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LocalResponseNormalizationLayer[]

represents a net layer that normalizes its input by averaging across neighboring input channels.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Ports  
Possible Issues  
See Also
Tech Notes
Related Guides
History
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LocalResponseNormalizationLayer

LocalResponseNormalizationLayer[]

represents a net layer that normalizes its input by averaging across neighboring input channels.

Details and Options

  • The following optional parameters can be included:
  • "Alpha"1.0scaling parameter
    "Beta"0.5power parameter
    "Bias"1.0bias parameter
    "ChannelWindowSize"2number of channels to average over
  • LocalResponseNormalizationLayer[…][input] explicitly computes the output from applying the layer.
  • LocalResponseNormalizationLayer[…][{input1,input2,…}] explicitly computes outputs for each of the inputi.
  • When given a NumericArray as input, the output will be a NumericArray.
  • LocalResponseNormalizationLayer is typically used inside NetChain, NetGraph, etc.
  • LocalResponseNormalizationLayer exposes the following ports for use in NetGraph etc.:
  • "Input"a rank-3 array
    "Output"a rank-3 array
  • When it cannot be inferred from other layers in a larger net, the option "Input"->{n1,n2,n3} can be used to fix the input dimensions of LocalResponseNormalizationLayer.
  • The output array is obtained via , where D_(ijk)=((alpha)/(2c+1) sum_( x = max(1, i-c))^( min(N, c+i))T_(xjk)^2+b)^(beta), Tijk is the input, is the "Alpha" parameter, is the "Beta" parameter, is the "ChannelWindowSize" and N is the number of channels in the input Tijk.
  • Options[LocalResponseNormalizationLayer] gives the list of default options to construct the layer. Options[LocalResponseNormalizationLayer[…]] gives the list of default options to evaluate the layer on some data.
  • Information[LocalResponseNormalizationLayer[…]] gives a report about the layer.
  • Information[LocalResponseNormalizationLayer[…],prop] gives the value of the property prop of LocalResponseNormalizationLayer[…]. Possible properties are the same as for NetGraph.

Examples

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Basic Examples  (2)

Create a LocalResponseNormalizationLayer:

Wolfram Language code: LocalResponseNormalizationLayer[]

Create a LocalResponseNormalizationLayer with input dimensions specified:

Wolfram Language code: lrn = LocalResponseNormalizationLayer["Input" -> {5, 2, 1}]

Apply the layer to an input:

Wolfram Language code: lrn[RandomReal[1, {5, 2, 1}]]//MatrixForm

Scope  (1)

Ports  (1)

Create a LocalResponseNormalizationLayer with input dimensions specified:

Wolfram Language code: lrn = LocalResponseNormalizationLayer["Input" -> {5, 1, 1}]

Apply the layer to an input:

Wolfram Language code: data = {{{-2}}, {{-1}}, {{0}}, {{1}}, {{2}}}; lrn[data]

Thread the layer across a batch of inputs:

Wolfram Language code: lrn[{data, -data}]

Possible Issues  (1)

The number of input channels must be larger than 2×(channel window size)+ 1:

Wolfram Language code: LocalResponseNormalizationLayer["ChannelWindowSize" -> 5, "Input" -> {3, 25, 25}]
Wolfram Research (2017), LocalResponseNormalizationLayer, Wolfram Language function, https://reference.wolfram.com/language/ref/LocalResponseNormalizationLayer.html.

Text

Wolfram Research (2017), LocalResponseNormalizationLayer, Wolfram Language function, https://reference.wolfram.com/language/ref/LocalResponseNormalizationLayer.html.

CMS

Wolfram Language. 2017. "LocalResponseNormalizationLayer." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LocalResponseNormalizationLayer.html.

APA

Wolfram Language. (2017). LocalResponseNormalizationLayer. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LocalResponseNormalizationLayer.html

BibTeX

@misc{reference.wolfram_2026_localresponsenormalizationlayer, author="Wolfram Research", title="{LocalResponseNormalizationLayer}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/LocalResponseNormalizationLayer.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_localresponsenormalizationlayer, organization={Wolfram Research}, title={LocalResponseNormalizationLayer}, year={2017}, url={https://reference.wolfram.com/language/ref/LocalResponseNormalizationLayer.html}, note=[Accessed: 12-June-2026]}