diff --git a/colossalai/amp/naive_amp/_fp16_optimizer.py b/colossalai/amp/naive_amp/_fp16_optimizer.py
index b1fc621c2..01842590f 100644
--- a/colossalai/amp/naive_amp/_fp16_optimizer.py
+++ b/colossalai/amp/naive_amp/_fp16_optimizer.py
@@ -14,7 +14,7 @@ from colossalai.context.parallel_mode import ParallelMode
 from colossalai.core import global_context as gpc
 from colossalai.logging import get_dist_logger
 from colossalai.utils import (print_rank_0, copy_tensor_parallel_attributes,
-                              clip_grad_norm_fp32, count_zeros_fp32, multi_tensor_applier, is_using_pp)
+                              clip_grad_norm_fp32, count_zeros_fp32, multi_tensor_applier)
 
 
 def _zero_grad_group_helper(group, set_to_none):
diff --git a/colossalai/nn/optimizer/cpu_adam.py b/colossalai/nn/optimizer/cpu_adam.py
index 21f607c48..55f50bfdc 100644
--- a/colossalai/nn/optimizer/cpu_adam.py
+++ b/colossalai/nn/optimizer/cpu_adam.py
@@ -1,10 +1,4 @@
-# modified from https://github.com/microsoft/DeepSpeed/blob/master/deepspeed/ops/adam/cpu_adam.py
-
-import math
 import torch
-import time
-from pathlib import Path
-import colossalai
 
 
 class CPUAdam(torch.optim.Optimizer):