diff --git a/colossalai/nn/layer/colossalai_layer/dropout.py b/colossalai/nn/layer/colossalai_layer/dropout.py
index ff86e0745..f1dc297a1 100644
--- a/colossalai/nn/layer/colossalai_layer/dropout.py
+++ b/colossalai/nn/layer/colossalai_layer/dropout.py
@@ -9,6 +9,14 @@ from ..utils import get_tensor_parallel_mode
 
 
 class Dropout(nn.Module):
+    """
+    Dropout layer of colossalai
+
+    :param p: dropout rate, defaults to 0.5
+    :type p: float, optional
+    :param inplace: If set to ``True``, will do this operation in-place, defaults tp ``False``
+    :type inplace: bool, optional
+    """
     def __init__(self, p: float = 0.5, inplace: bool = False) -> None:
         super().__init__()
         self.tensor_parallel = get_tensor_parallel_mode()
diff --git a/colossalai/nn/layer/colossalai_layer/embedding.py b/colossalai/nn/layer/colossalai_layer/embedding.py
index 6a580a29d..cd93ddbd9 100644
--- a/colossalai/nn/layer/colossalai_layer/embedding.py
+++ b/colossalai/nn/layer/colossalai_layer/embedding.py
@@ -24,6 +24,20 @@ _parallel_patchembedding = {
 
 
 class Embedding(nn.Module):
+    """
+    Embedding for colossalai
+
+    :param num_embeddings: number of embeddings
+    :type num_embeddings: int
+    :param embedding_dim: dimension of embedding
+    :type embedding_dim: int
+    :param padding_idx: index of padding, defaults to None
+    :type padding_idx: int, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to normal initializer
+    :type weight_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  num_embeddings: int,
                  embedding_dim: int,
@@ -63,6 +77,28 @@ class Embedding(nn.Module):
 
 
 class PatchEmbedding(nn.Module):
+    """
+    2D Image to Patch Embedding
+
+    :param img_size: image size
+    :type img_size: int
+    :param patch_size: patch size
+    :type patch_size: int
+    :param in_chans: number of channels of input image
+    :type in_chans: int
+    :param embed_size: size of embedding
+    :type embed_size: int
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param flatten: whether to flatten output tensor, defaults to True
+    :type flatten: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    :param position_embed_initializer: The intializer of position embedding, defaults to zero
+    :type position_embed_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  img_size: int,
                  patch_size: int,
diff --git a/colossalai/nn/layer/colossalai_layer/linear.py b/colossalai/nn/layer/colossalai_layer/linear.py
index 7c78941a2..606daff9c 100644
--- a/colossalai/nn/layer/colossalai_layer/linear.py
+++ b/colossalai/nn/layer/colossalai_layer/linear.py
@@ -25,6 +25,22 @@ _parallel_classifier = {
 
 
 class Linear(nn.Module):
+    """
+    Linear layer of colossalai
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param out_features: size of each output sample
+    :type out_features: int
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  out_features: int,
@@ -64,6 +80,22 @@ class Linear(nn.Module):
 
 
 class Classifier(nn.Module):
+    """
+    Classifier layer of colossalai
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param num_classes: number of total classes for the dataset
+    :type num_classes: int
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(
         self,
         in_features: int,
diff --git a/colossalai/nn/layer/colossalai_layer/normalization.py b/colossalai/nn/layer/colossalai_layer/normalization.py
index f1dab93f9..b29e1fbab 100644
--- a/colossalai/nn/layer/colossalai_layer/normalization.py
+++ b/colossalai/nn/layer/colossalai_layer/normalization.py
@@ -15,6 +15,19 @@ _parallel_layernorm = {'2d': LayerNorm2D, '2.5d': LayerNorm2p5D, '3d': LayerNorm
 
 
 class LayerNorm(nn.Module):
+    r"""
+    Layer Normalization for colossalai
+
+    :param normalized_shape: input shape from an expected input
+        of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
+        If a single integer is used, it is treated as a singleton list, and this module will
+        normalize over the last dimension which is expected to be of that specific size.
+    :type normalized_shape: int
+    :param eps: a value added to the denominator for numerical stability, defaults to 1e-05
+    :type eps: float, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    """
     def __init__(self, normalized_shape: int, eps=1e-05, dtype=None) -> None:
         super().__init__()
         tensor_parallel = get_tensor_parallel_mode()
diff --git a/colossalai/nn/layer/parallel_1d/_operation.py b/colossalai/nn/layer/parallel_1d/_operation.py
index aee28926a..d6b851e92 100644
--- a/colossalai/nn/layer/parallel_1d/_operation.py
+++ b/colossalai/nn/layer/parallel_1d/_operation.py
@@ -7,6 +7,18 @@ except:
 
 
 class FusedLayerNormAffineFunction1D(torch.autograd.Function):
+  r"""
+  Layernorm
+
+  :param input: input maxtrix
+  :param weight: weight matrix
+  :param bias: bias matrix
+  :param normalized_shape: input shape from an expected input
+        of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
+        If a single integer is used, it is treated as a singleton list, and this module will
+        normalize over the last dimension which is expected to be of that specific size.
+  :param eps: a value added to the denominator for numerical stability
+  """
 
   @staticmethod
   def forward(ctx, input, weight, bias, normalized_shape, eps):
diff --git a/colossalai/nn/layer/parallel_1d/_utils.py b/colossalai/nn/layer/parallel_1d/_utils.py
index db589afe5..602bd6c3f 100644
--- a/colossalai/nn/layer/parallel_1d/_utils.py
+++ b/colossalai/nn/layer/parallel_1d/_utils.py
@@ -76,7 +76,12 @@ def _gather(input_, parallel_mode, dim=-1):
 
 
 class _ReduceGrad(torch.autograd.Function):
-    """Pass the input to the model parallel region."""
+    """
+    Pass the input to the model parallel region.
+
+    :param input_: input matrix
+    :param parallel_mode: parallel mode
+    """
     @staticmethod
     def symbolic(graph, input_):
         return input_
@@ -92,7 +97,12 @@ class _ReduceGrad(torch.autograd.Function):
 
 
 class _ReduceInput(torch.autograd.Function):
-    """All-reduce the input from the model parallel region."""
+    """
+    All-reduce the input from the model parallel region.
+    
+    :param input_: input matrix
+    :param parallel_mode: parallel mode
+    """
     @staticmethod
     def symbolic(graph, input_):
         return _reduce(input_)
@@ -107,7 +117,13 @@ class _ReduceInput(torch.autograd.Function):
 
 
 class _SplitForwardGatherBackward(torch.autograd.Function):
-    """Split the input and keep only the corresponding chuck to the rank."""
+    """
+    Split the input and keep only the corresponding chuck to the rank.
+    
+    :param input_: input matrix
+    :param parallel_mode: parallel mode
+    :param dim: dimension
+    """
     @staticmethod
     def symbolic(graph, input_):
         return _split(input_)
@@ -124,7 +140,13 @@ class _SplitForwardGatherBackward(torch.autograd.Function):
 
 
 class _GatherForwardSplitBackward(torch.autograd.Function):
-    """Gather the input from model parallel region and concatinate."""
+    """
+    Gather the input from model parallel region and concatinate.
+    
+    :param input_: input matrix
+    :param parallel_mode: parallel mode
+    :param dim: dimension
+    """
     @staticmethod
     def symbolic(graph, input_):
         return _gather(input_)
diff --git a/colossalai/nn/layer/parallel_1d/layers.py b/colossalai/nn/layer/parallel_1d/layers.py
index 832d7d9df..9e3fe9bdd 100644
--- a/colossalai/nn/layer/parallel_1d/layers.py
+++ b/colossalai/nn/layer/parallel_1d/layers.py
@@ -26,6 +26,24 @@ from ._utils import (gather_forward_split_backward, get_parallel_input, reduce_g
 
