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.. _op_ai_onnx_LRN-1:

LRN - version 1
===============

This page documents version **1** of operator **LRN**. See :doc:`LRN` for the latest version (since version 13).

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

Local Response Normalization proposed in the `AlexNet paper <https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf>`_.
It normalizes over local input regions.
The local region is defined across the channels. For an element X[n, c, d1, ..., dk] in a tensor
of shape (N x C x D1 x D2, ..., Dk), its region is
{X[n, i, d1, ..., dk] | max(0, c - floor((size - 1) / 2)) <= i <= min(C - 1, c + ceil((size - 1) / 2))}.

square_sum[n, c, d1, ..., dk] = sum(X[n, i, d1, ..., dk] ^ 2),
where max(0, c - floor((size - 1) / 2)) <= i <= min(C - 1, c + ceil((size - 1) / 2)).

Y[n, c, d1, ..., dk] = X[n, c, d1, ..., dk] / (bias + alpha / size \* square_sum[n, c, d1, ..., dk] ) ^ beta

**Inputs**

- **X** (*T*): Input data tensor from the previous operator; dimensions for image case are (N x C x H x W), where N is the batch size, C is the number of channels, and H and W are the height and the width of the data. For non image case, the dimensions are in the form of (N x C x D1 x D2 ... Dn), where N is the batch size. Optionally, if dimension denotation is in effect, the operation expects the input data tensor to arrive with the dimension denotation of [DATA_BATCH, DATA_CHANNEL, DATA_FEATURE, DATA_FEATURE ...].

**Outputs**

- **Y** (*T*): Output tensor, which has the shape and type as input tensor

**Attributes**

- **alpha** (*float*): Scaling parameter.
- **beta** (*float*): The exponent.
- **bias** (*float*)
- **size** (*int*): The number of channels to sum over

**Type Constraints**

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