Developer Guide for Intel® Data Analytics Acceleration Library 2019 Update 1

Local Response Normalization Backward Layer

For a given dimension k ∈ {1, ..., p} of size n k , the forward local response normalization layer normalizes the input tensor XR n 1 x n 2 x ... x n p . For more details and notations, see Forward Local Response Normalization Layer.

For a dimension k ∈ {1, ..., p} of size n k , the backward local response normalization layer computes the value:

where:

Problem Statement

See [Krizh2012] for an exact definition of local response normalization.

Given p-dimensional tensors:

The problem is to compute the p-dimensional tensor Z = (z i 1...i p ) ∈ R n 1 x n 2 x ... x n p .