 @LAYERS.register_module
 class Linear1D(torch.nn.Module):
+    """
+    Linear layer for 1D parallelism
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param out_features: size of each output sample
+    :type out_features: int
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param skip_bias_add: If set to ``True``, it will skip bias add for linear layer, which is preserved for kernel fusion, defaults to False
+    :type skip_bias_add: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  out_features: int,
@@ -70,8 +88,24 @@ class Linear1D(torch.nn.Module):
 
 @LAYERS.register_module
 class Classifier1D(ParallelLayer):
-    """RowLinear with given weight"""
-
+    """RowLinear with given weight
+    Classifier of 1D parallelism
+    
+    :param in_features: size of input features
+    :type in_features: int
+    :param num_classes: number of classes in the dataset
+    :type num_classes: int
+    :param weight: weight of the classifier, defaults to True
+    :type weight: torch.nn.Parameter, optional
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to ``True``
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  num_classes: int,
@@ -144,7 +178,7 @@ class Linear1D_Col(ParallelLayer):
     :type in_features: int
     :param output_size: second dimension of matrix A.
     :type output_size: int
-    :param bias: If true, add bias, defaults to True
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to ``True``
     :type bias: bool, optional
     :param dtype: The dtype of parameters, defaults to None
     :type dtype: torch.dtype, optional
@@ -228,7 +262,7 @@ class Linear1D_Row(ParallelLayer):
     :type in_features: int
     :param out_features: size of each output sample
     :type out_features: int
-    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to ``True``
     :type bias: bool, optional
     :param dtype: The dtype of parameters, defaults to None
     :type dtype: torch.dtype, optional
@@ -303,7 +337,16 @@ class Linear1D_Row(ParallelLayer):
 
 @LAYERS.register_module
 class MixedFusedLayerNorm1D(torch.nn.Module):
-    """ Experimental
+    r"""
+    Layer Normalization for 1D parallelism
+
+    :param normalized_shape: input shape from an expected input
+        of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
+        If a single integer is used, it is treated as a singleton list, and this module will
+        normalize over the last dimension which is expected to be of that specific size.
+    :type normalized_shape: int
+    :param eps: a value added to the denominator for numerical stability, defaults to 1e-05
+    :type eps: float, optional
     """
 
     def __init__(self, normalized_shape, eps=1e-5):
@@ -327,6 +370,20 @@ class MixedFusedLayerNorm1D(torch.nn.Module):
 
 @LAYERS.register_module
 class Embedding1D(ParallelLayer):
+    """
+    Embedding for 1D parallelism
+
+    :param num_embeddings: number of embeddings
+    :type num_embeddings: int
+    :param embedding_dim: dimension of embedding
+    :type embedding_dim: int
+    :param padding_idx: index of padding, defaults to None
+    :type padding_idx: int, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to normal initializer
+    :type weight_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  num_embeddings: int,
                  embedding_dim: int,
@@ -377,6 +434,14 @@ class Embedding1D(ParallelLayer):
 
 @LAYERS.register_module
 class Dropout1D(ParallelLayer):
+    """
+    Dropout layer of 1D parallelism
+
+    :param p: dropout rate, defaults to 0.5
+    :type p: float, optional
+    :param inplace: If set to ``True``, will do this operation in-place, defaults tp ``False``
+    :type inplace: bool, optional
+    """
     def __init__(self, p: float = 0.5, inplace: bool = False):
         super().__init__()
         self.parallel_input = get_parallel_input()
diff --git a/colossalai/nn/layer/parallel_2d/_operation.py b/colossalai/nn/layer/parallel_2d/_operation.py
index ef899a5ec..a8f3aa565 100644
--- a/colossalai/nn/layer/parallel_2d/_operation.py
+++ b/colossalai/nn/layer/parallel_2d/_operation.py
@@ -20,7 +20,8 @@ def matmul_2d(
     row_parallel_mode=ParallelMode.PARALLEL_2D_ROW,
     col_parallel_mode=ParallelMode.PARALLEL_2D_COL,
 ):
-    """Matrix multiplication for 2D parallelism
+    """
+    Matrix multiplication for 2D parallelism
     :param a: matrix :math:`A`
     :type a: torch.tensor
     :param b: matrix :math:`B`
@@ -56,7 +57,35 @@ def matmul_2d(
 
 
 class classifier_2d(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = AB`
+    """
+    Classifier
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param bias: matrix of bias
+    :type bias: torch.tensor, optional
+    :param summa_dim: dimension of SUMMA fo 2D parallelism
+    :type summa_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -130,7 +159,33 @@ class classifier_2d(torch.autograd.Function):
 
 
 class Matmul_AB_2D(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = AB`
+    """
+    Matrix multiplication for :math:`C = AB`
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param summa_dim: dimension of SUMMA fo 2D parallelism
+    :type summa_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -238,7 +293,33 @@ class Matmul_AB_2D(torch.autograd.Function):
 
 
 class Matmul_ABT_2D(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = AB^T`
+    """
+    Matrix multiplication for :math:`C = AB^T`
+    
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param summa_dim: dimension of SUMMA fo 2D parallelism
+    :type summa_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -352,7 +433,33 @@ class Matmul_ABT_2D(torch.autograd.Function):
 
 
 class Matmul_ATB_2D(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = A^TB`
+    """
+    Matrix multiplication for :math:`C = A^TB`
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param summa_dim: dimension of SUMMA fo 2D parallelism
+    :type summa_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -466,7 +573,33 @@ class Matmul_ATB_2D(torch.autograd.Function):
 
 
 class add_bias_2d(torch.autograd.Function):
-    """Matrix add bias: :math:`C = A + b`
+    """
+    Matrix add bias: :math:`C = A + b`
+
+    :param input_: matrix :math:`A`
+    :type input_: torch.tensor
+    :param bias: matrix :math:`b`
+    :type bias: torch.tensor
+    :param output_size_per_partition: size of ouput per partition
+    :type output_size_per_partition: int
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param skip_bias_add: If set to ``True``, it will skip bias add for linear layer, which is preserved for kernel fusion
+    :type skip_bias_add: bool
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -519,9 +652,30 @@ class add_bias_2d(torch.autograd.Function):
 
