(l-onnx-doc-LRN)=

# LRN


(l-onnx-op-lrn-13)=

## LRN - 13

### Version

- **name**: [LRN (GitHub)](https://github.com/onnx/onnx/blob/main/docs/Operators.md#LRN)
- **domain**: `main`
- **since_version**: `13`
- **function**: `False`
- **support_level**: `SupportType.COMMON`
- **shape inference**: `True`

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

### Summary

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`

### Attributes

* **alpha - FLOAT** (default is `'0.0001'`):

  Scaling parameter.

* **beta - FLOAT** (default is `'0.75'`):

  The exponent.

* **bias - FLOAT** (default is `'1.0'`):

* **size - INT** (required) :

  The number of channels to sum over

### Inputs

- **X** (heterogeneous) - **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** (heterogeneous) - **T**:

  Output tensor, which has the shape and type as input tensor

### Type Constraints

* **T** in ( `tensor(bfloat16)`, `tensor(double)`, `tensor(float)`, `tensor(float16)` ):

  Constrain input and output  types to float tensors.

```{toctree}
text_diff_LRN_1_13
```

(l-onnx-op-lrn-1)=

## LRN - 1

### Version

- **name**: [LRN (GitHub)](https://github.com/onnx/onnx/blob/main/docs/Operators.md#LRN)
- **domain**: `main`
- **since_version**: `1`
- **function**: `False`
- **support_level**: `SupportType.COMMON`
- **shape inference**: `True`

This version of the operator has been available
**since version 1**.

### Summary

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

### Attributes

* **alpha - FLOAT** (default is `'0.0001'`):

  Scaling parameter.

* **beta - FLOAT** (default is `'0.75'`):

  The exponent.

* **bias - FLOAT** (default is `'1.0'`):

* **size - INT** (required) :

  The number of channels to sum over

### Inputs

- **X** (heterogeneous) - **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** (heterogeneous) - **T**:

  Output tensor, which has the shape and type as input tensor

### Type Constraints

* **T** in ( `tensor(double)`, `tensor(float)`, `tensor(float16)` ):

  Constrain input and output  types to float tensors.