  In this paper, we introduce a novel concept for learning of the parameters in
a neural network. Our idea is grounded on modeling a learning problem that
addresses a trade-off between (i) satisfying local objectives at each node and
(ii) achieving desired data propagation through the network under (iii) local
propagation constraints. We consider two types of nonlinear transforms which
describe the network representations. One of the nonlinear transforms serves as
activation function. The other one enables a locally adjusted, deviation
corrective components to be included in the update of the network weights in
order to enable attaining target specific representations at the last network
node. Our learning principle not only provides insight into the understanding
and the interpretation of the learning dynamics, but it offers theoretical
guarantees over decoupled and parallel parameter estimation strategy that
enables learning in synchronous and asynchronous mode. Numerical experiments
validate the potential of our approach on image recognition task. The
preliminary results show advantages in comparison to the state-of-the-art
methods, w.r.t. the learning time and the network size while having competitive
recognition accuracy.
