diff --git a/exps/LFNA/lfna-v1.py b/exps/LFNA/lfna-v1.py
new file mode 100644
index 0000000..9c9b90a
--- /dev/null
+++ b/exps/LFNA/lfna-v1.py
@@ -0,0 +1,212 @@
+#####################################################
+# Copyright (c) Xuanyi Dong [GitHub D-X-Y], 2021.04 #
+#####################################################
+# python exps/LFNA/lfna-v1.py
+#####################################################
+import sys, time, copy, torch, random, argparse
+from tqdm import tqdm
+from copy import deepcopy
+from pathlib import Path
+
+lib_dir = (Path(__file__).parent / ".." / ".." / "lib").resolve()
+if str(lib_dir) not in sys.path:
+    sys.path.insert(0, str(lib_dir))
+from procedures import prepare_seed, prepare_logger, save_checkpoint, copy_checkpoint
+from log_utils import time_string
+from log_utils import AverageMeter, convert_secs2time
+
+from utils import split_str2indexes
+
+from procedures.advanced_main import basic_train_fn, basic_eval_fn
+from procedures.metric_utils import SaveMetric, MSEMetric, ComposeMetric
+from datasets.synthetic_core import get_synthetic_env
+from models.xcore import get_model
+
+
+class Population:
+    def __init__(self):
+        self._time2model = dict()
+
+    def append(self, timestamp, model):
+        if timestamp in self._time2model:
+            raise ValueError("This timestamp has been added.")
+        self._time2model[timestamp] = model
+
+
+def main(args):
+    prepare_seed(args.rand_seed)
+    logger = prepare_logger(args)
+
+    cache_path = (logger.path(None) / ".." / "env-info.pth").resolve()
+    if cache_path.exists():
+        env_info = torch.load(cache_path)
+    else:
+        env_info = dict()
+        dynamic_env = get_synthetic_env()
+        env_info["total"] = len(dynamic_env)
+        for idx, (timestamp, (_allx, _ally)) in enumerate(tqdm(dynamic_env)):
+            env_info["{:}-timestamp".format(idx)] = timestamp
+            env_info["{:}-x".format(idx)] = _allx
+            env_info["{:}-y".format(idx)] = _ally
+        env_info["dynamic_env"] = dynamic_env
+        torch.save(env_info, cache_path)
+
+    total_time = env_info["total"]
+    for i in range(total_time):
+        for xkey in ("timestamp", "x", "y"):
+            nkey = "{:}-{:}".format(i, xkey)
+            assert nkey in env_info, "{:} no in {:}".format(nkey, list(env_info.keys()))
+    train_time_bar = total_time // 2
+    base_model = get_model(
+        dict(model_type="simple_mlp"),
+        act_cls="leaky_relu",
+        norm_cls="simple_learn_norm",
+        mean=0,
+        std=1,
+        input_dim=1,
+        output_dim=1,
+    )
+
+    w_container = base_model.named_parameters_buffers()
+    print("There are {:} weights.".format(w_container.numel()))
+
+    pool = Population()
+    pool.append(0, w_container)
+
+    # LFNA meta-training
+    per_epoch_time, start_time = AverageMeter(), time.time()
+    for iepoch in range(args.epochs):
+        import pdb
+
+        pdb.set_trace()
+        print("-")
+
+    for i, idx in enumerate(to_evaluate_indexes):
+
+        need_time = "Time Left: {:}".format(
+            convert_secs2time(
+                per_timestamp_time.avg * (len(to_evaluate_indexes) - i), True
+            )
+        )
+        logger.log(
+            "[{:}]".format(time_string())
+            + " [{:04d}/{:04d}][{:04d}]".format(i, len(to_evaluate_indexes), idx)
+            + " "
+            + need_time
+        )
+        # train the same data
+        assert idx != 0
+        historical_x = env_info["{:}-x".format(idx)]
+        historical_y = env_info["{:}-y".format(idx)]
+        # build model
+        mean, std = historical_x.mean().item(), historical_x.std().item()
+        model_kwargs = dict(input_dim=1, output_dim=1, mean=mean, std=std)
+        model = get_model(dict(model_type="simple_mlp"), **model_kwargs)
