Hypergraphs Achieve Efficient SNN Mapping for Neuromorphic Hardware with Billions of Neurons

Spiking Neural Networks (SNNs) present a significant challenge when deployed on neuromorphic hardware, specifically regarding the efficient allocation of neurons to processing cores. Marco Ronzani and Cristina Silvano, both from Politecnico di Milano, lead a new study demonstrating how representing SNNs as hypergraphs , rather than traditional graphs , dramatically improves mapping techniques and reduces computational cost. This innovative approach captures the replication of spikes within cores, revealing a strong correlation between hyperedge characteristics and mapping quality. By grouping neurons via shared hyperedges, the researchers show substantial reductions in communication traffic and hardware resource usage, surpassing current state-of-the-art methods across various SNN scales and execution time regimes. This work, also involving contributions from et al., identifies a promising suite of algorithms poised to enable effective SNN mapping even as networks and hardware continue to grow in complexity.

This innovative hypergraph model allows for a more accurate representation of how spikes are handled on-chip, potentially leading to significant energy savings and performance improvements. The study meticulously explores the correlation between hyperedge overlap and locality with high-quality mappings, establishing these properties as instrumental in devising effective mapping algorithms. Results indicate that hypergraph-based techniques achieve better mappings than current methods, particularly as SNNs and hardware scale towards billions of neurons, a crucial step towards realising truly large-scale neuromorphic systems.

The team’s findings suggest that focusing on hyperedge properties, specifically overlap and locality, is key to developing scalable and efficient mapping solutions. This approach moves beyond simply minimising the distance between connected neurons and instead prioritises grouping neurons that share common destinations, thereby maximising the benefits of on-chip spike replication. To establish this hypergraph model, the study defined a directed weighted hypergraph (h-graph), GS = (N, ES, wS), where nodes represent neurons and hyperedges represent axons originating from each neuron. Each hyperedge, denoted as (s, D), has a single source ‘s’ and a set of destinations ‘D’, with a weight ‘wS’ corresponding to spike frequency.
Crucially, the team ensured a one-to-one correspondence between hyperedges and neurons, allowing spike frequency to be interpreted as the source neuron’s activity. This representation allows for a more compact and efficient description of network connectivity, particularly in complex, recurrent SNNs. The team formally defined a partitioning function ρ: N→P, mapping each neuron to a partition ‘p’ within a core, and subsequently constructed a new h-graph GP representing the partitioned network. Valid partitioning adhered to hardware constraints, limiting partition size to Cnpc neurons and inbound hyperedges to Capc, ensuring feasibility on the neuromorphic chip. This rigorous approach enabled the researchers to quantify the impact of hypergraph-based techniques on mapping quality.

Hypergraphs optimise spiking neural network neuromorphic mapping

This work addresses the challenge of mapping neurons to cores on NMH, where operational cost is directly linked to spike movement and active core count. Data shows that exploiting the overlap and locality of hyperedges is instrumental in devising effective mapping algorithms, leading to reduced communication overhead. Measurements confirm that this approach minimizes the number of spikes transmitted between cores, directly impacting energy consumption and latency. Tests prove that hypergraph-based techniques can achieve better mappings than existing methods, particularly in scenarios demanding high throughput and low latency.

Scientists recorded improvements in resource utilization, with a demonstrable reduction in the number of cores required to accommodate a given SNN. This novel approach allows for a more holistic optimization of the SNN, leading to substantial gains in performance and efficiency. The research establishes a foundation for future work in SNN mapping, offering a powerful new tool for harnessing the potential of neuromorphic computing.

Hypergraphs optimise spiking neural network neuromorphic mapping

The findings firmly establish hypergraphs as a valuable abstraction for SNN mapping, enabling more efficient partitioning and placement of neurons onto neuromorphic chips. Specifically, algorithms leveraging hyperedge overlap for partitioning and spectral initial placement for positioning achieved mappings up to twice as efficient as existing graph-based methods across various SNN architectures, layered, recurrent, and biologically plausible, while maintaining scalability. The authors acknowledge a limitation in focusing primarily on single-chip mapping, and future work will address multi-chip generalisation and refinement of hypergraph-based heuristics. To facilitate further research, the team intends to release their benchmark hypergraphs and algorithm implementations as open source, laying a foundation for continued improvement in SNN mapping tools and ultimately, brain-scale neuromorphic computing.