 
 class layernorm_2d(torch.autograd.Function):
+    """
+    Layernorm
+
+    :param input_: input maxtrix
+    :type input_: torch.tensor
+    :param E_x: mean
+    :type E_x: torch.tensor
+    :param Var_x: variance
+    :type Var_x: torch.tensor
+    :param hidden_size: hidden size
+    :type hidden_size: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float32)
-    def forward(ctx: Any, input_: Tensor, E_x: Tensor, Var_x: Tensor, hidden_size: int, row_parallel_mode: ParallelMode,
+    def forward(ctx: Any, 
+                input_: Tensor, 
+                E_x: Tensor, 
+                Var_x: Tensor, 
+                hidden_size: int, 
+                row_parallel_mode: ParallelMode,
                 col_parallel_mode: ParallelMode) -> Tensor:
         input_ = input_ - E_x
         # in here, input = x - E[x], Var_x = 1 / sqrt(Var[x] + eps)
@@ -556,6 +710,18 @@ class layernorm_2d(torch.autograd.Function):
 
 
 class all_gather_weight_2d(torch.autograd.Function):
+    """
+    all gather the weight of 2D parallelism
+
+    :param inputs: input maxtrix
+    :type inputs: torch.tensor
+    :param dim: dimension of all gather
+    :type dim: int
+    :param summa_dim: dimension of SUMMA fo 2D parallelism
+    :type summa_dim: int
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx: Any, inputs: Tensor, dim: int, summa_dim: int, col_parallel_mode: ParallelMode) -> Tensor:
@@ -574,6 +740,14 @@ class all_gather_weight_2d(torch.autograd.Function):
 
 
 class SplitFirst(torch.autograd.Function):
+    """
+    :param inputs: input maxtrix
+    :type inputs: torch.tensor
+    :param summa_dim: dimension of SUMMA fo 2D parallelism
+    :type summa_dim: int
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx: Any, inputs: Tensor, summa_dim: int, col_parallel_mode: ParallelMode) -> Tensor:
@@ -604,7 +778,14 @@ def split_tensor_2d(input_: Tensor, dim: int = 0) -> Tensor:
 
 
 class reduce_by_batch_2d(torch.autograd.Function):
-    """All-reduce the input from the model parallel region."""
+    """
+    All-reduce the input from the model parallel region.
+
+    :param input_: input maxtrix
+    :type input_: torch.tensor
+    :param reduce_mean:  If set to ``True``, it will divide the output by column parallel size, default to False
+    :type reduce_mean: int, optional
+    """
     @staticmethod
     def symbolic(graph, input_, reduce_mean: bool = False):
         output = all_reduce(input_, ParallelMode.PARALLEL_2D_COL)
diff --git a/colossalai/nn/layer/parallel_2d/layers.py b/colossalai/nn/layer/parallel_2d/layers.py
index d113ec94c..f2c8af63b 100644
--- a/colossalai/nn/layer/parallel_2d/layers.py
+++ b/colossalai/nn/layer/parallel_2d/layers.py
@@ -21,7 +21,8 @@ from ._utils import assert_summa_initialization, get_summa_dim_from_env
 
 @LAYERS.register_module
 class Linear2D(ParallelLayer):
-    """ Linear layer for 2D parallelism
+    """
+    Linear layer for 2D parallelism
 
     :param in_features: size of each input sample
     :type in_features: int
@@ -33,6 +34,10 @@ class Linear2D(ParallelLayer):
     :type dtype: torch.dtype, optional
     :param skip_bias_add: If set to ``True``, it will skip bias add for linear layer, which is preserved for kernel fusion, defaults to False
     :type skip_bias_add: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
     """
     def __init__(self,
                  in_features: int,
@@ -113,7 +118,8 @@ class Linear2D(ParallelLayer):
 
 @LAYERS.register_module
 class LayerNorm2D(ParallelLayer):
-    r"""Layer Normalization for 2D parallelism
+    r"""
+    Layer Normalization for 2D parallelism
 
     :param normalized_shape: input shape from an expected input
         of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
@@ -184,18 +190,27 @@ class LayerNorm2D(ParallelLayer):
 
 @LAYERS.register_module
 class PatchEmbedding2D(ParallelLayer):
-    """ 2D Image to Patch Embedding
+    """
+    2D Image to Patch Embedding
 
-    :param img_size: iamge size
+    :param img_size: image size
     :type img_size: int
     :param patch_size: patch size
     :type patch_size: int
-    :param embed_dim: dimension of embedding
-    :type embed_dim: int
-    :param in_chans: number of channels of input image, defaults to 3
-    :type in_chans: int, optional
+    :param in_chans: number of channels of input image
+    :type in_chans: int
+    :param embed_size: size of embedding
+    :type embed_size: int
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
     :param flatten: whether to flatten output tensor, defaults to True
     :type flatten: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    :param position_embed_initializer: The intializer of position embedding, defaults to zero
+    :type position_embed_initializer: typing.Callable, optional
     """
     def __init__(self,
                  img_size: int,
@@ -275,6 +290,20 @@ class PatchEmbedding2D(ParallelLayer):
 
 @LAYERS.register_module
 class Embedding2D(ParallelLayer):
+    """
+    Embedding for 2D parallelism
+
+    :param num_embeddings: number of embeddings
+    :type num_embeddings: int
+    :param embedding_dim: dimension of embedding
+    :type embedding_dim: int
+    :param padding_idx: index of padding, defaults to None
+    :type padding_idx: int, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to normal initializer
+    :type weight_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  num_embeddings: int,
                  embedding_dim: int,
@@ -325,6 +354,24 @@ class Embedding2D(ParallelLayer):
 
 @LAYERS.register_module
 class Classifier2D(ParallelLayer):
+    """
+    Classifier for 2D parallelism
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param num_classes: number of classes
+    :type num_classes: int
+    :param weight: weight of the classifier, defaults to True
+    :type weight: torch.nn.Parameter, optional
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to ``True``
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  num_classes: int,
diff --git a/colossalai/nn/layer/parallel_2p5d/_operation.py b/colossalai/nn/layer/parallel_2p5d/_operation.py
index a1dbcd3cd..f583a0f02 100644
--- a/colossalai/nn/layer/parallel_2p5d/_operation.py
+++ b/colossalai/nn/layer/parallel_2p5d/_operation.py
@@ -28,7 +28,35 @@ def split_tensor_2p5d(input_: Tensor, dim: int = 0) -> Tensor:
 
 
 class classifier_2p5d(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = AB`
+    """
+    Classifier
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param bias: matrix of bias
+    :type bias: torch.tensor, optional
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -101,7 +129,35 @@ class classifier_2p5d(torch.autograd.Function):
 
 
 class Matmul_AB_2p5D(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = AB`
+    """
+    Matrix multiplication for :math:`C = AB`
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param dep_rank: the rank of depth
+    :type dep_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -202,7 +258,35 @@ class Matmul_AB_2p5D(torch.autograd.Function):
 
 
 class Matmul_ABT_2p5D(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = AB^T`
+    """
+    Matrix multiplication for :math:`C = AB^T`
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param dep_rank: the rank of depth
+    :type dep_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -308,7 +392,35 @@ class Matmul_ABT_2p5D(torch.autograd.Function):
 
