Repository: kozistr/pytorch_optimizer

Issue:
looksam support
## Paper or Code
https://arxiv.org/pdf/2203.02714
https://github.com/rollovd/LookSAM/tree/master

Discussion:

Solution patch:
diff --git a/README.md b/README.md
index 36326f37..25d2cbb2 100644
--- a/README.md
+++ b/README.md
@@ -10,7 +10,7 @@
 
 ## The reasons why you use `pytorch-optimizer`.
 
-* Wide range of supported optimizers. Currently, **97 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
+* Wide range of supported optimizers. Currently, **98 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
 * Including many variants such as `ADOPT`, `Cautious`, `AdamD`, `StableAdamW`, and `Gradient Centrailiaztion`
 * Easy to use, clean, and tested codes
 * Active maintenance
@@ -204,6 +204,8 @@ get_supported_optimizers(['adam*', 'ranger*'])
 | FOCUS         | *First Order Concentrated Updating Scheme*                                                        | [github](https://github.com/liuyz0/FOCUS)                                                                      | <https://arxiv.org/abs/2501.12243>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250112243M/exportcitation)                                                        |
 | PSGD          | *Preconditioned Stochastic Gradient Descent*                                                      | [github](https://github.com/lixilinx/psgd_torch)                                                               | <https://arxiv.org/abs/1512.04202>                                                          | [cite](https://github.com/lixilinx/psgd_torch?tab=readme-ov-file#resources)                                                         |
 | EXAdam        | *The Power of Adaptive Cross-Moments*                                                             | [github](https://github.com/AhmedMostafa16/EXAdam)                                                             | <https://arxiv.org/abs/2412.20302>                                                          | [cite](https://github.com/AhmedMostafa16/EXAdam?tab=readme-ov-file#citation)                                                        |
+| GCSAM         | *Gradient Centralized Sharpness Aware Minimization*                                               | [github](https://github.com/mhassann22/GCSAM)                                                                  | <https://arxiv.org/abs/2501.11584>                                                          | [cite](https://github.com/mhassann22/GCSAM?tab=readme-ov-file#citation)                                                             |
+| LookSAM       | *Towards Efficient and Scalable Sharpness-Aware Minimization*                                     | [github](https://github.com/rollovd/LookSAM)                                                                   | <https://arxiv.org/abs/2203.02714>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220302714L/exportcitation)                                                        |
 
 ## Supported LR Scheduler
 
diff --git a/docs/changelogs/v3.4.1.md b/docs/changelogs/v3.4.1.md
index 675f866d..426531a6 100644
--- a/docs/changelogs/v3.4.1.md
+++ b/docs/changelogs/v3.4.1.md
@@ -1,5 +1,13 @@
 ### Change Log
 
+### Feature
+
+* Support `GCSAM` optimizer. (#343, #344)
+    * [Gradient Centralized Sharpness Aware Minimization](https://arxiv.org/abs/2501.11584)
+    * you can use it from `SAM` optimizer by setting `use_gc=True`.
+* Support `LookSAM` optimizer. (#343, #344)
+    * [Towards Efficient and Scalable Sharpness-Aware Minimization](https://arxiv.org/abs/2203.02714)
+
 ### Update
 
 * Support alternative precision training for `Shampoo` optimizer. (#339)
diff --git a/docs/index.md b/docs/index.md
index 36326f37..25d2cbb2 100644
--- a/docs/index.md
+++ b/docs/index.md
@@ -10,7 +10,7 @@
 
