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An important issue in neural network research is how to choose the number ofnodes and layers such as to solve a classification problem. We provide newintuitions based on earlier results by An et al. (2015) by deriving an upperbound on the number of nodes in networks with two hidden layers such thatlinear separability can be achieved. Concretely, we show that if the data canbe described in terms of N finite sets and the used activation function f isnon-constant, increasing and has a left asymptote, we can derive how many nodesare needed to linearly separate these sets. This will be an upper bound thatdepends on the structure of the data. This structure can be analyzed using analgorithm. For the leaky rectified linear activation function, we proveseparately that under some conditions on the slope, the same number of layersand nodes as for the aforementioned activation functions is sufficient. Weempirically validate our claims.

Generalization of an Upper Bound on the Number of Nodes Needed to Achieve Linear Separability