Posit and Floating-Point Based Izhikevich Neuron: A Comparison of Arithmetic

Preprint submitted to Elsevier. It has not been certified by peer review.Reduced precision number formats are gaining popularity in many areas of computational science, due to their potential to improve energy efficiency, silicon use, and speed. However, this is often at the expense of introducing arithmetic errors which affect the accuracy of a system. The optimal balance must be struck, judiciously choosing a number format using as few bits as possible, while minimising accuracy loss. In this study, we examine one such format, posit arithmetic as a replacement for floating-point when conducting spiking neuron simulations, specifically using the Izhikevich neuron model. This model is capable of simulating complex neural firing behaviours, 20 of which were originally identified by Izhikevich and are used in this study. We compare the accuracy, spike count, and spike timing of the two arithmetic systems at different bit-depths against a 64-bit floating-point gold-standard. Additionally, we test a rescaled set of Izhikevich equations to mitigate against arithmetic errors by taking advantage of posit arithmetic’s tapered accuracy.Our findings indicate that there is no difference in performance between 32-bit posit, 32-bit floating-point, and our reference standard for 95% of the tested firing types. However, at 16-bit, both arithmetic systems diverge from the 64-bit reference, albeit non-uniformly. For instance, the posit implementation demonstrates an accumulated spike timing error of 0.5ms over a 1000ms simulation compared to 9ms for floating-point – an 18x improvement using posit arithmetic for regular (tonic) spiking. This finding holds particular importance given the prevalence of this particular firing type in specific regions of the brain. Furthermore, when we rescale the neuron equations, this error is eliminated altogether. Hence, our results demonstrate that posit arithmetic is not only a viable replacement for 64-bit floating-point in these simulations, it can do so while using 4× fewer bits. As a Posit Arithmetic Unit has similar area to a Floating Point Unit with the same bit width, this constitutes a significant saving of hardware resources while maintaining full accuracy compared to 64-bit floating-point.TFH was part funded by Sundance Multiprocesssor Ltd., UK and an EPSRC Doctoral Training Partnerships (DTP) grant. JK was funded by the EPSRC (grant EP/V052241/1)