Local Response Normalization.

    input, depth_radius=5, bias=1, alpha=1, beta=0.5, name=None

The 4-D input tensor is treated as a 3-D array of 1-D vectors (along the last dimension), and each vector is normalized independently. Within a given vector, each component is divided by the weighted, squared sum of inputs within depth_radius. In detail,

sqr_sum[a, b, c, d] =
    sum(input[a, b, c, d - depth_radius : d + depth_radius + 1] ** 2)
output = input / (bias + alpha * sqr_sum) ** beta

For details, see Krizhevsky et al., ImageNet classification with deep convolutional neural networks (NIPS 2012).


  • input: A Tensor. Must be one of the following types: half, bfloat16, float32. 4-D.
  • depth_radius: An optional int. Defaults to 5. 0-D. Half-width of the 1-D normalization window.
  • bias: An optional float. Defaults to 1. An offset (usually positive to avoid dividing by 0).
  • alpha: An optional float. Defaults to 1. A scale factor, usually positive.
  • beta: An optional float. Defaults to 0.5. An exponent.
  • name: A name for the operation (optional).


A Tensor. Has the same type as input.