  The way how recurrently connected networks of spiking neurons in the brain
acquire powerful information processing capabilities through learning has
remained a mystery. This lack of understanding is linked to a lack of learning
algorithms for recurrent networks of spiking neurons (RSNNs) that are both
functionally powerful and can be implemented by known biological mechanisms.
Since RSNNs are simultaneously a primary target for implementations of
brain-inspired circuits in neuromorphic hardware, this lack of algorithmic
insight also hinders technological progress in that area. The gold standard for
learning in recurrent neural networks in machine learning is back-propagation
through time (BPTT), which implements stochastic gradient descent with regard
to a given loss function. But BPTT is unrealistic from a biological
perspective, since it requires a transmission of error signals backwards in
time and in space, i.e., from post- to presynaptic neurons. We show that an
online merging of locally available information during a computation with
suitable top-down learning signals in real-time provides highly capable
approximations to BPTT. For tasks where information on errors arises only late
during a network computation, we enrich locally available information through
feedforward eligibility traces of synapses that can easily be computed in an
online manner. The resulting new generation of learning algorithms for
recurrent neural networks provides a new understanding of network learning in
the brain that can be tested experimentally. In addition, these algorithms
provide efficient methods for on-chip training of RSNNs in neuromorphic
hardware.
