# MeanVarianceNormalization¶

## MeanVarianceNormalization - 13¶

### Version¶

• domain: main

• since_version: 13

• function: True

• support_level: SupportType.COMMON

• shape inference: False

This version of the operator has been available since version 13.

### Summary¶

A MeanVarianceNormalization Function: Perform mean variance normalization on the input tensor X using formula: (X-EX)/sqrt(E(X-EX)^2)

#### Function Body¶

The function definition for this operator.

<
domain: "",
opset_import: ["" : 18]
>
MeanVarianceNormalization <axes>(X) => (Y)
{
Exponent = Constant <value: tensor = float {2}> ()
Epsilon = Constant <value: tensor = float {1e-09}> ()
axes = Constant <value_ints: ints = @axes> ()
X_RM = ReduceMean (X, axes)
EX_squared = Pow (X_RM, Exponent)
X_squared = Pow (X, Exponent)
E_Xsquared = ReduceMean (X_squared, axes)
Variance = Sub (E_Xsquared, EX_squared)
STD = Sqrt (Variance)
X_variance = Sub (X, X_RM)
Y = Div (X_variance, Processed_STD)
}


### Attributes¶

• axes - INTS (default is ['0', '2', '3']):

A list of integers, along which to reduce. The default is to calculate along axes [0,2,3] for calculating mean and variance along each channel. Two variables with the same C-coordinate are associated with the same mean and variance.

### Inputs¶

• X (heterogeneous) - T:

Input tensor

### Outputs¶

• Y (heterogeneous) - T:

Output tensor

### Type Constraints¶

• T in ( tensor(bfloat16), tensor(double), tensor(float), tensor(float16) ):

Constrain input and output types to all numeric tensors.

## MeanVarianceNormalization - 9¶

### Version¶

• domain: main

• since_version: 9

• function: True

• support_level: SupportType.COMMON

• shape inference: False

This version of the operator has been available since version 9.

### Summary¶

A MeanVarianceNormalization Function: Perform mean variance normalization on the input tensor X using formula:
(X-EX)/sqrt(E(X-EX)^2)

#### Function Body¶

The function definition for this operator.

<
domain: "",
opset_import: ["" : 9]
>
MeanVarianceNormalization <axes>(X) => (Y)
{
Exponent = Constant <value: tensor = float {2}> ()
Epsilon = Constant <value: tensor = float {1e-09}> ()
X_RM = ReduceMean <axes: ints = @axes> (X)
EX_squared = Pow (X_RM, Exponent)
X_squared = Pow (X, Exponent)
E_Xsquared = ReduceMean <axes: ints = @axes> (X_squared)
Variance = Sub (E_Xsquared, EX_squared)
STD = Sqrt (Variance)
X_variance = Sub (X, X_RM)
Y = Div (X_variance, Processed_STD)
}


### Attributes¶

• axes - INTS (default is ['0', '2', '3']):

A list of integers, along which to reduce. The default is to calculate along axes [0,2,3] for calculating mean and variance along each channel. Two variables with the same C-coordinate are associated with the same mean and variance.

### Inputs¶

• X (heterogeneous) - T:

Input tensor

### Outputs¶

• Y (heterogeneous) - T:

Output tensor

### Type Constraints¶

• T in ( tensor(double), tensor(float), tensor(float16) ):

Constrain input and output types to all numeric tensors.