Before revision:  Here, we describe a rigorous derivation of error-backpropagation-based learning for hierarchical networks of leaky integrate-and-fire neurons . We explicitly address two issues that are relevant for both biological plausibility and applicability to neuromorphic substrates by incorporating dynamics with finite time constants and by optimizing the backward pass with respect to substrate variability. This narrows the gap between previous models of first-spike-time learning and biological neuronal dynamics, thereby also enabling fast and energy-efficient inference on analog neuromorphic devices that inherit these dynamics from their biological archetypes, which we demonstrate on two generations of the BrainScaleS analog neuromorphic architecture .
After revision:  Here, we describe a rigorous derivation of error-backpropagation-based learning for hierarchical networks of leaky integrate-and-fire neurons , relying solely on input and output spike times, and show how it can implement error backpropagation in hierarchical spiking networks. Furthermore, we emulate our framework on the BrainScaleS analog neuromorphic architecture .