  In this paper, a novel architecture of Recurrent Neural Network (RNN) is
designed and experimented. The proposed RNN adopts a computational memory based
on the concept of stigmergy. The basic principle of a Stigmergic Memory (SM) is
that the activity of deposit/removal of a quantity in the SM stimulates the
next activities of deposit/removal. Accordingly, subsequent SM activities tend
to reinforce/weaken each other, generating a coherent coordination between the
SM activities and the input temporal stimulus. We show that, in a problem of
supervised classification, the SM encodes the temporal input in an emergent
representational model, by coordinating the deposit, removal and classification
activities. This study lays down a basic framework for the derivation of a
SM-RNN. A formal ontology of SM is discussed, and the SM-RNN architecture is
detailed. To appreciate the computational power of an SM-RNN, comparative NNs
have been selected and trained to solve the MNIST handwritten digits
recognition benchmark in its two variants: spatial (sequences of bitmap rows)
and temporal (sequences of pen strokes).