+        # build optimizer
+        optimizer = torch.optim.Adam(model.parameters(), lr=args.init_lr, amsgrad=True)
+        criterion = torch.nn.MSELoss()
+        lr_scheduler = torch.optim.lr_scheduler.MultiStepLR(
+            optimizer,
+            milestones=[
+                int(args.epochs * 0.25),
+                int(args.epochs * 0.5),
+                int(args.epochs * 0.75),
+            ],
+            gamma=0.3,
+        )
+        train_metric = MSEMetric()
+        best_loss, best_param = None, None
+        for _iepoch in range(args.epochs):
+            preds = model(historical_x)
+            optimizer.zero_grad()
+            loss = criterion(preds, historical_y)
+            loss.backward()
+            optimizer.step()
+            lr_scheduler.step()
+            # save best
+            if best_loss is None or best_loss > loss.item():
+                best_loss = loss.item()
+                best_param = copy.deepcopy(model.state_dict())
+        model.load_state_dict(best_param)
+        with torch.no_grad():
+            train_metric(preds, historical_y)
+        train_results = train_metric.get_info()
+
+        metric = ComposeMetric(MSEMetric(), SaveMetric())
+        eval_dataset = torch.utils.data.TensorDataset(
+            env_info["{:}-x".format(idx)], env_info["{:}-y".format(idx)]
+        )
+        eval_loader = torch.utils.data.DataLoader(
+            eval_dataset, batch_size=args.batch_size, shuffle=False, num_workers=0
+        )
+        results = basic_eval_fn(eval_loader, model, metric, logger)
+        log_str = (
+            "[{:}]".format(time_string())
+            + " [{:04d}/{:04d}]".format(idx, env_info["total"])
+            + " train-mse: {:.5f}, eval-mse: {:.5f}".format(
+                train_results["mse"], results["mse"]
+            )
+        )
+        logger.log(log_str)
+
+        save_path = logger.path(None) / "{:04d}-{:04d}.pth".format(
+            idx, env_info["total"]
+        )
+        save_checkpoint(
+            {
+                "model_state_dict": model.state_dict(),
+                "model": model,
+                "index": idx,
+                "timestamp": env_info["{:}-timestamp".format(idx)],
+            },
+            save_path,
+            logger,
+        )
+        logger.log("")
+
+        per_timestamp_time.update(time.time() - start_time)
+        start_time = time.time()
+
+    logger.log("-" * 200 + "\n")
+    logger.close()
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser("Use the data in the past.")
+    parser.add_argument(
+        "--save_dir",
+        type=str,
+        default="./outputs/lfna-synthetic/lfna-v1",
+        help="The checkpoint directory.",
+    )
+    parser.add_argument(
+        "--init_lr",
+        type=float,
+        default=0.1,
+        help="The initial learning rate for the optimizer (default is Adam)",
+    )
+    parser.add_argument(
+        "--batch_size",
+        type=int,
+        default=512,
+        help="The batch size",
+    )
+    parser.add_argument(
+        "--epochs",
+        type=int,
+        default=1000,
+        help="The total number of epochs.",
+    )
+    parser.add_argument(
+        "--workers",
+        type=int,
+        default=4,
+        help="The number of data loading workers (default: 4)",
+    )
+    # Random Seed
+    parser.add_argument("--rand_seed", type=int, default=-1, help="manual seed")
+    args = parser.parse_args()
+    if args.rand_seed is None or args.rand_seed < 0:
+        args.rand_seed = random.randint(1, 100000)
+    assert args.save_dir is not None, "The save dir argument can not be None"
+    main(args)
diff --git a/lib/models/xcore.py b/lib/models/xcore.py
index 13be1cc..14e826d 100644
--- a/lib/models/xcore.py
+++ b/lib/models/xcore.py
@@ -10,21 +10,26 @@ __all__ = ["get_model"]
 