 ## The reasons why you use `pytorch-optimizer`.
 
-* Wide range of supported optimizers. Currently, **97 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
+* Wide range of supported optimizers. Currently, **98 optimizers (+ `bitsandbytes`, `qgalore`, `torchao`)**, **16 lr schedulers**, and **13 loss functions** are supported!
 * Including many variants such as `ADOPT`, `Cautious`, `AdamD`, `StableAdamW`, and `Gradient Centrailiaztion`
 * Easy to use, clean, and tested codes
 * Active maintenance
@@ -204,6 +204,8 @@ get_supported_optimizers(['adam*', 'ranger*'])
 | FOCUS         | *First Order Concentrated Updating Scheme*                                                        | [github](https://github.com/liuyz0/FOCUS)                                                                      | <https://arxiv.org/abs/2501.12243>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2025arXiv250112243M/exportcitation)                                                        |
 | PSGD          | *Preconditioned Stochastic Gradient Descent*                                                      | [github](https://github.com/lixilinx/psgd_torch)                                                               | <https://arxiv.org/abs/1512.04202>                                                          | [cite](https://github.com/lixilinx/psgd_torch?tab=readme-ov-file#resources)                                                         |
 | EXAdam        | *The Power of Adaptive Cross-Moments*                                                             | [github](https://github.com/AhmedMostafa16/EXAdam)                                                             | <https://arxiv.org/abs/2412.20302>                                                          | [cite](https://github.com/AhmedMostafa16/EXAdam?tab=readme-ov-file#citation)                                                        |
+| GCSAM         | *Gradient Centralized Sharpness Aware Minimization*                                               | [github](https://github.com/mhassann22/GCSAM)                                                                  | <https://arxiv.org/abs/2501.11584>                                                          | [cite](https://github.com/mhassann22/GCSAM?tab=readme-ov-file#citation)                                                             |
+| LookSAM       | *Towards Efficient and Scalable Sharpness-Aware Minimization*                                     | [github](https://github.com/rollovd/LookSAM)                                                                   | <https://arxiv.org/abs/2203.02714>                                                          | [cite](https://ui.adsabs.harvard.edu/abs/2022arXiv220302714L/exportcitation)                                                        |
 
 ## Supported LR Scheduler
 
diff --git a/docs/optimizer.md b/docs/optimizer.md
index d79f288c..595f6110 100644
--- a/docs/optimizer.md
+++ b/docs/optimizer.md
@@ -240,6 +240,10 @@
     :docstring:
     :members:
 
+::: pytorch_optimizer.LookSAM
+    :docstring:
+    :members:
+
 ::: pytorch_optimizer.MADGRAD
     :docstring:
     :members:
diff --git a/pyproject.toml b/pyproject.toml
index bc7e6aa2..3a3c0dd0 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -17,10 +17,11 @@ keywords = [
     "DAdaptLion", "DeMo", "DiffGrad", "EXAdam", "FAdam", "FOCUS", "Fromage", "FTRL", "GaLore", "Grams", "Gravity",
     "GrokFast", "GSAM", "Kate", "Lamb", "LaProp", "LARS", "Lion", "LOMO", "Lookahead", "MADGRAD", "MARS", "MSVAG",
     "Muno", "Nero", "NovoGrad", "OrthoGrad", "PAdam", "PCGrad", "PID", "PNM", "Prodigy", "PSGD", "QHAdam", "QHM",
-    "RAdam", "Ranger", "Ranger21", "RotoGrad", "SAM", "ScheduleFreeSGD", "ScheduleFreeAdamW", "ScheduleFreeRAdam",
-    "SGDP", "Shampoo", "ScalableShampoo", "SGDW", "SignSGD", "SM3", "SOAP", "SopihaH", "SPAM", "SRMM", "StableAdamW",
-    "SWATS", "TAM", "Tiger", "TRAC", "WSAM", "Yogi", "BCE", "BCEFocal", "Focal", "FocalCosine", "SoftF1", "Dice",
-    "LDAM", "Jaccard", "Bi-Tempered", "Tversky", "FocalTversky", "LovaszHinge", "bitsandbytes", "WSD", "QGaLore",
+    "RAdam", "Ranger", "Ranger21", "RotoGrad", "SAM", "GCSAM", "LookSAM", "ScheduleFreeSGD", "ScheduleFreeAdamW",
+    "ScheduleFreeRAdam", "SGDP", "Shampoo", "ScalableShampoo", "SGDW", "SignSGD", "SM3", "SOAP", "SopihaH", "SPAM",
+    "SRMM", "StableAdamW", "SWATS", "TAM", "Tiger", "TRAC", "WSAM", "Yogi", "BCE", "BCEFocal", "Focal", "FocalCosine",
+    "SoftF1", "Dice", "LDAM", "Jaccard", "Bi-Tempered", "Tversky", "FocalTversky", "LovaszHinge", "bitsandbytes", "WSD",
+    "QGaLore",
 ]
 classifiers = [
     "License :: OSI Approved :: Apache Software License",
diff --git a/pytorch_optimizer/__init__.py b/pytorch_optimizer/__init__.py
index bee1fb8b..0eccaeed 100644
--- a/pytorch_optimizer/__init__.py
+++ b/pytorch_optimizer/__init__.py
@@ -119,6 +119,7 @@
     LaProp,
     Lion,
     Lookahead,
+    LookSAM,
     Muon,
     Nero,
     NovoGrad,
diff --git a/pytorch_optimizer/optimizer/__init__.py b/pytorch_optimizer/optimizer/__init__.py
index 2d213736..05629803 100644
--- a/pytorch_optimizer/optimizer/__init__.py
+++ b/pytorch_optimizer/optimizer/__init__.py
@@ -79,7 +79,7 @@
 from pytorch_optimizer.optimizer.ranger import Ranger
 from pytorch_optimizer.optimizer.ranger21 import Ranger21
 from pytorch_optimizer.optimizer.rotograd import RotoGrad
-from pytorch_optimizer.optimizer.sam import BSAM, GSAM, SAM, WSAM
+from pytorch_optimizer.optimizer.sam import BSAM, GSAM, SAM, WSAM, LookSAM
 from pytorch_optimizer.optimizer.schedulefree import ScheduleFreeAdamW, ScheduleFreeRAdam, ScheduleFreeSGD
 from pytorch_optimizer.optimizer.sgd import ASGD, SGDW, AccSGD, SGDSaI, SignSGD
 from pytorch_optimizer.optimizer.sgdp import SGDP
diff --git a/pytorch_optimizer/optimizer/sam.py b/pytorch_optimizer/optimizer/sam.py
index 114002fe..67f53dd5 100644
--- a/pytorch_optimizer/optimizer/sam.py
+++ b/pytorch_optimizer/optimizer/sam.py
@@ -11,6 +11,7 @@
 from pytorch_optimizer.base.exception import NoClosureError
 from pytorch_optimizer.base.optimizer import BaseOptimizer
 from pytorch_optimizer.base.types import BETAS, CLOSURE, DEFAULTS, OPTIMIZER, PARAMETERS
+from pytorch_optimizer.optimizer.gc import centralize_gradient
 from pytorch_optimizer.optimizer.utils import disable_running_stats, enable_running_stats
 
