# BatchNorm3D¶

class paddle.nn. BatchNorm3D ( num_features, momentum=0.9, epsilon=1e-05, weight_attr=None, bias_attr=None, data_format='NCHW', use_global_stats=None, name=None ) [source]

Applies Batch Normalization over a 5D input (a mini-batch of 3D inputswith additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

When use_global_stats = False, the $$\\mu_{\\beta}$$ and $$\\sigma_{\\beta}^{2}$$ are the statistics of one mini-batch. Calculated as follows:

$\begin{split}\\mu_{\\beta} &\\gets \\frac{1}{m} \\sum_{i=1}^{m} x_i \\qquad &//\\ \ mini-batch\ mean \\\\ \\sigma_{\\beta}^{2} &\\gets \\frac{1}{m} \\sum_{i=1}^{m}(x_i - \\ \\mu_{\\beta})^2 \\qquad &//\ mini-batch\ variance \\\\\end{split}$

When use_global_stats = True, the $$\\mu_{\\beta}$$ and $$\\sigma_{\\beta}^{2}$$ are not the statistics of one mini-batch. They are global or running statistics (moving_mean and moving_variance). It usually got from the pre-trained model. Calculated as follows:

$\begin{split}moving\_mean = moving\_mean * momentum + \mu_{\beta} * (1. - momentum) \quad &// global mean \\ moving\_variance = moving\_variance * momentum + \sigma_{\beta}^{2} * (1. - momentum) \quad &// global variance \\\end{split}$

The normalization function formula is as follows:

$\begin{split}\\hat{x_i} &\\gets \\frac{x_i - \\mu_\\beta} {\\sqrt{\\ \\sigma_{\\beta}^{2} + \\epsilon}} \\qquad &//\ normalize \\\\ y_i &\\gets \\gamma \\hat{x_i} + \\beta \\qquad &//\ scale\ and\ shift\end{split}$
• $$\\epsilon$$ : add a smaller value to the variance to prevent division by zero

• $$\\gamma$$ : trainable proportional parameter

• $$\\beta$$ : trainable deviation parameter

Parameters
• num_features (int) – Indicate the number of channels of the input Tensor.

• epsilon (float, optional) – The small value added to the variance to prevent division by zero. Default: 1e-5.

• momentum (float, optional) – The value used for the moving_mean and moving_var computation. Default: 0.9.

• weight_attr (ParamAttr|bool, optional) – The parameter attribute for Parameter scale of batch_norm. If it is set to None or one attribute of ParamAttr, batch_norm will create ParamAttr as weight_attr. If it is set to Fasle, the weight is not learnable. If the Initializer of the weight_attr is not set, the parameter is initialized with Xavier. Default: None.

• bias_attr (ParamAttr|bool, optional) – The parameter attribute for the bias of batch_norm. If it is set to None or one attribute of ParamAttr, batch_norm will create ParamAttr as bias_attr. If it is set to Fasle, the weight is not learnable. If the Initializer of the bias_attr is not set, the bias is initialized zero. Default: None.

• data_format (str, optional) – Specify the input data format, the data format can be “NCDHW” or “NDHWC. Default: NCDHW.

• use_global_stats (bool|None, optional) – Whether to use global mean and variance. If set to False, use the statistics of one mini-batch, if set to True, use the global statistics, if set to None, use global statistics in the test phase and use the statistics of one mini-batch in the training phase. Default: None.

• name (str, optional) – Name for the BatchNorm, default is None. For more information, please refer to Name..

Shape:
• x: 5-D tensor with shape: (batch, num_features, dims, height, weight) when data_format is “NCDHW”,

or (batch, dims, height, weight, num_features) when data_format is “NDHWC”.

• output: 5-D tensor with same shape as input x.

Returns

None

Examples

import paddle
import numpy as np

np.random.seed(123)
x_data = np.random.random(size=(2, 1, 2, 2, 3)).astype('float32')