The layer corresponds to the inverse of the max-pooling operation under certain simplifying conditions. Despite these conditions being unrealistic and extreme, the subsequent layers are able to learn to compensate for the unusual output, so the samples generated by the model as a whole are still visually pleasing. Thus, un-pooling makes the max-pooling operation invertible.


University of Michigan - Ann Arbor

An approach for dealing with the pooling layer issue that works as follows: 

1. The stride of the max-pooling operation is constrained to be equal to the width of the pooling region. 
2. The maximum input within each pooling region is assumed to be the input in the upper-left corner. 
3. All nonmaximal inputs within each pooling region are assumed to be zero.

The inverse un-pooling operation allocates a tensor of zeros, then copies each value from spatial coordinate $i$ of the input to spatial coordinate $i\times k$ of the output, where $k$ is an integer that defines the size of the pooling region.

Un-pooling

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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