 
@@ -58,6 +59,7 @@ def closure():
     :param base_optimizer: OPTIMIZER. base optimizer.
     :param rho: float. size of the neighborhood for computing the max loss.
     :param adaptive: bool. element-wise Adaptive SAM.
+    :param use_gc: bool. perform gradient centralization, GCSAM variant.
     :param perturb_eps: float. eps for perturbation.
     :param kwargs: Dict. parameters for optimizer.
     """
@@ -68,12 +70,14 @@ def __init__(
         base_optimizer: OPTIMIZER,
         rho: float = 0.05,
         adaptive: bool = False,
+        use_gc: bool = False,
         perturb_eps: float = 1e-12,
         **kwargs,
     ):
         self.validate_non_negative(rho, 'rho')
         self.validate_non_negative(perturb_eps, 'perturb_eps')
 
+        self.use_gc = use_gc
         self.perturb_eps = perturb_eps
 
         defaults: DEFAULTS = {'rho': rho, 'adaptive': adaptive}
@@ -92,16 +96,20 @@ def reset(self):
 
     @torch.no_grad()
     def first_step(self, zero_grad: bool = False):
-        grad_norm = self.grad_norm()
+        grad_norm = self.grad_norm().add_(self.perturb_eps)
         for group in self.param_groups:
-            scale = group['rho'] / (grad_norm + self.perturb_eps)
+            scale = group['rho'] / grad_norm
 
             for p in group['params']:
                 if p.grad is None:
                     continue
 
+                grad = p.grad
+                if self.use_gc:
+                    centralize_gradient(grad, gc_conv_only=False)
+
                 self.state[p]['old_p'] = p.clone()
-                e_w = (torch.pow(p, 2) if group['adaptive'] else 1.0) * p.grad * scale.to(p)
+                e_w = (torch.pow(p, 2) if group['adaptive'] else 1.0) * grad * scale.to(p)
 
                 p.add_(e_w)
 
