Recursive processing of directed acyclic graphs

Recursive neural networks are a new connectionist model particularly tailored to process Directed Positional Acyclic Graphs (DPAGs). While this assumption is reasonable in some applications, it introduces unnecessary constraints in others. In this paper, it is shown that the constraint on the ordering can be relaxed by using an appropriate weight sharing, that guarantees the independence of the network output with respect to the permutations of the arcs leaving from each node. Some theoretical properties of the proposed architecture are given, able to guarantee that the approximation capabilities are maintaned, despite of the weight sharing.