Spiking Matters: Exact Gradients for Deep Spiking Networks and Neuromorphic Hardware

Inspired by the brain's unparalleled capacity for intelligent and efficient processing, spiking neural networks offer a transformative path towards energy-efficient computation for machine intelligence, and inspire a new class of neuromorphic, or brain-inspired, hardware. However, training spiking neurons accurately and efficiently has previously posed a major obstacle in this endeavour. This thesis pioneers a solution to the exact training of deep spiking networks. Our approach is inherently sparse: it is based on analytical equations that enable truly event-based computation, relying only on spike times. Their derivation enables, for the first time, exact error backpropagation in hierarchical networks of leaky integrate-and-fire neurons. To validate our method, we design the Yin-Yang dataset with the specific purpose of isolating true difficulty from mere scale. Using this benchmark we highlight the performance and robustness of our approach. With a time-to-first-spike coding, inspired by information processing in the brain, we demonstrate fast and energy-efficient classification on the neuromorphic system BrainScaleS-2. Because our method harmonises ideally with neuronal transmission delays, it enables the natural co-training of weights and delays in both software and hardware. This allows the exploration of the computational power of delays. Jointly analysing the structure and dynamics of deep networks, we find striking connections to computational models of neuronal sensory integration. The present work connects studies on the computational properties of networks with experiments on analogue hardware as well as the comparison to the biological archetype. The algorithm's fundamental spiking nature pushes neuromorphic hardware to maximum efficiency. Bridging neuromorphic engineering and neuroscience, our integrated approach not only advances performance and efficiency of machine intelligence, but also drives forward the understanding of fundamental mechanisms behind spatio-temporal processing in the brain.