| --- |
| title: Local Response Normalization (LRN) |
| --- |
| |
| # Local Response Normalization (LRN) |
|
|
| * Layer type: `LRN` |
| * [Doxygen Documentation](http://caffe.berkeleyvision.org/doxygen/classcaffe_1_1LRNLayer.html) |
| * Header: [`./include/caffe/layers/lrn_layer.hpp`](https://github.com/BVLC/caffe/blob/master/include/caffe/layers/lrn_layer.hpp) |
| * CPU Implementation: [`./src/caffe/layers/lrn_layer.cpp`](https://github.com/BVLC/caffe/blob/master/src/caffe/layers/lrn_layer.cpp) |
| * CUDA GPU Implementation: [`./src/caffe/layers/lrn_layer.cu`](https://github.com/BVLC/caffe/blob/master/src/caffe/layers/lrn_layer.cu) |
| * Parameters (`LRNParameter lrn_param`) |
| - Optional |
| - `local_size` [default 5]: the number of channels to sum over (for cross channel LRN) or the side length of the square region to sum over (for within channel LRN) |
| - `alpha` [default 1]: the scaling parameter (see below) |
| - `beta` [default 5]: the exponent (see below) |
| - `norm_region` [default `ACROSS_CHANNELS`]: whether to sum over adjacent channels (`ACROSS_CHANNELS`) or nearby spatial locations (`WITHIN_CHANNEL`) |
|
|
| The local response normalization layer performs a kind of "lateral inhibition" by normalizing over local input regions. In `ACROSS_CHANNELS` mode, the local regions extend across nearby channels, but have no spatial extent (i.e., they have shape `local_size x 1 x 1`). In `WITHIN_CHANNEL` mode, the local regions extend spatially, but are in separate channels (i.e., they have shape `1 x local_size x local_size`). Each input value is divided by $$(1 + (\alpha/n) \sum_i x_i^2)^\beta$$, where $$n$$ is the size of each local region, and the sum is taken over the region centered at that value (zero padding is added where necessary). |
|
|
| ## Parameters |
|
|
| * Parameters (`LRNParameter lrn_param`) |
| * From [`./src/caffe/proto/caffe.proto`](https://github.com/BVLC/caffe/blob/master/src/caffe/proto/caffe.proto): |
|
|
| {% highlight Protobuf %} |
| {% include proto/LRNParameter.txt %} |
| {% endhighlight %} |
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