  The pooling operation is a cornerstone element of convolutional neural
networks. These elements generate receptive fields for neurons, in which local
perturbations should have minimal effect on the output activations, increasing
robustness and invariance of the network. In this paper we will present an
altered version of the most commonly applied method, maximum pooling, where
pooling in theory is substituted by a continuous time differential equation,
which generates a location sensitive pooling operation, more similar to
biological receptive fields. We will present how this continuous method can be
approximated numerically using discrete operations which fit ideally on a GPU.
In our approach the kernel size is substituted by diffusion strength which is a
continuous valued parameter, this way it can be optimized by gradient descent
algorithms. We will evaluate the effect of continuous pooling on accuracy and
computational need using commonly applied network architectures and datasets.