 
 class Matmul_ATB_2p5D(torch.autograd.Function):
-    """Matrix multiplication for :math:`C = A^TB`
+    """
+    Matrix multiplication for :math:`C = A^TB`
+
+    :param a: matrix :math:`A`
+    :type a: torch.tensor
+    :param b: matrix :math:`B`
+    :type b: torch.tensor
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param out_shape: shape of output tensor
+    :type out_shape: tuple
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param dep_rank: the rank of depth
+    :type dep_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -411,7 +523,35 @@ class Matmul_ATB_2p5D(torch.autograd.Function):
 
 
 class Add_Bias_2p5D(torch.autograd.Function):
-    """Matrix add bias: :math:`C = A + b`
+    """
+    Matrix add bias: :math:`C = A + b`
+
+    :param input: matrix :math:`A`
+    :type input: torch.tensor
+    :param bias: matrix :math:`b`
+    :type bias: torch.tensor
+    :param output_size_per_partition: output size in each partition
+    :type output_size_per_partition: int
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param row_rank: the rank of row
+    :type row_rank: int
+    :param col_rank: the rank of column
+    :type col_rank: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param skip_bias_add: If set to ``True``, it will skip bias add for linear layer, which is preserved for kernel fusion
+    :type skip_bias_add: bool
+    :param data_parallel_rank: data parallel rank
+    :type data_parallel_rank: int
+    :param pipeline_parallel_rank: pipeline parallel rank
+    :type pipeline_parallel_rank: int
+    :param pipeline_parallel_size: pipeline parallel size
+    :type pipeline_parallel_size: int
+    :param tensor_parallel_size: tensor parallel size
+    :type tensor_parallel_size: int
     """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
@@ -482,6 +622,20 @@ class Add_Bias_2p5D(torch.autograd.Function):
 
 
 class layernorm_2p5d(torch.autograd.Function):
+    """
+    Layernorm
+
+    :param input: input maxtrix
+    :type input: torch.tensor
+    :param E_x: mean
+    :type E_x: torch.tensor
+    :param Var_x: variance
+    :type Var_x: torch.tensor
+    :param hidden_size: hidden size
+    :type hidden_size: int
+    :param row_parallel_mode: row parallel mode
+    :type row_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float32)
     def forward(ctx: Any, input: Tensor, E_x: Tensor, Var_x: Tensor, hidden_size: int,
@@ -518,6 +672,18 @@ class layernorm_2p5d(torch.autograd.Function):
 
 
 class all_gather_weight_2p5d(torch.autograd.Function):
+    """
+    all gather the weight of 2.5D parallelism
+
+    :param inputs: input maxtrix
+    :type inputs: torch.tensor
+    :param dim: dimension of all gather
+    :type dim: int
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx: Any, inputs: Tensor, dim: int, tesseract_dim: int, col_parallel_mode: ParallelMode) -> Tensor:
@@ -536,6 +702,14 @@ class all_gather_weight_2p5d(torch.autograd.Function):
 
 
 class SplitFirst(torch.autograd.Function):
+    """
+    :param inputs: input maxtrix
+    :type inputs: torch.tensor
+    :param tesseract_dim: dimension of TESSERACT fo 2.5D parallelism
+    :type tesseract_dim: int
+    :param col_parallel_mode: column parallel mode
+    :type col_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx: Any, inputs: Tensor, tesseract_dim: int, col_parallel_mode: ParallelMode) -> Tensor:
@@ -566,7 +740,14 @@ def split_tensor_2p5d(input_: Tensor, dim: int = 0) -> Tensor:
 
 
 class reduce_by_batch_2p5d(torch.autograd.Function):
-    """All-reduce the input from the model parallel region."""
+    """
+    All-reduce the input from the model parallel region.
+
+    :param input_: input maxtrix
+    :type input_: torch.tensor
+    :param reduce_mean:  If set to ``True``, it will divide the output by column parallel size, default to False
+    :type reduce_mean: int, optional
+    """
     @staticmethod
     def symbolic(graph, input_, reduce_mean: bool = False):
         output = all_reduce(input_, ParallelMode.PARALLEL_2P5D_COL)
diff --git a/colossalai/nn/layer/parallel_2p5d/layers.py b/colossalai/nn/layer/parallel_2p5d/layers.py
index d7bd265bd..9f0e6679e 100644
--- a/colossalai/nn/layer/parallel_2p5d/layers.py
+++ b/colossalai/nn/layer/parallel_2p5d/layers.py
@@ -21,7 +21,8 @@ from ._utils import (assert_tesseract_initialization, get_tesseract_dim_dep_from
 
 @LAYERS.register_module
 class Linear2p5D(ParallelLayer):
-    """Linear layer for 2.5D parallelism
+    """
+    Linear layer for 2.5D parallelism
 
     :param in_features: size of each input sample
     :type in_features: int
@@ -31,6 +32,10 @@ class Linear2p5D(ParallelLayer):
     :type bias: bool, optional
     :param dtype: The dtype of parameters, defaults to None
     :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
     """
     def __init__(self,
                  in_features: int,
@@ -125,7 +130,8 @@ class Linear2p5D(ParallelLayer):
 
 @LAYERS.register_module
 class LayerNorm2p5D(ParallelLayer):
-    r"""Layer Normalization for 2.5D parallelism
+    r"""
+    Layer Normalization for 2.5D parallelism
 
     :param normalized_shape: input shape from an expected input
         of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
@@ -196,17 +202,27 @@ class LayerNorm2p5D(ParallelLayer):
 
 @LAYERS.register_module
 class PatchEmbedding2p5D(ParallelLayer):
-    """ 2D Image to Patch Embedding
-    :param img_size: iamge size
+    """
+    2D Image to Patch Embedding
+
+    :param img_size: image size
     :type img_size: int
     :param patch_size: patch size
     :type patch_size: int
-    :param embed_dim: dimension of embedding
-    :type embed_dim: int
-    :param in_chans: number of channels of input image, defaults to 3
-    :type in_chans: int, optional
+    :param in_chans: number of channels of input image
+    :type in_chans: int
+    :param embed_size: size of embedding
+    :type embed_size: int
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
     :param flatten: whether to flatten output tensor, defaults to True
     :type flatten: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    :param position_embed_initializer: The intializer of position embedding, defaults to zero
+    :type position_embed_initializer: typing.Callable, optional
     """
     def __init__(self,
                  img_size: int,
@@ -286,6 +302,20 @@ class PatchEmbedding2p5D(ParallelLayer):
 
 @LAYERS.register_module
 class Embedding2p5D(ParallelLayer):
+    """
+    Embedding for 2.5D parallelism
+
+    :param num_embeddings: number of embeddings
+    :type num_embeddings: int
+    :param embedding_dim: dimension of embedding
+    :type embedding_dim: int
+    :param padding_idx: index of padding, defaults to None
+    :type padding_idx: int, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to normal initializer
+    :type weight_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  num_embeddings: int,
                  embedding_dim: int,
@@ -336,6 +366,24 @@ class Embedding2p5D(ParallelLayer):
 
