Executing Spiking Neural Networks (SNNs) on neuromorphic hardware poses the problem of mapping neurons to cores. SNNs operate by propagating spikes between neurons that form a graph through synapses. Neuromorphic hardware mimics them through a network-on-chip, transmitting spikes, and a mesh of cores, each managing several neurons. Its operational cost is tied to spike movement and active cores. A mapping comprises two tasks: partitioning the SNN's graph to fit inside cores and placement of each partition on the hardware mesh. Both are NP-hard problems, and as SNNs and hardware scale towards billions of neurons, they become increasingly difficult to tackle effectively. In this work, we propose to raise the abstraction of SNNs from graphs to hypergraphs, redesigning mapping techniques accordingly. The resulting model faithfully captures the replication of spikes inside cores by exposing the notion of hyperedge co-membership between neurons. We further show that the overlap and locality of hyperedges strongly correlate with high-quality mappings, making these properties instrumental in devising mapping algorithms. By exploiting them directly, grouping neurons through shared hyperedges, communication traffic and hardware resource usage can be reduced be yond what just contracting individual connections attains. To substantiate this insight, we consider several partitioning and placement algorithms, some newly devised, others adapted from literature, and compare them over progressively larger and bio-plausible SNNs. Our results show that hypergraph based techniques can achieve better mappings than the state-of-the-art at several execution time regimes. Based on these observations, we identify a promising selection of algorithms to achieve effective mappings at any scale.

翻译：执行脉冲神经网络于神经形态硬件时，需解决神经元映射至计算核心的问题。脉冲神经网络通过突触形成的图结构，在神经元间传播脉冲信号。神经形态硬件采用片上网络传输脉冲，配合处理核心阵列（每个核心管理多个神经元）进行模拟。其运行成本与脉冲迁移量及活跃核心数相关。映射任务包含两个步骤：将脉冲神经网络的图结构分割适配至核心，以及将各分区部署至硬件网格。这两者均为NP难问题，随着脉冲神经网络与硬件规模扩展至数十亿神经元，高效求解变得愈发困难。本文提出将脉冲神经网络的抽象层级从图提升至超图，并据此重新设计映射技术。该模型通过揭示神经元间超边共成员关系，准确捕捉了核心内脉冲复制现象。进一步研究发现，超边的重叠度与局部性与高质量映射显著相关，这些特性成为设计映射算法的关键。通过直接利用这些特性，将共享超边的神经元分组，可超越单纯收缩单条连接所能达到的效果，显著降低通信流量与硬件资源消耗。为验证这一观点，我们采用多种分区与布局算法（部分为新设计，部分改编自文献），在规模递增且具有生物合理性的脉冲神经网络上进行对比实验。结果表明，基于超图的技术能在多种执行时间场景下实现优于现有技术的映射方案。基于这些观察，我们筛选出能实现任意规模有效映射的算法组合。