Event-based backpropagation can compute exact gradients for spiking neural networks.

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.

Demonstrating Advantages of Neuromorphic Computation: A Pilot Study.

Neuromorphic devices represent an attempt to mimic aspects of the brain's architecture and dynamics with the aim of replicating its hallmark functional capabilities in terms of computational power, robust learning and energy efficiency. We employ a single-chip prototype of the BrainScaleS 2 neuromorphic system to implement a proof-of-concept demonstration of reward-modulated spike-timing-dependent plasticity in a spiking network that learns to play a simplified version of the Pong video game by smooth pursuit. This system combines an electronic mixed-signal substrate for emulating neuron and synapse dynamics with an embedded digital processor for on-chip learning, which in this work also serves to simulate the virtual environment and learning agent. The analog emulation of neuronal membrane dynamics enables a 1000-fold acceleration with respect to biological real-time, with the entire chip operating on a power budget of 57 mW. Compared to an equivalent simulation using state-of-the-art software, the on-chip emulation is at least one order of magnitude faster and three orders of magnitude more energy-efficient. We demonstrate how on-chip learning can mitigate the effects of fixed-pattern noise, which is unavoidable in analog substrates, while making use of temporal variability for action exploration. Learning compensates imperfections of the physical substrate, as manifested in neuronal parameter variability, by adapting synaptic weights to match respective excitability of individual neurons.