@@ -670,3 +678,187 @@ def step(self, closure: CLOSURE = None):
         self.third_step()
 
         return loss
+
+
+class LookSAM(BaseOptimizer):
+    r"""Towards Efficient and Scalable Sharpness-Aware Minimization.
+
+    Example:
+    -------
+        Here's an example::
+
+            model = YourModel()
+            base_optimizer = Ranger21
+            optimizer = LookSAM(model.parameters(), base_optimizer)
+
+            for input, output in data:
+                # first forward-backward pass
+
+                loss = loss_function(output, model(input))
+                loss.backward()
+                optimizer.first_step(zero_grad=True)
+
+                # second forward-backward pass
+                # make sure to do a full forward pass
+                loss_function(output, model(input)).backward()
+                optimizer.second_step(zero_grad=True)
+
+        Alternative example with a single closure-based step function::
+
+            model = YourModel()
+            base_optimizer = Ranger21
+            optimizer = LookSAM(model.parameters(), base_optimizer)
+
+            def closure():
+                loss = loss_function(output, model(input))
+                loss.backward()
+                return loss
+
+            for input, output in data:
+                loss = loss_function(output, model(input))
+                loss.backward()
+                optimizer.step(closure)
+                optimizer.zero_grad()
+
+    :param params: PARAMETERS. iterable of parameters to optimize or dicts defining parameter groups.
+    :param base_optimizer: OPTIMIZER. base optimizer.
+    :param rho: float. size of the neighborhood for computing the max loss.
+    :param k: int. lookahead step.
+    :param alpha: float. lookahead blending alpha.
+    :param adaptive: bool. element-wise Adaptive SAM.
+    :param use_gc: bool. perform gradient centralization, GCSAM variant.
+    :param perturb_eps: float. eps for perturbation.
+    :param kwargs: Dict. parameters for optimizer.
+    """
+
+    def __init__(
+        self,
+        params: PARAMETERS,
+        base_optimizer: OPTIMIZER,
+        rho: float = 0.1,
+        k: int = 10,
+        alpha: float = 0.7,
+        adaptive: bool = False,
+        use_gc: bool = False,
+        perturb_eps: float = 1e-12,
+        **kwargs,
+    ):
+        self.validate_non_negative(rho, 'rho')
+        self.validate_positive(k, 'k')
+        self.validate_range(alpha, 'alpha', 0.0, 1.0, '()')
+        self.validate_non_negative(perturb_eps, 'perturb_eps')
+
+        self.k = k
+        self.alpha = alpha
+        self.use_gc = use_gc
+        self.perturb_eps = perturb_eps
+
+        defaults: DEFAULTS = {'rho': rho, 'adaptive': adaptive}
+        defaults.update(kwargs)
+
+        super().__init__(params, defaults)
+
+        self.base_optimizer: Optimizer = base_optimizer(self.param_groups, **kwargs)
+        self.param_groups = self.base_optimizer.param_groups
+
+    def __str__(self) -> str:
+        return 'LookSAM'
+
+    @torch.no_grad()
+    def reset(self):
+        pass
+
+    def get_step(self):
+        return (
+            self.param_groups[0]['step']
+            if 'step' in self.param_groups[0]
+            else next(iter(self.base_optimizer.state.values()))['step'] if self.base_optimizer.state else 0
+        )
+
+    @torch.no_grad()
+    def first_step(self, zero_grad: bool = False) -> None:
+        if self.get_step() % self.k != 0:
+            return
+
+        grad_norm = self.grad_norm().add_(self.perturb_eps)
+        for group in self.param_groups:
+            scale = group['rho'] / grad_norm
+
+            for i, p in enumerate(group['params']):
+                if p.grad is None:
+                    continue
+
+                grad = p.grad
+                if self.use_gc:
+                    centralize_gradient(grad, gc_conv_only=False)
+
+                self.state[p]['old_p'] = p.clone()
+                self.state[f'old_grad_p_{i}']['old_grad_p'] = grad.clone()
+
+                e_w = (torch.pow(p, 2) if group['adaptive'] else 1.0) * grad * scale.to(p)
+                p.add_(e_w)
+
+        if zero_grad:
+            self.zero_grad()
+
+    @torch.no_grad()
+    def second_step(self, zero_grad: bool = False):
+        step = self.get_step()
+
+        for group in self.param_groups:
+            for i, p in enumerate(group['params']):
+                if p.grad is None:
+                    continue
+
+                grad = p.grad
+                grad_norm = grad.norm(p=2)
+
+                if step % self.k == 0:
+                    old_grad_p = self.state[f'old_grad_p_{i}']['old_grad_p']
+
+                    g_grad_norm = old_grad_p / old_grad_p.norm(p=2)
+                    g_s_grad_norm = grad / grad_norm
+
+                    self.state[f'gv_{i}']['gv'] = torch.sub(
+                        grad, grad_norm * torch.sum(g_grad_norm * g_s_grad_norm) * g_grad_norm
+                    )
+                else:
+                    gv = self.state[f'gv_{i}']['gv']
+                    grad.add_(grad_norm / (gv.norm(p=2) + 1e-8) * gv, alpha=self.alpha)
+
+                p.data = self.state[p]['old_p']
+
+        self.base_optimizer.step()
+
+        if zero_grad:
+            self.zero_grad()
+
+    @torch.no_grad()
+    def step(self, closure: CLOSURE = None):
+        if closure is None:
+            raise NoClosureError(str(self))
+
+        self.first_step(zero_grad=True)
+
+        with torch.enable_grad():
+            closure()
+
+        self.second_step()
+
+    def grad_norm(self) -> torch.Tensor:
+        shared_device = self.param_groups[0]['params'][0].device
+        return torch.norm(
+            torch.stack(
+                [
+                    ((torch.abs(p) if group['adaptive'] else 1.0) * p.grad).norm(p=2).to(shared_device)
+                    for group in self.param_groups
+                    for p in group['params']
+                    if p.grad is not None
+                ]
+            ),
+            p=2,
+        )
+
+    def load_state_dict(self, state_dict: Dict):
+        super().load_state_dict(state_dict)
+        self.base_optimizer.param_groups = self.param_groups


