  Spiking activity of neurons engaged in learning and performing a task show
complex spatiotemporal dynamics. While the output of recurrent network models
can learn to perform various tasks, the possible range of recurrent dynamics
that emerge after learning remains unknown. Here we show that modifying the
recurrent connectivity with a recursive least squares algorithm provides
sufficient flexibility for synaptic and spiking rate dynamics of spiking
networks to produce a wide range of spatiotemporal activity. We apply the
training method to learn arbitrary firing patterns, stabilize irregular spiking
activity of a balanced network, and reproduce the heterogeneous spiking rate
patterns of cortical neurons engaged in motor planning and movement. We
identify sufficient conditions for successful learning, characterize two types
of learning errors, and assess the network capacity. Our findings show that
synaptically-coupled recurrent spiking networks possess a vast computational
capability that can support the diverse activity patterns in the brain.
