diff --git a/deeplink_ext/internlm_ops/adamw/deeplink.py b/deeplink_ext/internlm_ops/adamw/deeplink.py
index 7bc5b2b2..e2bc8732 100644
--- a/deeplink_ext/internlm_ops/adamw/deeplink.py
+++ b/deeplink_ext/internlm_ops/adamw/deeplink.py
@@ -2,23 +2,27 @@
 
 import torch
 import deeplink_ext.cpp_extensions as ext
+
 assert hasattr(ext, "adamw")
 
-def adamw(params: List[Tensor],
-          grads: List[Tensor],
-          exp_avgs: List[Tensor],
-          exp_avg_sqs: List[Tensor],
-          max_exp_avg_sqs: List[Tensor],
-          state_steps: List[int],
-          *,
-          amsgrad: bool,
-          beta1: float,
-          beta2: float,
-          lr: float,
-          weight_decay: float,
-          eps: float,
-          maximize: bool,
-          norm_coeff_scale: float):
+
+def adamw(
+    params: List[Tensor],
+    grads: List[Tensor],
+    exp_avgs: List[Tensor],
+    exp_avg_sqs: List[Tensor],
+    max_exp_avg_sqs: List[Tensor],
+    state_steps: List[int],
+    *,
+    amsgrad: bool,
+    beta1: float,
+    beta2: float,
+    lr: float,
+    weight_decay: float,
+    eps: float,
+    maximize: bool,
+    norm_coeff_scale: float
+):
     r"""Functional API that performs AdamW algorithm computation.
     See :class:`~torch.optim.AdamW` for details.
     """
@@ -32,13 +36,35 @@ def adamw(params: List[Tensor],
         exp_avg_sq = exp_avg_sqs[i]
         step = state_steps[i]
         max_exp_avg_sq = max_exp_avg_sqs[i]
-        param, exp_avg, exp_avg_sq = ext.adamw(param, exp_avg, exp_avg_sq, max_exp_avg_sq, grad, lr, 
-                                            beta1, beta2, eps, weight_decay, step, amsgrad)
+        param, exp_avg, exp_avg_sq = ext.adamw(
+            param,
+            exp_avg,
+            exp_avg_sq,
+            max_exp_avg_sq,
+            grad,
+            lr,
+            beta1,
+            beta2,
+            eps,
+            weight_decay,
+            step,
+            amsgrad,
+        )
     return params, exp_avgs, exp_avg_sq
 
+
 class DeepLinkAdamW(torch.optim.optimizer):
-    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
-                 weight_decay=1e-2, amsgrad=False, *, maximize: bool = False):
+    def __init__(
+        self,
+        params,
+        lr=1e-3,
+        betas=(0.9, 0.999),
+        eps=1e-8,
+        weight_decay=1e-2,
+        amsgrad=False,
+        *,
+        maximize: bool = False
+    ):
         if not 0.0 <= lr:
             raise ValueError("Invalid learning rate: {}".format(lr))
         if not 0.0 <= eps:
@@ -49,16 +75,22 @@ def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
             raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
         if not 0.0 <= weight_decay:
             raise ValueError("Invalid weight_decay value: {}".format(weight_decay))
-        defaults = dict(lr=lr, betas=betas, eps=eps,
-                        weight_decay=weight_decay, amsgrad=amsgrad, maximize=maximize)
+        defaults = dict(
+            lr=lr,
+            betas=betas,
+            eps=eps,
+            weight_decay=weight_decay,
+            amsgrad=amsgrad,
+            maximize=maximize,
+        )
         super(DeeplinkAdamW, self).__init__(params, defaults)
-    
+
     def __setstate__(self, state):
         super(DeeplinkAdamW, self).__setstate__(state)
         for group in self.param_groups:
             group.setdefault("amsgrad", False)
-            group.setdefault('maximize', False)
-    
+            group.setdefault("maximize", False)
+
     @torch.no_grad()
     def step(self, closure=None):
         """Performs a single optimization step.
@@ -79,53 +111,61 @@ def step(self, closure=None):
             state_sums = []
             max_exp_avg_sqs = []
             state_steps = []
-            amsgrad = group['amsgrad']
-            beta1, beta2 = group['betas']
+            amsgrad = group["amsgrad"]
+            beta1, beta2 = group["betas"]
 
-            for p in group['params']:
+            for p in group["params"]:
                 if p.grad is None:
                     continue
                 params_with_grad.append(p)
                 if p.grad.is_sparse:
-                    raise RuntimeError('AdamW does not support sparse gradients')
+                    raise RuntimeError("AdamW does not support sparse gradients")
                 grads.append(p.grad)
 
                 state = self.state[p]
 
                 # State initialization
                 if len(state) == 0:
-                    state['step'] = 0
+                    state["step"] = 0
                     # Exponential moving average of gradient values
-                    state['exp_avg'] = torch.zeros_like(p, memory_format=torch.preserve_format)
+                    state["exp_avg"] = torch.zeros_like(
+                        p, memory_format=torch.preserve_format
+                    )
                     # Exponential moving average of squared gradient values
-                    state['exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)
+                    state["exp_avg_sq"] = torch.zeros_like(
+                        p, memory_format=torch.preserve_format
+                    )
                     if amsgrad:
                         # Maintains max of all exp. moving avg. of sq. grad. values
-                        state['max_exp_avg_sq'] = torch.zeros_like(p, memory_format=torch.preserve_format)
+                        state["max_exp_avg_sq"] = torch.zeros_like(
+                            p, memory_format=torch.preserve_format
+                        )
 
-                exp_avgs.append(state['exp_avg'])
-                exp_avg_sqs.append(state['exp_avg_sq'])
+                exp_avgs.append(state["exp_avg"])
+                exp_avg_sqs.append(state["exp_avg_sq"])
 
                 if amsgrad:
-                    max_exp_avg_sqs.append(state['max_exp_avg_sq'])
+                    max_exp_avg_sqs.append(state["max_exp_avg_sq"])
 
                 # update the steps for each param group update
-                state['step'] += 1
+                state["step"] += 1
                 # record the step after step update
-                state_steps.append(state['step'])
+                state_steps.append(state["step"])
 
             # adamw_torch(params_with_grad,
-            adamw(params_with_grad,
-                    grads,
-                    exp_avgs,
-                    exp_avg_sqs,
-                    max_exp_avg_sqs,
-                    state_steps,
-                    amsgrad=amsgrad,
-                    beta1=beta1,
-                    beta2=beta2,
-                    lr=group['lr'],
-                    weight_decay=group['weight_decay'],
-                    eps=group['eps'],
-                    maximize=group['maximize'])
+            adamw(
+                params_with_grad,
+                grads,
+                exp_avgs,
+                exp_avg_sqs,
+                max_exp_avg_sqs,
+                state_steps,
+                amsgrad=amsgrad,
+                beta1=beta1,
+                beta2=beta2,
+                lr=group["lr"],
+                weight_decay=group["weight_decay"],
+                eps=group["eps"],
+                maximize=group["maximize"],
+            )
         return loss