diff --git a/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md
index 2df85f3b8..0fc7e0cae 100644
--- a/.github/ISSUE_TEMPLATE/bug_report.md
+++ b/.github/ISSUE_TEMPLATE/bug_report.md
@@ -15,8 +15,11 @@ A clear and concise description of what the bug is.
 
 * OS : (e.g. Linux, Windows, MacOS)
 * PyTorch version : (e.g. 2.0.1, 1.13, >=1.8, <1.10)
-* Python version :  (e.g. 3.8, 3.11
-* reproducible codes :
+* Python version :  (e.g. 3.8, 3.11)
+* pytorch-optimizer version : (e.g. 3.3.0)
+* reproducible codes : please share your reproducible codes, scripts, or links. If sharing the code is complicated, you can manually write minimal code to reproduce bugs!
+
+Here's an [example](https://github.com/kozistr/pytorch_optimizer/issues/305#issue-2721453417).
 
 ## Log
 
diff --git a/README.md b/README.md
index d565c09f5..6f550c2f8 100644
--- a/README.md
+++ b/README.md
@@ -10,11 +10,11 @@
 
 ## The reasons why you use `pytorch-optimizer`.
 
-1. Wide range of supported optimizers. Currently, **83 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
-2. Including many variants such as `Cautious`, `AdamD`, `Gradient Centrailiaztion`
-3. Easy to use, clean, and tested codes
-4. Active maintenance
-5. Somewhat a bit more optimized compared to the original implementation
+* Wide range of supported optimizers. Currently, **83 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
+* Including many variants such as `Cautious`, `AdamD`, `Gradient Centrailiaztion`
+* Easy to use, clean, and tested codes
+* Active maintenance
+* Somewhat a bit more optimized compared to the original implementation
 
 Highly inspired by [pytorch-optimizer](https://github.com/jettify/pytorch-optimizer).
 
diff --git a/docs/changelogs/v3.3.1.md b/docs/changelogs/v3.3.1.md
index 291e8341a..9b6eed730 100644
--- a/docs/changelogs/v3.3.1.md
+++ b/docs/changelogs/v3.3.1.md
@@ -2,9 +2,17 @@
 
 ### Feature
 
+* Support `Cautious` variant to `AdaShift` optimizer. (#310)
+* Save the state of the `Lookahead` optimizer too. (#310)
+
 ### Bug
 
 * Fix `bias_correction` in `AdamG` optimizer. (#305, #308)
+* Fix a potential bug when loading the state for `Lookahead` optimizer. (#306, #310)
+
+### Docs
+
+* Add more visualizations. (#310)
 
 ### Contributions
 
diff --git a/docs/index.md b/docs/index.md
index d565c09f5..6f550c2f8 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -10,11 +10,11 @@
 
 ## The reasons why you use `pytorch-optimizer`.
 
-1. Wide range of supported optimizers. Currently, **83 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
-2. Including many variants such as `Cautious`, `AdamD`, `Gradient Centrailiaztion`
-3. Easy to use, clean, and tested codes
-4. Active maintenance
-5. Somewhat a bit more optimized compared to the original implementation
+* Wide range of supported optimizers. Currently, **83 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
+* Including many variants such as `Cautious`, `AdamD`, `Gradient Centrailiaztion`
+* Easy to use, clean, and tested codes
+* Active maintenance
+* Somewhat a bit more optimized compared to the original implementation
 
 Highly inspired by [pytorch-optimizer](https://github.com/jettify/pytorch-optimizer).
 
diff --git a/docs/visualization.md b/docs/visualization.md
index 961035763..0d797b81d 100644
--- a/docs/visualization.md
+++ b/docs/visualization.md
@@ -74,6 +74,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_AdaPNM.png)
 
+### AdaShift
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_AdaShift.png)
+
 ### AdaSmooth
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_AdaSmooth.png)
@@ -170,6 +174,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_Lamb.png)
 
