A neural network is said to be nonoverlapping if there is at most one edge outgoing from each node. We investigate the number of examples that a learning algorithm needs when using nonoverlapping neural networks as hypotheses. We derive bounds for this sample complexity in terms of the Vapnik-Chervonenkis dimension. ... more >>>

An \emph{arithmetic read-once formula} (ROF for short) is a formula (a circuit whose underlying graph is a tree) in which the operations are $\{+,\times\}$ and such that every input variable labels at most one leaf. A \emph{preprocessed ROF} (PROF for short) is a ROF in which we are allowed to ... more >>>