BatchNormTraining

BatchNormTraining  // Compute mean and variance from the input.

Description¶

Inputs¶

Name	Element Type	Shape
`input`	real	\((\bullet, C, \ldots)\)
`gamma`	same as `input`	\((C)\)
`beta`	same as `input`	\((C)\)

Attributes¶

Name	Type	Notes
`epsilon`	`double`	Small bias added to variance to avoid division by 0.

Outputs¶

Name	Element Type	Shape
`normalized`	same as `gamma`	Same as `input`
`batch_mean`	same as `gamma`	\((C)\)
`batch_variance`	same as `gamma`	\((C)\)

The batch_mean and batch_variance outputs are computed per-channel from input.

Mathematical Definition¶

The axes of the input fall into two categories: positional and channel, with channel being axis 1. For each position, there are \(C\) channel values, each normalized independently.

Normalization of a channel sample is controlled by two values:

the batch_mean \(\mu\), and
the batch_variance \(\sigma^2\);

and by two scaling attributes: \(\gamma\) and \(\beta\).

The values for \(\mu\) and \(\sigma^2\) come from computing the mean and variance of input.

\[\begin{split}\mu_c &= \mathop{\mathbb{E}}\left(\mathtt{input}_{\bullet, c, \ldots}\right)\\ \sigma^2_c &= \mathop{\mathtt{Var}}\left(\mathtt{input}_{\bullet, c, \ldots}\right)\\ \mathtt{normlized}_{\bullet, c, \ldots} &= \frac{\mathtt{input}_{\bullet, c, \ldots}-\mu_c}{\sqrt{\sigma^2_c+\epsilon}}\gamma_c+\beta_c\end{split}\]

Backprop¶

\[\begin{split}[\overline{\texttt{input}}, \overline{\texttt{gamma}}, \overline{\texttt{beta}}]=\\ \mathop{\texttt{BatchNormTrainingBackprop}}(\texttt{input},\texttt{gamma},\texttt{beta},\texttt{mean},\texttt{variance},\overline{\texttt{normed_input}}).\end{split}\]

C++ Interface¶

class BatchNormTraining : public ngraph::op::Op¶

Batchnorm for training operation.

Public Functions

const NodeTypeInfo &get_type_info() const¶: Returns the NodeTypeInfo for the node’s class. During transition to type_info, returns a dummy type_info for Node if the class has not been updated yet.

BatchNormTraining(const Output<Node> &input, const Output<Node> &gamma, const Output<Node> &beta, double epsilon)¶

Parameters

input: Must have rank >= 2, [., C, …]
gamma: gamma scaling for normalized value. [C]
beta: bias added to the scaled normalized value [C]
epsilon: Avoids divsion by 0 if input has 0 variance

NGRAPH_DEPRECATED_DOC BatchNormTraining(double eps, const Output<Node> &gamma, const Output<Node> &beta, const Output<Node> &input)¶

In this version of BatchNorm:

MEAN AND VARIANCE: computed directly from the content of ‘input’.

OUTPUT VALUE: A tuple with the following structure: [0] - The normalization of ‘input’. [1] - The per-channel means of (pre-normalized) ‘input’. [2] - The per-channel variances of (pre-normalized) ‘input’.

AUTODIFF SUPPORT: yes: ‘generate_adjoints(…)’ works as expected.

SHAPE DETAILS: gamma: must have rank 1, with the same span as input’s channel axis. beta: must have rank 1, with the same span as input’s channel axis. input: must have rank >= 2. The second dimension represents the channel axis and must have a span of at least 1. output[0]: shall have the same shape as ‘input’. output[1]: shall have rank 1, with the same span as input’s channel axis. output[2]: shall have rank 1, with the same span as input’s channel axis.

void validate_and_infer_types()¶: Throws if the node is invalid.