The anatomical connectivity among neurons has been experimentally found to be largely non-random across brain areas. This means that certain connectivity motifs occur at a higher frequency than would be expected by chance. Of particular interest, short-term synaptic plasticity properties were found to colocalize with specific motifs: an over-expression of bidirectional motifs has been found in neuronal pairs where short-term facilitation dominates synaptic transmission among the neurons, whereas an over-expression of unidirectional motifs has been observed in neuronal pairs where short-term depression dominates. In previous work we found that, given a network with fixed short-term properties, the interaction between short- and long-term plasticity of synaptic transmission is sufficient for the emergence of specific motifs. Here, we introduce an error-driven learning mechanism for short-term plasticity that may explain how such observed correspondences develop from randomly initialized dynamic synapses. By allowing synapses to change their properties, neurons are able to adapt their own activity depending on an error signal. This results in more rich dynamics and also, provided that the learning mechanism is target-specific, leads to specialized groups of synapses projecting onto functionally different targets, qualitatively replicating the experimental results of Wang and collaborators.