+### LaProp
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_LaProp.png)
+
 ### LARS
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_LARS.png)
@@ -186,6 +194,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_MSVAG.png)
 
+### Muon
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_Muon.png)
+
 ### Nero
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_Nero.png)
@@ -238,6 +250,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_ScheduleFreeAdamW.png)
 
+### ScheduleFreeRAdam
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_ScheduleFreeRAdam.png)
+
 ### ScheduleFreeSGD
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rastrigin_ScheduleFreeSGD.png)
@@ -368,6 +384,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_AdaPNM.png)
 
+### AdaShift
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_AdaShift.png)
+
 ### AdaSmooth
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_AdaSmooth.png)
@@ -464,6 +484,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_Lamb.png)
 
+### LaProp
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_LaProp.png)
+
 ### LARS
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_LARS.png)
@@ -480,6 +504,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_MSVAG.png)
 
+### Muon
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_Muon.png)
+
 ### Nero
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_Nero.png)
@@ -532,6 +560,10 @@
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_ScheduleFreeAdamW.png)
 
+### ScheduleFreeRAdam
+
+![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_ScheduleFreeRAdam.png)
+
 ### ScheduleFreeSGD
 
 ![image](https://raw.githubusercontent.com/kozistr/pytorch_optimizer/main/docs/visualizations/rosenbrock_ScheduleFreeSGD.png)
diff --git a/docs/visualizations/rastrigin_AdaShift.png b/docs/visualizations/rastrigin_AdaShift.png
new file mode 100644
index 000000000..d99aea838
Binary files /dev/null and b/docs/visualizations/rastrigin_AdaShift.png differ
diff --git a/docs/visualizations/rastrigin_AdamG.png b/docs/visualizations/rastrigin_AdamG.png
index 62724d85c..7bb51a1f3 100644
Binary files a/docs/visualizations/rastrigin_AdamG.png and b/docs/visualizations/rastrigin_AdamG.png differ
diff --git a/docs/visualizations/rastrigin_LaProp.png b/docs/visualizations/rastrigin_LaProp.png
new file mode 100644
index 000000000..ff077af57
Binary files /dev/null and b/docs/visualizations/rastrigin_LaProp.png differ
diff --git a/docs/visualizations/rastrigin_Muon.png b/docs/visualizations/rastrigin_Muon.png
new file mode 100644
index 000000000..a7cea61da
Binary files /dev/null and b/docs/visualizations/rastrigin_Muon.png differ
diff --git a/docs/visualizations/rastrigin_ScheduleFreeRAdam.png b/docs/visualizations/rastrigin_ScheduleFreeRAdam.png
new file mode 100644
index 000000000..01f943801
Binary files /dev/null and b/docs/visualizations/rastrigin_ScheduleFreeRAdam.png differ
diff --git a/docs/visualizations/rosenbrock_AdaShift.png b/docs/visualizations/rosenbrock_AdaShift.png
new file mode 100644
index 000000000..462ecc73c
Binary files /dev/null and b/docs/visualizations/rosenbrock_AdaShift.png differ
diff --git a/docs/visualizations/rosenbrock_AdamG.png b/docs/visualizations/rosenbrock_AdamG.png
index e8f1e5b05..f7eab6eb9 100644
Binary files a/docs/visualizations/rosenbrock_AdamG.png and b/docs/visualizations/rosenbrock_AdamG.png differ
diff --git a/docs/visualizations/rosenbrock_LaProp.png b/docs/visualizations/rosenbrock_LaProp.png
new file mode 100644
index 000000000..6a29ee9db
Binary files /dev/null and b/docs/visualizations/rosenbrock_LaProp.png differ
diff --git a/docs/visualizations/rosenbrock_Muon.png b/docs/visualizations/rosenbrock_Muon.png
new file mode 100644
index 000000000..a86b0b496
Binary files /dev/null and b/docs/visualizations/rosenbrock_Muon.png differ
diff --git a/docs/visualizations/rosenbrock_ScheduleFreeRAdam.png b/docs/visualizations/rosenbrock_ScheduleFreeRAdam.png
new file mode 100644
index 000000000..feaeba150
Binary files /dev/null and b/docs/visualizations/rosenbrock_ScheduleFreeRAdam.png differ
diff --git a/examples/visualize_optimizers.py b/examples/visualize_optimizers.py
index 44c41925e..80f645877 100644
--- a/examples/visualize_optimizers.py
+++ b/examples/visualize_optimizers.py
@@ -31,6 +31,8 @@ def execute_steps(func, initial_state, optimizer_class, optimizer_config, num_it
 
