  Despite considerable theoretical progress in the training of neural networks
viewed as a multi-agent system of neurons, particularly concerning biological
plausibility and decentralized training, their applicability to real-world
problems remains limited due to scalability issues. In contrast,
error-backpropagation has demonstrated its effectiveness for training deep
networks in practice. In this study, we propose a local objective for neurons
that, when pursued by neurons individually, align them to exhibit similarities
to error-backpropagation in terms of efficiency and scalability during
training. For this purpose, we examine a neural network comprising
decentralized, self-interested neurons seeking to maximize their local
objective -- attention from subsequent layer neurons -- and identify the
optimal strategy for neurons. We also analyze the relationship between this
strategy and backpropagation, establishing conditions under which the derived
strategy is equivalent to error-backpropagation. Lastly, we demonstrate the
learning capacity of these multi-agent neural networks through experiments on
three datasets and showcase their superior performance relative to
error-backpropagation in a catastrophic forgetting benchmark.