 
 from xlayers.super_core import SuperSequential
-from xlayers.super_core import SuperSimpleNorm
-from xlayers.super_core import SuperLeakyReLU
 from xlayers.super_core import SuperLinear
+from xlayers.super_core import super_name2norm
+from xlayers.super_core import super_name2activation
 
 
 def get_model(config: Dict[Text, Any], **kwargs):
     model_type = config.get("model_type", "simple_mlp")
     if model_type == "simple_mlp":
+        act_cls = super_name2activation[kwargs["act_cls"]]
+        norm_cls = super_name2norm[kwargs["norm_cls"]]
+        mean, std = kwargs.get("mean", None), kwargs.get("std", None)
+        hidden_dim1 = kwargs.get("hidden_dim1", 200)
+        hidden_dim2 = kwargs.get("hidden_dim2", 100)
         model = SuperSequential(
-            SuperSimpleNorm(kwargs["mean"], kwargs["std"]),
-            SuperLinear(kwargs["input_dim"], 200),
-            SuperLeakyReLU(),
-            SuperLinear(200, 100),
-            SuperLeakyReLU(),
-            SuperLinear(100, kwargs["output_dim"]),
+            norm_cls(mean=mean, std=std),
+            SuperLinear(kwargs["input_dim"], hidden_dim1),
+            act_cls(),
+            SuperLinear(hidden_dim1, hidden_dim2),
+            act_cls(),
+            SuperLinear(hidden_dim2, kwargs["output_dim"]),
         )
     else:
         raise TypeError("Unkonwn model type: {:}".format(model_type))
diff --git a/lib/xlayers/super_core.py b/lib/xlayers/super_core.py
index 58a0c2f..fceb3e7 100644
--- a/lib/xlayers/super_core.py
+++ b/lib/xlayers/super_core.py
@@ -9,13 +9,27 @@ from .super_module import SuperModule
 from .super_container import SuperSequential
 from .super_linear import SuperLinear
 from .super_linear import SuperMLPv1, SuperMLPv2
+
 from .super_norm import SuperSimpleNorm
 from .super_norm import SuperLayerNorm1D
+from .super_norm import SuperSimpleLearnableNorm
+from .super_norm import SuperIdentity
+
+super_name2norm = {
+    "simple_norm": SuperSimpleNorm,
+    "simple_learn_norm": SuperSimpleLearnableNorm,
+    "layer_norm_1d": SuperLayerNorm1D,
+    "identity": SuperIdentity,
+}
+
 from .super_attention import SuperAttention
 from .super_transformer import SuperTransformerEncoderLayer
 
 from .super_activations import SuperReLU
 from .super_activations import SuperLeakyReLU
 
+super_name2activation = {"relu": SuperReLU, "leaky_relu": SuperLeakyReLU}
+
+
 from .super_trade_stem import SuperAlphaEBDv1
 from .super_positional_embedding import SuperPositionalEncoder
diff --git a/lib/xlayers/super_module.py b/lib/xlayers/super_module.py
index 9004f34..d4e07eb 100644
--- a/lib/xlayers/super_module.py
+++ b/lib/xlayers/super_module.py
@@ -30,6 +30,45 @@ class SuperRunMode(Enum):
     Default = "fullmodel"
 
 
+class TensorContainer:
+    """A class to maintain both parameters and buffers for a model."""
+
+    def __init__(self):
+        self._names = []
+        self._tensors = []
+        self._param_or_buffers = []
+        self._name2index = dict()
+
+    def append(self, name, tensor, param_or_buffer):
+        if not isinstance(tensor, torch.Tensor):
+            raise TypeError(
+                "The input tensor must be torch.Tensor instead of {:}".format(
+                    type(tensor)
+                )
+            )
+        self._names.append(name)
+        self._tensors.append(tensor)
+        self._param_or_buffers.append(param_or_buffer)
+        assert name not in self._name2index, "The [{:}] has already been added.".format(
+            name
+        )
+        self._name2index[name] = len(self._names) - 1
+
+    def numel(self):
+        total = 0
+        for tensor in self._tensors:
+            total += tensor.numel()
+        return total
+
+    def __len__(self):
+        return len(self._names)
+
+    def __repr__(self):
+        return "{name}({num} tensors)".format(
+            name=self.__class__.__name__, num=len(self)
+        )
+
+
 class SuperModule(abc.ABC, nn.Module):
     """This class equips the nn.Module class with the ability to apply AutoDL."""
 
@@ -71,6 +110,14 @@ class SuperModule(abc.ABC, nn.Module):
             )
         self._abstract_child = abstract_child
 
+    def named_parameters_buffers(self):
+        container = TensorContainer()
+        for name, param in self.named_parameters():
+            container.append(name, param, True)
+        for name, buf in self.named_buffers():
+            container.append(name, buf, False)
+        return container
+
     @property
     def abstract_search_space(self):
         raise NotImplementedError
diff --git a/lib/xlayers/super_norm.py b/lib/xlayers/super_norm.py
index 0103781..5671c0f 100644
--- a/lib/xlayers/super_norm.py
+++ b/lib/xlayers/super_norm.py
@@ -89,8 +89,8 @@ class SuperSimpleNorm(SuperModule):
 
     def __init__(self, mean, std, inplace=False) -> None:
         super(SuperSimpleNorm, self).__init__()
-        self._mean = mean
-        self._std = std
+        self.register_buffer("_mean", torch.tensor(mean, dtype=torch.float))
+        self.register_buffer("_std", torch.tensor(std, dtype=torch.float))
         self._inplace = inplace
 