     if optimizer_class.__name__ == 'Ranger21':
         optimizer_config.update({'num_iterations': num_iters})
+    if optimizer_class.__name__ == 'AdaShift':
+        optimizer_config.update({'keep_num': 1})
 
     optimizer = optimizer_class([x], **optimizer_config)
 
@@ -155,7 +157,7 @@ def main():
     optimizers = [
         (optimizer, -6, 0.5)
         for optimizer_name, optimizer in OPTIMIZERS.items()
-        if optimizer_name.lower() not in {'alig', 'lomo', 'adalomo', 'bsam', 'adammini'}
+        if optimizer_name.lower() not in {'alig', 'lomo', 'adalomo', 'bsam', 'adammini', 'demo'}
     ]
     optimizers.extend([(torch.optim.AdamW, -6, 0.5), (torch.optim.Adam, -6, 0.5), (torch.optim.SGD, -6, -1.0)])
 
diff --git a/pytorch_optimizer/optimizer/a2grad.py b/pytorch_optimizer/optimizer/a2grad.py
index 6da2604f5..46ac668fe 100644
--- a/pytorch_optimizer/optimizer/a2grad.py
+++ b/pytorch_optimizer/optimizer/a2grad.py
@@ -1,5 +1,5 @@
 import math
-from typing import Optional
+from typing import Literal, Optional
 
 import torch
 
@@ -7,6 +7,8 @@
 from pytorch_optimizer.base.optimizer import BaseOptimizer
 from pytorch_optimizer.base.types import CLOSURE, DEFAULTS, LOSS, PARAMETERS
 
+VARIANTS = Literal['uni', 'inc', 'exp']
+
 
 class A2Grad(BaseOptimizer):
     r"""Optimal Adaptive and Accelerated Stochastic Gradient Descent.
@@ -26,7 +28,7 @@ def __init__(
         beta: float = 10.0,
         lips: float = 10.0,
         rho: float = 0.5,
-        variant: str = 'uni',
+        variant: VARIANTS = 'uni',
         **kwargs,
     ):
         self.validate_learning_rate(lr)
diff --git a/pytorch_optimizer/optimizer/adashift.py b/pytorch_optimizer/optimizer/adashift.py
index bd8179d05..64f78b7ea 100644
--- a/pytorch_optimizer/optimizer/adashift.py
+++ b/pytorch_optimizer/optimizer/adashift.py
@@ -17,6 +17,7 @@ class AdaShift(BaseOptimizer):
     :param keep_num: int. number of gradients used to compute first moment estimation.
     :param reduce_func: Optional[Callable]. function applied to squared gradients to further reduce the correlation.
         If None, no function is applied.
+    :param cautious: bool. whether to use cautious feature.
     :param eps: float. term added to the denominator to improve numerical stability.
     """
 
@@ -27,6 +28,7 @@ def __init__(
         betas: BETAS = (0.9, 0.999),
         keep_num: int = 10,
         reduce_func: Optional[Callable] = torch.max,
+        cautious: bool = False,
         eps: float = 1e-10,
         **kwargs,
     ):
@@ -36,6 +38,7 @@ def __init__(
         self.validate_non_negative(eps, 'eps')
 
         self.reduce_func: Callable = reduce_func if reduce_func is not None else lambda x: x
+        self.cautious = cautious
 
         defaults: DEFAULTS = {'lr': lr, 'betas': betas, 'keep_num': keep_num, 'eps': eps}
         super().__init__(params, defaults)
@@ -101,13 +104,16 @@ def step(self, closure: CLOSURE = None) -> LOSS:
                 exp_avg = state['exp_avg']
                 exp_avg.sub_(offset_grad, alpha=first_grad_weight).mul_(beta1).add_(grad, alpha=last_grad_weight)
 
