# local_response_norm¶

paddle.nn.functional. local_response_norm ( x, size, alpha=0.0001, beta=0.75, k=1.0, data_format='NCHW', name=None ) [source]

Local Response Normalization performs a type of “lateral inhibition” by normalizing over local input regions. For more information, please refer to ImageNet Classification with Deep Convolutional Neural Networks

The formula is as follows:

$\begin{split}Output(i, x, y) = Input(i, x, y) / \\left(k + \\alpha \\sum\\limits^{\\min(C-1, i + size/2)}_{j = \\max(0, i - size/2)}(Input(j, x, y))^2\\right)^{\\beta}\end{split}$

In the above equation:

• $$size$$ : The number of channels to sum over.

• $$k$$ : The offset (avoid being divided by 0).

• $$\\alpha$$ : The scaling parameter.

• $$\\beta$$ : The exponent parameter.

Parameters
• x (Tensor) – The input 3-D/4-D/5-D tensor. The data type is float32.

• size (int) – The number of channels to sum over.

• alpha (float, optional) – The scaling parameter, positive. Default:1e-4

• beta (float, optional) – The exponent, positive. Default:0.75

• k (float, optional) – An offset, positive. Default: 1.0

• data_format (str, optional) – Specify the data format of the input, and the data format of the output will be consistent with that of the input. An optional string from: If x is 3-D Tensor, the string could be “NCL” or “NLC” . When it is “NCL”, the data is stored in the order of: [batch_size, input_channels, feature_length]. If x is 4-D Tensor, the string could be “NCHW”, “NHWC”. When it is “NCHW”, the data is stored in the order of: [batch_size, input_channels, input_height, input_width]. If x is 5-D Tensor, the string could be “NCDHW”, “NDHWC” . When it is “NCDHW”, the data is stored in the order of: [batch_size, input_channels, input_depth, input_height, input_width].

• name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Returns

A tensor storing the transformation result with the same shape and data type as input.

Examples:

import paddle

x = paddle.rand(shape=(3, 3, 112, 112), dtype="float32")