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.

This paper presents a locally decoupled network parameter learning with local propagation. Three elements are taken into account: (i) sets of nonlinear transforms that describe the representations at all nodes, (ii) a local objective at each node related to the corresponding local representation goal, and (iii) a local propagation model that relates the nonlinear error vectors at each node with the goal error vectors from the directly connected nodes. The modeling concepts (i), (ii) and (iii) offer several advantages, including (a) a unified learning principle for any network that is represented as a graph, (b) understanding and interpretation of the local and the global learning dynamics, (c) decoupled and parallel parameter learning, (d) a possibility for learning in infinitely long, multi-path and multi-goal networks. Numerical experiments validate the potential of the learning principle. 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 comparable recognition accuracy.