Test patch:
diff --git a/tests/constants.py b/tests/constants.py
index 084309c0..c24bc06c 100644
--- a/tests/constants.py
+++ b/tests/constants.py
@@ -102,6 +102,7 @@
     'sam',
     'gsam',
     'wsam',
+    'looksam',
     'pcgrad',
     'lookahead',
     'trac',
diff --git a/tests/test_gradients.py b/tests/test_gradients.py
index adb8fe91..8ba6d0c7 100644
--- a/tests/test_gradients.py
+++ b/tests/test_gradients.py
@@ -2,7 +2,7 @@
 import torch
 
 from pytorch_optimizer.base.exception import NoSparseGradientError
-from pytorch_optimizer.optimizer import SAM, TRAC, WSAM, AdamP, Lookahead, OrthoGrad, load_optimizer
+from pytorch_optimizer.optimizer import SAM, TRAC, WSAM, AdamP, Lookahead, LookSAM, OrthoGrad, load_optimizer
 from tests.constants import NO_SPARSE_OPTIMIZERS, SPARSE_OPTIMIZERS, VALID_OPTIMIZER_NAMES
 from tests.utils import build_environment, simple_parameter, simple_sparse_parameter, sphere_loss
 
@@ -116,12 +116,13 @@ def test_sparse_supported(sparse_optimizer):
             optimizer.step()
 
 
-def test_sam_no_gradient():
+@pytest.mark.parametrize('optimizer', [SAM, LookSAM])
+def test_sam_no_gradient(optimizer):
     (x_data, y_data), model, loss_fn = build_environment()
     model.fc1.weight.requires_grad = False
     model.fc1.weight.grad = None
 
-    optimizer = SAM(model.parameters(), AdamP)
+    optimizer = optimizer(model.parameters(), AdamP)
     optimizer.zero_grad()
 
     loss = loss_fn(y_data, model(x_data))
diff --git a/tests/test_optimizer_parameters.py b/tests/test_optimizer_parameters.py
index e187e3ff..76b88ef4 100644
--- a/tests/test_optimizer_parameters.py
+++ b/tests/test_optimizer_parameters.py
@@ -7,6 +7,7 @@
     TRAC,
     WSAM,
     Lookahead,
+    LookSAM,
     OrthoGrad,
     PCGrad,
     Ranger21,
@@ -110,6 +111,12 @@ def test_wsam_methods():
     optimizer.load_state_dict(optimizer.state_dict())
 