 @LAYERS.register_module
 class Classifier2p5D(ParallelLayer):
+    """
+    Classifier for 2.5D parallelism
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param num_classes: number of classes
+    :type num_classes: int
+    :param weight: weight of the classifier, defaults to True
+    :type weight: torch.nn.Parameter, optional
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  num_classes: int,
diff --git a/colossalai/nn/layer/parallel_3d/_operation.py b/colossalai/nn/layer/parallel_3d/_operation.py
index 96ed775ec..19ceb897e 100644
--- a/colossalai/nn/layer/parallel_3d/_operation.py
+++ b/colossalai/nn/layer/parallel_3d/_operation.py
@@ -12,6 +12,28 @@ from torch.cuda.amp import custom_bwd, custom_fwd
 
 
 class linear_3d(torch.autograd.Function):
+    """
+    Linear layer for 3D parallelism
+
+    :param input_: matrix of input
+    :type input_: torch.tensor
+    :param weight: matrix of weight
+    :type weight: torch.tensor
+    :param bias: matrix of bias
+    :type bias: torch.tensor, optional
+    :param input_parallel_mode: input parallel mode
+    :type input_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param weight_parallel_mode: weight parallel mode
+    :type weight_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param output_parallel_mode: output parallel mode
+    :type output_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param input_dim: dimension of input, defaults to 0
+    :type input_dim: int, optional
+    :param weight_dim: dimension of weight, defaults to -1
+    :type weight_dim: int, optional
+    :param output_dim: dimension of output, defaults to 0
+    :type output_dim: int, optional
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx,
@@ -74,6 +96,22 @@ class linear_3d(torch.autograd.Function):
 
 
 class classifier_3d(torch.autograd.Function):
+    """
+    Classifier
+
+    :param input_: matrix of input
+    :type input_: torch.tensor
+    :param weight: matrix of weight
+    :type weight: torch.tensor
+    :param bias: matrix of bias
+    :type bias: torch.tensor, optional
+    :param input_parallel_mode: input parallel mode
+    :type input_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param weight_parallel_mode: weight parallel mode
+    :type weight_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param output_parallel_mode: output parallel mode
+    :type output_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx, input_: Tensor, weight: Tensor, bias: Optional[Tensor], input_parallel_mode: ParallelMode,
@@ -129,6 +167,29 @@ class classifier_3d(torch.autograd.Function):
 
 
 class layernorm_3d(torch.autograd.Function):
+    """
+    Layernorm
+
+    :param input_: input maxtrix
+    :type input_: torch.tensor
+    :param weight: matrix of weight
+    :type weight: torch.tensor
+    :param bias: matrix of bias
+    :type bias: torch.tensor
+    :param normalized_shape: input shape from an expected input
+        of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
+        If a single integer is used, it is treated as a singleton list, and this module will
+        normalize over the last dimension which is expected to be of that specific size.
+    :type normalized_shape: int
+    :param eps: a value added to the denominator for numerical stability
+    :type eps: float
+    :param input_parallel_mode: input parallel mode
+    :type input_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param weight_parallel_mode: weight parallel mode
+    :type weight_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param output_parallel_mode: output parallel mode
+    :type output_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float32)
     def forward(ctx, input_: Tensor, weight: Tensor, bias: Tensor, normalized_shape: int, eps: float,
@@ -189,6 +250,18 @@ def split_tensor_3d(input_: Tensor,
 
 
 class reduce_by_batch_3d(torch.autograd.Function):
+    """
+    All-reduce the input from the model parallel region.
+
+    :param input_: input maxtrix
+    :type input_: torch.tensor
+    :param input_parallel_mode: input parallel mode
+    :type input_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param weight_parallel_mode: weight parallel mode
+    :type weight_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param reduce_mean:  If set to ``True``, it will divide the output by (input parallel size * weight parallel size), default to False
+    :type reduce_mean: int, optional
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float32)
     def forward(ctx,
@@ -215,6 +288,18 @@ class reduce_by_batch_3d(torch.autograd.Function):
 
 
 class broadcast_weight_3d_from_diagonal(torch.autograd.Function):
+    """
+    broadcast weight from diagonal
+
+    :param input_: input maxtrix
+    :type input_: torch.tensor
+    :param input_parallel_mode: input parallel mode
+    :type input_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param weight_parallel_mode: weight parallel mode
+    :type weight_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    :param weight_parallel_mode: output parallel mode
+    :type weight_parallel_mode: colossalai.context.parallel_mode.ParallelMode
+    """
     @staticmethod
     @custom_fwd(cast_inputs=torch.float16)
     def forward(ctx, input_: Tensor, input_parallel_mode: ParallelMode, weight_parallel_mode: ParallelMode,
diff --git a/colossalai/nn/layer/parallel_3d/layers.py b/colossalai/nn/layer/parallel_3d/layers.py
index 4871d1443..66f2b98a5 100644
--- a/colossalai/nn/layer/parallel_3d/layers.py
+++ b/colossalai/nn/layer/parallel_3d/layers.py
@@ -24,6 +24,19 @@ from ._utils import get_depth_from_env, get_last_group, get_parallel_mode_from_e
 
 @LAYERS.register_module
 class LayerNorm3D(ParallelLayer):
+    r"""
+    Layer Normalization for 3D parallelism
+
+    :param normalized_shape: input shape from an expected input
+        of size. :math:`[* \times \text{normalized_shape}[0] \times \text{normalized_shape}[1] \times \ldots \times \text{normalized_shape}[-1]]`
+        If a single integer is used, it is treated as a singleton list, and this module will
+        normalize over the last dimension which is expected to be of that specific size.
+    :type normalized_shape: int
+    :param eps: a value added to the denominator for numerical stability, defaults to 1e-12
+    :type eps: float, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    """
     def __init__(self, normalized_shape: int, eps: float = 1e-12, dtype: dtype = None):
         super().__init__()
         self.input_parallel_mode = get_parallel_mode_from_env(INPUT_GROUP_3D)
@@ -55,6 +68,22 @@ class LayerNorm3D(ParallelLayer):
 
 @LAYERS.register_module
 class Linear3D(ParallelLayer):
+    """
+    Linear layer for 3D parallelism
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param out_features: size of each output sample
+    :type out_features: int
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  out_features: int,
@@ -113,6 +142,24 @@ class Linear3D(ParallelLayer):
 
 @LAYERS.register_module
 class Classifier3D(ParallelLayer):
+    """
+    Classifier for 3D parallelism
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param num_classes: number of classes
+    :type num_classes: int
+    :param weight: weight of the classifier, defaults to True
+    :type weight: torch.nn.Parameter, optional
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  num_classes: int,
@@ -173,6 +220,28 @@ class Classifier3D(ParallelLayer):
 
