  This paper proposes the Mesh Neural Network (MNN), a novel architecture which
allows neurons to be connected in any topology, to efficiently route
information. In MNNs, information is propagated between neurons throughout a
state transition function. State and error gradients are then directly computed
from state updates without backward computation. The MNN architecture and the
error propagation schema is formalized and derived in tensor algebra. The
proposed computational model can fully supply a gradient descent process, and
is potentially suitable for very large scale sparse NNs, due to its
expressivity and training efficiency, with respect to NNs based on
back-propagation and computational graphs.
