Recurrent networks can be trained using a generalization of backpropagation, called backpropagation through time, but a gap exists between the mathematics of this learning algorithm and biological plausibility. E-prop is a biologically inspired alternative that opens up possibilities for a new generation of online training algorithms for recurrent networks.
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Manneschi, L., Vasilaki, E. An alternative to backpropagation through time. Nat Mach Intell 2, 155–156 (2020). https://doi.org/10.1038/s42256-020-0162-9