2D Average Pooling Backward Layer

The forward two-dimensional (2D) average pooling layer is a form of non-linear downsampling of an input tensor X = (x (1) ... x (p)) of size n 1 x n 2 x ... x n p . For more details, see Forward 2D Average Pooling Layer. The backward 2D average pooling layer back-propagates the input gradient G = (g (1) ... g (p)) of size m 1 x m 2 x ... x m p computed on the preceding layer. The result of the backward 2D average pooling layer Z = (z (1) ... z (p)) is the tensor of the same size n 1 x n 2 x ... x n p as the input of the forward computation. The backward layer propagates the elements of the gradient multiplied by the coefficient 1/(f k 1 *f k 2 ) to the corresponding pooled subtensors of the tensor Z:

Problem Statement

Given a p-dimensional tensor GR n 1 x n 2 x ... x n p with the gradient computed on the preceding layer, the problem is to compute the p-dimensional tensor ZR n 1 x n 2 x ... x n p with the result:

For more complete information about compiler optimizations, see our Optimization Notice.
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