In many practical situations, we do not know the exact relation between different quantities; this relation needs to be determined based on the empirical data. This determination is not easy -- especially in the presence of different types of uncertainty. When the data comes in the form of time series and images, many efficient techniques for such determination use algorithms for training convolutional neural network. As part of this training, such networks "pool" several values corresponding to nearby temporal or spatial points into a single value. Empirically, the most efficient pooling algorithm consists of taking the maximum of the pooled values; the next optimal is taking the arithmetic mean. In this paper, we provide a theoretical explanation for this empirical optimality.