 @LAYERS.register_module
 class PatchEmbedding3D(ParallelLayer):
+    """
+    2D Image to Patch Embedding
+
+    :param img_size: image size
+    :type img_size: int
+    :param patch_size: patch size
+    :type patch_size: int
+    :param in_chans: number of channels of input image
+    :type in_chans: int
+    :param embed_size: size of embedding
+    :type embed_size: int
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param flatten: whether to flatten output tensor, defaults to True
+    :type flatten: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    :param position_embed_initializer: The intializer of position embedding, defaults to zero
+    :type position_embed_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  img_size: int,
                  patch_size: int,
@@ -256,6 +325,20 @@ class PatchEmbedding3D(ParallelLayer):
 
 @LAYERS.register_module
 class Embedding3D(ParallelLayer):
+    """
+    Embedding for 3D parallelism
+
+    :param num_embeddings: number of embeddings
+    :type num_embeddings: int
+    :param embedding_dim: dimension of embedding
+    :type embedding_dim: int
+    :param padding_idx: index of padding, defaults to None
+    :type padding_idx: int, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to normal initializer
+    :type weight_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  num_embeddings: int,
                  embedding_dim: int,
diff --git a/colossalai/nn/layer/vanilla/layers.py b/colossalai/nn/layer/vanilla/layers.py
index dc33c461e..6f3d07abd 100644
--- a/colossalai/nn/layer/vanilla/layers.py
+++ b/colossalai/nn/layer/vanilla/layers.py
@@ -32,7 +32,8 @@ def drop_path(x, drop_prob: float = 0., training: bool = False):
 
 
 class DropPath(nn.Module):
-    """Drop paths (Stochastic Depth) per sample  (when applied in main path of residual blocks).
+    """
+    Drop paths (Stochastic Depth) per sample  (when applied in main path of residual blocks).
     Adapted from https://github.com/rwightman/pytorch-image-models/blob/master/timm/models/layers/drop.py
     """
     def __init__(self, drop_prob=None):
@@ -97,7 +98,27 @@ class WrappedDropPath(nn.Module):
 
 @LAYERS.register_module
 class VanillaPatchEmbedding(nn.Module):
-    """ 2D Image to Patch Embedding
+    """ 
+    2D Image to Patch Embedding
+
+    :param img_size: image size
+    :type img_size: int
+    :param patch_size: patch size
+    :type patch_size: int
+    :param in_chans: number of channels of input image
+    :type in_chans: int
+    :param embed_size: size of embedding
+    :type embed_size: int
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param flatten: whether to flatten output tensor, defaults to True
+    :type flatten: bool, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    :param position_embed_initializer: The intializer of position embedding, defaults to zero
+    :type position_embed_initializer: typing.Callable, optional
     """
     def __init__(self,
                  img_size: int,
@@ -148,6 +169,24 @@ class VanillaPatchEmbedding(nn.Module):
 
 @LAYERS.register_module
 class VanillaClassifier(nn.Module):
+    """
+    Classifier
+
+    :param in_features: size of each input sample
+    :type in_features: int
+    :param num_classes: number of classes
+    :type num_classes: int
+    :param weight: weight of the classifier, defaults to True
+    :type weight: torch.nn.Parameter, optional
+    :param bias: If set to ``False``, the layer will not learn an additive bias, defaults to True
+    :type bias: bool, optional
+    :param dtype: The dtype of parameters, defaults to None
+    :type dtype: torch.dtype, optional
+    :param weight_initializer: The intializer of weight, defaults to kaiming uniform initializer
+    :type weight_initializer: typing.Callable, optional
+    :param bias_initializer: The intializer of bias, defaults to xavier uniform initializer
+    :type bias_initializer: typing.Callable, optional
+    """
     def __init__(self,
                  in_features: int,
                  num_classes: int,
diff --git a/colossalai/nn/loss/loss_2d.py b/colossalai/nn/loss/loss_2d.py
index 7aef949f6..a1fb0a7fa 100644
--- a/colossalai/nn/loss/loss_2d.py
+++ b/colossalai/nn/loss/loss_2d.py
@@ -7,7 +7,8 @@ from torch.nn.modules.loss import _Loss
 
 @LOSSES.register_module
 class CrossEntropyLoss2D(_Loss):
-    """Cross entropy loss for 2D parallelism
+    """
+    Cross entropy loss for 2D parallelism
 
     :param reduction: whether to average the loss, defaults to True
     :type reduction: bool, optional
diff --git a/colossalai/nn/loss/loss_2p5d.py b/colossalai/nn/loss/loss_2p5d.py
index d7596d924..a849259b4 100644
--- a/colossalai/nn/loss/loss_2p5d.py
+++ b/colossalai/nn/loss/loss_2p5d.py
@@ -7,7 +7,9 @@ from torch.nn.modules.loss import _Loss
 
 @LOSSES.register_module
 class CrossEntropyLoss2p5D(_Loss):
-    """Cross entropy loss for 2.5D parallelism
+    """
+    Cross entropy loss for 2.5D parallelism
+    
     :param reduction: whether to average the loss, defaults to True
     :type reduction: bool, optional
     """
diff --git a/colossalai/nn/loss/loss_3d.py b/colossalai/nn/loss/loss_3d.py
index 59b6ffeeb..9b8083069 100644
--- a/colossalai/nn/loss/loss_3d.py
+++ b/colossalai/nn/loss/loss_3d.py
@@ -7,14 +7,11 @@ from torch.nn.modules.loss import _Loss
 
 @LOSSES.register_module
 class CrossEntropyLoss3D(_Loss):
-    """Cross entropy loss for 3D parallelism
+    """
+    Cross entropy loss for 3D parallelism
 
     :param depth: depth for 3D parallelism
     :type depth: int
-    :param input_parallel_mode: parallel mode for input tensor
-    :type input_parallel_mode: ParallelMode
-    :param weight_parallel_mode: parallel mode for weight
-    :type weight_parallel_mode: ParallelMode
     :param reduction: whether to average the loss, defaults to True
     :type reduction: bool, optional
     """
diff --git a/colossalai/nn/metric/accuracy_2d.py b/colossalai/nn/metric/accuracy_2d.py
index cc207b02c..5bcbfa65c 100644
--- a/colossalai/nn/metric/accuracy_2d.py
+++ b/colossalai/nn/metric/accuracy_2d.py
@@ -6,6 +6,12 @@ from ._utils import calc_acc
 
 
 class Accuracy2D(nn.Module):
+    """
+    Accuracy for 2D parallelism
+
+    :param logits: predicted labels
+    :param targets: true labels
+    """
     def __init__(self):
         super().__init__()
 
diff --git a/colossalai/nn/metric/accuracy_2p5d.py b/colossalai/nn/metric/accuracy_2p5d.py
index 90dc4af26..b7c9c6afb 100644
--- a/colossalai/nn/metric/accuracy_2p5d.py
+++ b/colossalai/nn/metric/accuracy_2p5d.py
@@ -6,6 +6,12 @@ from ._utils import calc_acc
 
 
 class Accuracy2p5D(nn.Module):
+    """
+    Accuracy for 2p5D parallelism
+
+    :param logits: predicted labels
+    :param targets: true labels
+    """
     def __init__(self):
         super().__init__()
 
diff --git a/colossalai/nn/metric/accuracy_3d.py b/colossalai/nn/metric/accuracy_3d.py
index 576800510..57b1874ba 100644
--- a/colossalai/nn/metric/accuracy_3d.py
+++ b/colossalai/nn/metric/accuracy_3d.py
@@ -8,6 +8,12 @@ from ._utils import calc_acc
 
 
 class Accuracy3D(nn.Module):
+    """
+    Accuracy for 3D parallelism
+
+    :param logits: predicted labels
+    :param targets: true labels
+    """
     def __init__(self):
         super().__init__()
         self.input_parallel_mode = get_parallel_mode_from_env(INPUT_GROUP_3D)
diff --git a/colossalai/trainer/hooks/_base_hook.py b/colossalai/trainer/hooks/_base_hook.py
index e4b5edfbf..0b32f4ca2 100644
--- a/colossalai/trainer/hooks/_base_hook.py
+++ b/colossalai/trainer/hooks/_base_hook.py
@@ -10,10 +10,9 @@ class BaseHook(ABC):
     """This class allows users to add desired actions in specific time points
     during training or evaluation.
 
