Encoding Numbers with Graded Spikes

Neuromorphic computing is a promising avenue to improve processors past the limits imposed by the decline of Moore’s Law and Dennard Scaling. However, some neuromorphic computing workflows are heavily bottlenecked by passing data in-between a neuromorphic processor and a CPU because intermediate values need to be processed with arithmetic and Boolean operations. An active research field seeks to eliminate this bottleneck by executing arithmetic and Boolean operations on neuromorphic processors. Specifically, researchers encode numbers in spikes, then use hand-crafted spiking neural networks (SNNs) to perform the necessary operations on the encoded numbers. The performance of an encoding is often evaluated using addition as a proxy for the other arithmetic and boolean operations. However, how to effectively utilize graded spikes, which enable neurons to send and receive an integer value with each spike, is still an open question. Answering this question is challenging because we lack neuron models that support graded spikes. We propose the Overflow neuron model, which does support graded spikes, to mitigate this challenge. We then use the Overflow neuron to create three novel unsigned integer encodings and adder SNNs that take advantage of graded spikes. We compare how our graded spike-based encodings scale against existing encodings, demonstrating that using graded spikes can decrease the number of neurons, synapses, and spikes in SNNs. Finally, we estimate the hardware costs of using graded spikes and show that the reduction in neurons, synapses, and spikes from using graded spike-based encodings translates into a reduction in power consumption and latency. In summary, we utilize graded spikes to perform addition on neuromorphic processors and show that our graded spike-based methods outperform non-graded spike-based methods.