     @property
@@ -111,7 +111,7 @@ class SuperSimpleNorm(SuperModule):
         if (std == 0).any():
             raise ValueError(
                 "std evaluated to zero after conversion to {}, leading to division by zero.".format(
-                    dtype
+                    tensor.dtype
                 )
             )
         while mean.ndim < tensor.ndim:
@@ -119,6 +119,75 @@ class SuperSimpleNorm(SuperModule):
         return tensor.sub_(mean).div_(std)
 
     def extra_repr(self) -> str:
-        return "mean={mean}, std={mean}, inplace={inplace}".format(
-            mean=self._mean, std=self._std, inplace=self._inplace
+        return "mean={mean}, std={std}, inplace={inplace}".format(
+            mean=self._mean.item(), std=self._std.item(), inplace=self._inplace
         )
+
+
+class SuperSimpleLearnableNorm(SuperModule):
+    """Super simple normalization."""
+
+    def __init__(self, mean=0, std=1, eps=1e-6, inplace=False) -> None:
+        super(SuperSimpleLearnableNorm, self).__init__()
+        self.register_parameter(
+            "_mean", nn.Parameter(torch.tensor(mean, dtype=torch.float))
+        )
+        self.register_parameter(
+            "_std", nn.Parameter(torch.tensor(std, dtype=torch.float))
+        )
+        self._eps = eps
+        self._inplace = inplace
+
+    @property
+    def abstract_search_space(self):
+        return spaces.VirtualNode(id(self))
+
+    def forward_candidate(self, input: torch.Tensor) -> torch.Tensor:
+        # check inputs ->
+        return self.forward_raw(input)
+
+    def forward_raw(self, input: torch.Tensor) -> torch.Tensor:
+        if not self._inplace:
+            tensor = input.clone()
+        else:
+            tensor = input
+        mean, std = (
+            self._mean.to(tensor.device),
+            torch.abs(self._std.to(tensor.device)) + self._eps,
+        )
+        if (std == 0).any():
+            raise ValueError("std leads to division by zero.")
+        while mean.ndim < tensor.ndim:
+            mean, std = torch.unsqueeze(mean, dim=0), torch.unsqueeze(std, dim=0)
+        return tensor.sub_(mean).div_(std)
+
+    def extra_repr(self) -> str:
+        return "mean={mean}, std={std}, inplace={inplace}".format(
+            mean=self._mean.item(), std=self._std.item(), inplace=self._inplace
+        )
+
+
+class SuperIdentity(SuperModule):
+    """Super identity mapping layer."""
+
+    def __init__(self, inplace=False, **kwargs) -> None:
+        super(SuperIdentity, self).__init__()
+        self._inplace = inplace
+
+    @property
+    def abstract_search_space(self):
+        return spaces.VirtualNode(id(self))
+
+    def forward_candidate(self, input: torch.Tensor) -> torch.Tensor:
+        # check inputs ->
+        return self.forward_raw(input)
+
+    def forward_raw(self, input: torch.Tensor) -> torch.Tensor:
+        if not self._inplace:
+            tensor = input.clone()
+        else:
+            tensor = input
+        return tensor
+
+    def extra_repr(self) -> str:
+        return "inplace={inplace}".format(inplace=self._inplace)
diff --git a/tests/test_super_norm.py b/tests/test_super_norm.py
index c50f397..d5a21d6 100644
--- a/tests/test_super_norm.py
+++ b/tests/test_super_norm.py
@@ -51,3 +51,35 @@ class TestSuperSimpleNorm(unittest.TestCase):
         output_shape = (20, abstract_child["1"]["_out_features"].value)
         outputs = model(inputs)
         self.assertEqual(tuple(outputs.shape), output_shape)
+
+    def test_super_simple_learn_norm(self):
+        out_features = spaces.Categorical(12, 24, 36)
+        bias = spaces.Categorical(True, False)
+        model = super_core.SuperSequential(
+            super_core.SuperSimpleLearnableNorm(),
+            super_core.SuperIdentity(),
+            super_core.SuperLinear(10, out_features, bias=bias),
+        )
+        print("The simple super module is:\n{:}".format(model))
+        model.apply_verbose(True)
+
+        print(model.super_run_type)
+        self.assertTrue(model[1].bias)
+
+        inputs = torch.rand(20, 10)
+        print("Input shape: {:}".format(inputs.shape))
+        outputs = model(inputs)
+        self.assertEqual(tuple(outputs.shape), (20, 36))
+
+        abstract_space = model.abstract_search_space
+        abstract_space.clean_last()
+        abstract_child = abstract_space.random()
+        print("The abstract searc space:\n{:}".format(abstract_space))
+        print("The abstract child program:\n{:}".format(abstract_child))
+
+        model.set_super_run_type(super_core.SuperRunMode.Candidate)
+        model.apply_candidate(abstract_child)
+
+        output_shape = (20, abstract_child["1"]["_out_features"].value)
+        outputs = model(inputs)
+        self.assertEqual(tuple(outputs.shape), output_shape)