-    :param trainer: Trainer attached with current hook
     :param priority: Priority in the printing, hooks with small priority will be printed in front
-    :type trainer: Trainer
     :type priority: int
+    :param trainer: Trainer attached with current hook
     """
 
     def __init__(self, priority: int) -> None:
@@ -43,11 +42,11 @@ class BaseHook(ABC):
         """Actions after running a training iteration.
 
         :param output: Output of the model
+        :type output: torch.Tensor
         :param label: Labels of the input data
+        :type label: torch.Tensor
         :param loss: Loss between the output and input data
-        :type output: Tensor
-        :type label: Tensor
-        :type loss: Tensor
+        :type loss: torch.Tensor
         """
         pass
 
@@ -90,10 +89,10 @@ class BaseHook(ABC):
         """Actions after running a testing iteration.
 
         :param output: Output of the model
-        :param label: Labels of the input data
-        :param loss: Loss between the output and input data
         :type output: Tensor
+        :param label: Labels of the input data
         :type label: Tensor
+        :param loss: Loss between the output and input data
         :type loss: Tensor
         """
         pass
diff --git a/colossalai/trainer/hooks/_checkpoint_hook.py b/colossalai/trainer/hooks/_checkpoint_hook.py
index 939e957bd..9fc8d59c5 100644
--- a/colossalai/trainer/hooks/_checkpoint_hook.py
+++ b/colossalai/trainer/hooks/_checkpoint_hook.py
@@ -16,14 +16,15 @@ from ._lr_scheduler_hook import LRSchedulerHook
 class SaveCheckpointHook(BaseHook):
     """Saves the model by interval in training process.
 
-    :param interval: Saving interval 
-    :param checkpoint_dir: Directory of saving checkpoint 
-    :param suffix: Saving suffix of the file
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :param interval: Saving interval, defaults to 1
     :type interval: int, optional
-    :type checkpoint_dir: int, optional
+    :param checkpoint_dir: Directory of saving checkpoint, defaults to None
+    :type checkpoint_dir: str, optional
+    :param suffix: Saving suffix of the file, defaults to ''
     :type suffix: str, optional
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 10
     :type priority: int, optional
+    :param trainer: Trainer attached with current hook
     """
 
     def __init__(self,
@@ -71,16 +72,19 @@ class SaveCheckpointHook(BaseHook):
 class LoadCheckpointHook(BaseHook):
     """Loads the model before training process.
 
-    :param checkpoint_dir: Directory of saving checkpoint 
-    :param epoch: Epoch number to be set
-    :param finetune: Whether allows to load a part of the model
-    :param strict: Whether loads a model that has the same shape of parameters 
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :param checkpoint_dir: Directory of saving checkpoint, defaults to None
     :type checkpoint_dir: str, optional
+    :param epoch: Epoch number to be set, defaults to -1
     :type epoch: str, optional
+    :param finetune: Whether allows to load a part of the model, defaults to False
     :type finetune: bool, optional
+    :param strict: Whether loads a model that has the same shape of parameters, defaults to False
     :type strict: bool, optional
+    :param suffix: Suffic, defaults to ''
+    :type suffix: str, optional
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 0
     :type priority: int, optional
+    :param trainer: Trainer attached with current hook
     """
 
     def __init__(self,
diff --git a/colossalai/trainer/hooks/_log_hook.py b/colossalai/trainer/hooks/_log_hook.py
index bb42ea2c8..b8230fdf4 100644
--- a/colossalai/trainer/hooks/_log_hook.py
+++ b/colossalai/trainer/hooks/_log_hook.py
@@ -25,6 +25,15 @@ def _format_number(val, prec=5):
 
 
 class LogByEpochHook(BaseHook):
+    """hook to log by epoch
+
+    :param logger: logger for the log
+    :param interval: Recording interval, defaults to 1
+    :type interval: int, optional
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 1
+    :type priority: int, optional
+    :param trainer: Trainer attached with current hook
+    """
     def __init__(self,
                  logger,
                  interval: int = 1,
@@ -39,6 +48,12 @@ class LogByEpochHook(BaseHook):
 
 @HOOKS.register_module
 class LogMetricByStepHook(BaseHook):
+    """hook to log metric by step
+
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 10
+    :type priority: int, optional
+    :param trainer: Trainer attached with current hook
+    """
     def __init__(self, priority: int = 10):
         super().__init__(priority)
 
@@ -59,12 +74,13 @@ class LogMetricByStepHook(BaseHook):
 class LogMetricByEpochHook(LogByEpochHook):
     """Specialized Hook to record the metric to log.
 
-    :param trainer: Trainer attached with current hook
-    :type trainer: Trainer
-    :param interval: Recording interval
+    :param logger: logger for the log
+    :param interval: Recording interval, defaults to 1
     :type interval: int, optional
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 10
     :type priority: int, optional
+    :param trainer: Trainer attached with current hook
+    :param mode: Mode of metrics, 'train' and 'test'
     """
 
     def __init__(self,
@@ -102,12 +118,17 @@ class LogMetricByEpochHook(LogByEpochHook):
 class TensorboardHook(BaseHook):
     """Specialized Hook to record the metric to Tensorboard.
 
-    :param trainer: Trainer attached with current hook
-    :type trainer: Trainer
     :param log_dir: Directory of log
-    :type log_dir: str, optional
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :type log_dir: str
+    :param ranks: ranks of processors
+    :type ranks: typing.List
+    :param parallel_mode: Parallel mode, defaults to colossalai.context.parallel_mode.ParallelMode.GLOBAL
+    :type parallel_mode: colossalai.context.parallel_mode.ParallelMode, optional
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 10
     :type priority: int, optional
+    :param trainer: Trainer attached with current hook
+    :param mode: Mode of metrics, 'train' and 'test'
+    :type mode: str
     """
 
     def __init__(self,
@@ -184,14 +205,20 @@ class TensorboardHook(BaseHook):
 class LogTimingByEpochHook(LogByEpochHook):
     """Specialized Hook to write timing record to log.
 