-                reduced_grad_sq = self.reduce_func(offset_grad.mul_(offset_grad))
+                reduced_grad_sq = self.reduce_func(offset_grad.pow_(2))
 
                 exp_avg_sq = state['exp_avg_sq']
                 exp_avg_sq.mul_(beta2).add_(reduced_grad_sq, alpha=1.0 - beta2)
 
-                de_nom = exp_avg_sq.div(bias_correction).sqrt_().add_(group['eps'])
+                update = exp_avg.clone()
+                update.div_(exp_avg_sq.div(bias_correction).sqrt_().add_(group['eps']))
+                if self.cautious:
+                    self.apply_cautious(update, grad)
 
-                p.addcdiv_(exp_avg, de_nom, value=-group['lr'])
+                p.add_(update, alpha=-group['lr'])
 
         return loss
diff --git a/pytorch_optimizer/optimizer/lookahead.py b/pytorch_optimizer/optimizer/lookahead.py
index 63a15ee15..84e845207 100644
--- a/pytorch_optimizer/optimizer/lookahead.py
+++ b/pytorch_optimizer/optimizer/lookahead.py
@@ -31,12 +31,11 @@ def __init__(
         self._optimizer_step_pre_hooks: Dict[int, Callable] = {}
         self._optimizer_step_post_hooks: Dict[int, Callable] = {}
 
+        self.optimizer = optimizer
         self.alpha = alpha
         self.k = k
         self.pullback_momentum = pullback_momentum
 
-        self.optimizer = optimizer
-
         self.state: STATE = defaultdict(dict)
 
         for group in self.param_groups:
@@ -93,11 +92,12 @@ def clear_and_load_backup(self):
                 del state['backup_params']
 
     def state_dict(self) -> STATE:
-        return self.optimizer.state_dict()
+        return {'lookahead_state': self.state, 'base_optimizer': self.optimizer.state_dict()}
 
     def load_state_dict(self, state: STATE):
         r"""Load state."""
-        self.optimizer.load_state_dict(state)
+        self.state = state['lookahead_state']
+        self.optimizer.load_state_dict(state['base_optimizer'])
 
     @torch.no_grad()
     def zero_grad(self):
diff --git a/tests/constants.py b/tests/constants.py
index de3c1d446..21b4e0bf2 100644
--- a/tests/constants.py
+++ b/tests/constants.py
@@ -552,4 +552,5 @@
     (LaProp, {'lr': 1e0, 'cautious': True}, 2),
     (AdamP, {'lr': 1e0, 'cautious': True}, 2),
     (ADOPT, {'lr': 1e1, 'cautious': True}, 3),
+    (AdaShift, {'lr': 1e1, 'keep_num': 1, 'cautious': True}, 3),
 ]
diff --git a/tests/test_optimizer_parameters.py b/tests/test_optimizer_parameters.py
index e7610e9eb..901490136 100644
--- a/tests/test_optimizer_parameters.py
+++ b/tests/test_optimizer_parameters.py
@@ -77,15 +77,12 @@ def test_lookahead_parameters():
 
     _ = opt.__getstate__()
 
-    # test lookahead step `k`
     with pytest.raises(ValueError):
         Lookahead(optimizer, k=0)
 
-    # test ema ratio `alpha`
     with pytest.raises(ValueError):
         Lookahead(optimizer, alpha=-0.1)
 
-    # test invalid pullback momentum type
     with pytest.raises(ValueError):
         Lookahead(optimizer, pullback_momentum='invalid')