated by the
         shape_consistency method.