-    :param trainer: Trainer attached with current hook
-    :type trainer: Trainer
-    :param interval: Recording interval
+    :param timer: Timer for the hook
+    :type timer: colossalai.utils.MultiTimer
+    :param logger: Logger for the log
+    :type logger: colossalai.logging.DistributedLogger
+    :param interval: Recording interval, defaults to 1
     :type interval: int, optional
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 10
     :type priority: int, optional
-    :param log_eval: Whether writes in evaluation
+    :param log_eval: Whether writes in evaluation, defaults to True
     :type log_eval: bool, optional
+    :param ignore_num_train_steps: Number of training steps to ignore, defaults to 0
+    :type ignore_num_train_steps: int, optional
+    :param mode: Mode of metrics, 'train' and 'test'
+    :param trainer: Trainer attached with current hook
     """
     def __init__(self,
                  timer: MultiTimer,
@@ -249,13 +276,13 @@ class LogTimingByEpochHook(LogByEpochHook):
 class LogMemoryByEpochHook(LogByEpochHook):
     """Specialized Hook to write memory usage record to log.
 
-    :param trainer: Trainer attached with current hook
-    :type trainer: Trainer
-    :param interval: Recording interval
+    :param logger: Logger for the log
+    :type logger: colossalai.logging.DistributedLogger
+    :param interval: Recording interval, defaults to 1
     :type interval: int, optional
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 10
     :type priority: int, optional
-    :param log_eval: Whether writes in evaluation
+    :param log_eval: Whether writes in evaluation, defaults to True
     :type log_eval: bool, optional
     """
     def __init__(self,
@@ -263,7 +290,8 @@ class LogMemoryByEpochHook(LogByEpochHook):
                  interval: int = 1,
                  priority: int = 10,
                  log_eval: bool = True,
-                 report_cpu: bool = False) -> None:
+                 report_cpu: bool = False, # no reference
+                 ) -> None:
         super().__init__(logger=logger, interval=interval, priority=priority)
         self._log_eval = log_eval
         self._is_rank_to_log = is_dp_rank_0() and is_tp_rank_0()
diff --git a/colossalai/trainer/hooks/_lr_scheduler_hook.py b/colossalai/trainer/hooks/_lr_scheduler_hook.py
index 0677754ff..76cf12c53 100644
--- a/colossalai/trainer/hooks/_lr_scheduler_hook.py
+++ b/colossalai/trainer/hooks/_lr_scheduler_hook.py
@@ -8,14 +8,14 @@ from ._metric_hook import LearningRateMetric, MetricHook
 class LRSchedulerHook(MetricHook):
     """Build LR scheduler
 
-    :param trainer: Trainer attached with current hook
-    :type trainer: Trainer
-    :param lr_scheduler_cfg: The config of LR scheduler
-    :type lr_scheduler_cfg: dict
-    :param by_epoch: If `True`, the LR will be scheduled every epoch. Else, the LR will be scheduled every batch. Defaults to `True`.
+    :param lr_scheduler: LR scheduler
+    :param by_epoch: If `True`, the LR will be scheduled every epoch. Else, the LR will be scheduled every batch
     :type by_epoch: bool
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
+    :param store_lr_in_state: If `True`, store the learning rate in each state, defaults to `True`
+    :type store_lr_in_state: bool, optional
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 1
     :type priority: int, optional
+    :param trainer: Trainer attached with current hook
     """
     def __init__(
         self,
diff --git a/colossalai/trainer/hooks/_metric_hook.py b/colossalai/trainer/hooks/_metric_hook.py
index c4546b6f9..20d5409a7 100644
--- a/colossalai/trainer/hooks/_metric_hook.py
+++ b/colossalai/trainer/hooks/_metric_hook.py
@@ -133,6 +133,8 @@ class LearningRateMetric(Metric):
 
     :param epoch_only: Whether the metric only read for the full epoch
     :type epoch_only: bool
+    :param initial_lr: initial learning rate, defaults to 0.0
+    :type initial_lr: float, optional
     """
 
     def __init__(self, epoch_only: bool, initial_lr: float = 0.):
@@ -161,6 +163,8 @@ class AccuracyMetric(Metric):
 
     :param epoch_only: Whether the metric only read for the full epoch
     :type epoch_only: bool
+    :param accuracy_func: accuracy function for the classification task
+    :type accuracy_func: typing.Callable
     """
 
     def __init__(self, epoch_only: bool, accuracy_func: Callable):
@@ -182,7 +186,8 @@ class AccuracyMetric(Metric):
         and labels. It expects the output has logits and labels.
 
         :param logits: The logits output of the model
-        :param label: The labels of the input data
+        :param targets: real labels of the dataset
+        :param batch_size: batch size of the task
         """
         if isinstance(logits, (list, tuple)):
             logits = logits[0]
@@ -216,10 +221,10 @@ class MetricHook(BaseHook):
     update their states. Others are used to display and 
     record the metric.
 
-    :param trainer: Trainer attached with current hook
     :param priority: Priority in the printing, hooks with small priority will be printed in front
-    :type trainer: Trainer
     :type priority: int
+    :param trainer: Trainer attached with current hook
+    :type trainer: Trainer
     """
 
     def __init__(
@@ -238,10 +243,10 @@ class MetricHook(BaseHook):
 class LossHook(MetricHook):
     """Specialized hook class for :class:`Loss`.
 
-    :param trainer: Trainer attached with current hook
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
-    :type trainer: Trainer
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 0
     :type priority: int, optional
+    :param trainer: Trainer attached with current hook
+    :type trainer: Trainer
     """
 
     def __init__(self, priority: int = 0):
@@ -279,10 +284,12 @@ class LossHook(MetricHook):
 class AccuracyHook(MetricHook):
     """Specialized hook class for :class:`Accuracy`.
 
+    :param accuracy_func: Priority in the printing, hooks with small priority will be printed in front
+    :type accuracy_func: typing.Callable
+    :param priority: Priority in the printing, hooks with small priority will be printed in front, defaults to 0
+    :type priority: int, optional
     :param trainer: Trainer attached with current hook
-    :param priority: Priority in the printing, hooks with small priority will be printed in front
     :type trainer: Trainer
-    :type priority: int
     """
 
     def __init__(self, accuracy_func: Callable, priority: int = 0):
@@ -308,6 +315,13 @@ class AccuracyHook(MetricHook):
 
 
 class ThroughputMetric(Metric):
+    """Metric for :class:`Throughput`.
+
+    :param epoch_only: epoch only
+    :type epoch_only: bool
+    :param num_samples: number of samples
+    :param time: time
+    """
     def __init__(self, epoch_only: bool):
         super().__init__(epoch_only=epoch_only)
         self.accumulated_num_samples = torch.zeros(1, device=get_current_device())
@@ -345,6 +359,13 @@ class ThroughputMetric(Metric):
 
 @HOOKS.register_module
 class ThroughputHook(MetricHook):
+    """Specialized hook class for :class:`Throughput`.
+
+    :param priority: priority of throughput hook, defaults to 10
+    :type priority: int, optional
+    :param trainer: Trainer attached with current hook
+    :type trainer: Trainer
+    """
     def __init__(self, priority: int = 10):
         super().__init__(priority)