:nosearch:

.. _op_ai_onnx_BatchNormalization-1:

BatchNormalization - version 1
==============================

This page documents version **1** of operator **BatchNormalization**. See :doc:`BatchNormalization` for the latest version (since version 15).

- **Domain**: ``ai.onnx``
- **Since version**: 1

Carries out batch normalization as described in the paper
https://arxiv.org/abs/1502.03167. Depending on the mode it is being run,
there are multiple cases for the number of outputs, which we list below:

Output case #1: Y, mean, var, saved_mean, saved_var (training mode)
Output case #2: Y (test mode)

**Inputs**

- **X** (*T*): The input 4-dimensional tensor of shape NCHW.
- **scale** (*T*): The scale as a 1-dimensional tensor of size C to be applied to the output.
- **B** (*T*): The bias as a 1-dimensional tensor of size C to be applied to the output.
- **mean** (*T*): The running mean (training) or the estimated mean (testing) as a 1-dimensional tensor of size C.
- **var** (*T*): The running variance (training) or the estimated variance (testing) as a 1-dimensional tensor of size C.

**Outputs**

- **Y** (*T*): The output 4-dimensional tensor of the same shape as X.
- **mean** (*T*): The running mean after the BatchNormalization operator. Must be in-place with the input mean. Should not be used for testing.
- **var** (*T*): The running variance after the BatchNormalization operator. Must be in-place with the input var. Should not be used for testing.
- **saved_mean** (*T*): Saved mean used during training to speed up gradient computation. Should not be used for testing.
- **saved_var** (*T*): Saved variance used during training to speed up gradient computation. Should not be used for testing.

**Type Constraints**

- **T**: Constrain input and output types to float tensors.
  Allowed types: tensor(double), tensor(float), tensor(float16).