 
+def test_looksam_methods():
+    optimizer = LookSAM([simple_parameter()], load_optimizer('adamp'))
+    optimizer.reset()
+    optimizer.load_state_dict(optimizer.state_dict())
+
+
 def test_safe_fp16_methods():
     optimizer = SafeFP16Optimizer(load_optimizer('adamp')([simple_parameter()], lr=5e-1))
     optimizer.load_state_dict(optimizer.state_dict())
diff --git a/tests/test_optimizers.py b/tests/test_optimizers.py
index 7de615e8..e5112de9 100644
--- a/tests/test_optimizers.py
+++ b/tests/test_optimizers.py
@@ -15,6 +15,7 @@
     WSAM,
     DynamicLossScaler,
     Lookahead,
+    LookSAM,
     Muon,
     PCGrad,
     load_optimizer,
@@ -169,7 +170,7 @@ def test_lookahead(pullback_momentum, environment):
 def test_sam_optimizer(adaptive, environment):
     (x_data, y_data), model, loss_fn = environment
 
-    optimizer = SAM(model.parameters(), load_optimizer('asgd'), lr=5e-1, adaptive=adaptive)
+    optimizer = SAM(model.parameters(), load_optimizer('asgd'), lr=5e-1, adaptive=adaptive, use_gc=True)
 
     init_loss, loss = np.inf, np.inf
     for _ in range(5):
@@ -190,7 +191,51 @@ def test_sam_optimizer(adaptive, environment):
 def test_sam_optimizer_with_closure(adaptive, environment):
     (x_data, y_data), model, loss_fn = environment
 
-    optimizer = SAM(model.parameters(), load_optimizer('adamp'), lr=5e-1, adaptive=adaptive)
+    optimizer = SAM(model.parameters(), load_optimizer('adamw'), lr=5e-1, adaptive=adaptive)
+
+    def closure():
+        first_loss = loss_fn(y_data, model(x_data))
+        first_loss.backward()
+        return first_loss
+
+    init_loss, loss = np.inf, np.inf
+    for _ in range(5):
+        loss = loss_fn(y_data, model(x_data))
+        loss.backward()
+
+        optimizer.step(closure)
+        optimizer.zero_grad()
+
+        if init_loss == np.inf:
+            init_loss = loss
+
+    assert tensor_to_numpy(init_loss) > 2.0 * tensor_to_numpy(loss)
+
+
+def test_looksam_optimizer(environment):
+    (x_data, y_data), model, loss_fn = environment
+
+    optimizer = LookSAM(model.parameters(), load_optimizer('adamw'), k=2, lr=5e-1, use_gc=True)
+
+    init_loss, loss = np.inf, np.inf
+    for _ in range(5):
+        loss = loss_fn(y_data, model(x_data))
+        loss.backward()
+        optimizer.first_step(zero_grad=True)
+
+        loss_fn(y_data, model(x_data)).backward()
+        optimizer.second_step(zero_grad=True)
+
+        if init_loss == np.inf:
+            init_loss = loss
+
+    assert tensor_to_numpy(init_loss) > 2.0 * tensor_to_numpy(loss)
+
+
+def test_looksam_optimizer_with_closure(environment):
+    (x_data, y_data), model, loss_fn = environment
+
+    optimizer = LookSAM(model.parameters(), load_optimizer('adamw'), lr=5e-1)
 
     def closure():
         first_loss = loss_fn(y_data, model(x_data))
@@ -502,6 +547,12 @@ def test_no_closure():
     with pytest.raises(NoClosureError):
         optimizer.step()
 
+    optimizer = LookSAM([param], load_optimizer('adamp'))
+    optimizer.zero_grad()
+
+    with pytest.raises(NoClosureError):
+        optimizer.step()
+
 
 def test_nero_zero_scale():
     param = simple_parameter()