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W. S. Grant, J. Tanner, L. Itti.  2017.  Biologically plausible learning in neural networks with modulatory feedback. Neural Networks. 88:32-48.

Although Hebbian learning has long been a key component in understanding neural plasticity, it has not yet been successful in modeling modulatory feedback connections, which make up a significant portion of connections in the brain. We develop a new learning rule designed around the complications of learning modulatory feedback and composed of three simple concepts grounded in physiologically plausible evidence. Using border ownership as a prototypical example, we show that a Hebbian learning rule fails to properly learn modulatory connections, while our proposed rule correctly learns a stimulus-driven model. To the authors' knowledge, this is the first time a border ownership network has been learned. Additionally, we show that the rule can be used as a drop-in replacement for a Hebbian learning rule to learn a biologically consistent model of orientation selectivity, a network which lacks any modulatory connections. Our results predict that the mechanisms we use are integral for learning modulatory connections in the brain and furthermore that modulatory connections have a strong dependence on inhibition.