cs.ARAug 26, 2026

Beyond Edge Cuts: Activity-Weighted Multicast Hypergraph Mapping for Spiking Neural Networks on Mesh NoCs

Authors: Amirreza Khorasanian

Organizations: Electrical Engineering Student, Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran

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Abstract

Mapping spiking neural networks (SNNs) onto neuromorphic many-core platforms is often formulated with graph partitioning and pairwise placement costs. That abstraction is convenient, but it does not match the physical communication event: one spike from a source neuron is delivered to a set of postsynaptic destinations, and routes to several destinations can share mesh links. We present M-HySMap, a route-aware, activity-weighted multicast hypergraph mapping framework. Each source neuron induces a directed hyperedge to its postsynaptic fanout, weighted by profiled activity. The mapper starts from strong activity-aware graph/QAP seeds and then optimizes distinct destination-core fanout, the union of deterministic mesh routes, and link congestion. The central algorithmic observation is locality: moving one neuron can change only its own source-rooted hyperedge and the hyperedges of its predecessors. This permits exact incremental gain evaluation while caching every unaffected route contribution. We expose this combinatorial structure in detail, derive a conservative placement lower bound, and describe a portfolio of partition and placement neighborhoods that preserves the best incumbent. Across a 115-job evidence suite on Potjans-inspired recurrent SNNs and mesh NoCs from 4 x 4 to 6 x 6, plus a 7 x 7 stress case, M-HySMap reduces routed multicast hops by 10.6-19.6% over Activity+QAP and 19.7-41.1% over Edge+QAP. Incremental updates accelerate refinement by 4.7-12.7x while matching full recomputation to numerical precision.

Figures & tables

Figure 1: Edge cut counts remote synapses independently. A multicast-aware view first collapses targets onto distinct destination cores; therefore equal edge cut need not imply equal network traffic.
Figure 2: Route-aware multicast cost uses the union of deterministic XY paths. Shared links are counted once per source spike. The union is the exact route set under the fixed routing policy; it is not claimed to be a minimum Steiner tree.
Figure 3: Search architecture. Strong activity-aware graph/QAP seeds are refined by route-aware neuron moves, multicast placement swaps, and alternating joint schedules. The portfolio returns the minimum-objective incumbent among its candidates.
Figure 4: Moving vv affects hvh_{v} and predecessor-rooted hyperedges. Unrelated source contributions are provably unchanged and remain cached.
ConfigCoresSeedsNeuronsSynapses
0.0015, 4×44\times 4162079238±12238\pm 12
0.002, 4×44\times 41620108442±19442\pm 19
0.002, 5×55\times 52520108442±19442\pm 19
0.002, 6×66\times 63620108442±19442\pm 19
0.002, 7×77\times 7495108440±6440\pm 6
0.003, 4×44\times 416101631028±361028\pm 36
Table 1: Benchmark configurations. The 7×77\times 7 case is a smaller stress run.
ConfigSeedsEdge+QAPActivity+QAPM-HySMapvs Edgevs Activity
0.0015, 4×44\times 4201922±7751922\pm 7751409±6431409\pm 6431133±5631133\pm 56341.1%19.6%
0.002, 4×44\times 4208642±36188642\pm 36187332±33417332\pm 33415934±26775934\pm 267731.3%19.1%
0.002, 5×55\times 52010389±421010389\pm 42108535±36758535\pm 36757309±31617309\pm 316129.6%14.4%
0.002, 6×66\times 62013264±556313264\pm 556310624±499010624\pm 49909499±44049499\pm 440428.4%10.6%
0.002, 7×77\times 7513819±460813819\pm 460811079±348911079\pm 34899603±29749603\pm 297430.5%13.3%
0.003, 4×44\times 410113919±17494113919\pm 17494102637±16546102637\pm 1654684816±1463184816\pm 1463125.5%17.4%
Table 2: Main routed multicast hop results. Values are mean ±\pm standard deviation. Improvements are hop reductions achieved by M-HySMap.
Figure 5: Normalized routed multicast hops. Activity+QAP is 1.0 in each configuration; M-HySMap improves the routed metric in all eight configurations.
MethodNorm.HopsObj.Max link
Edge+QAP1.19261290654581986.1
Activity+QAP1.00055552593911860.8
QAP-seeded M-HySMap0.85747653500851523.7
M-HySMap0.84847527498241479.3
Table 3: Compact ablation summary averaged over configurations.
ConfigFull recompute (s)Incremental (s)SpeedupAvg. affectedMax error
0.0015, 4×44\times 40.4380.0617.2 ×\times2.481.8×10−121.8\times 10^{-12}
0.002, 4×44\times 41.0440.1139.2 ×\times2.719.1×10−129.1\times 10^{-12}
0.002, 5×55\times 51.6760.3564.7 ×\times2.608.2×10−128.2\times 10^{-12}
0.002, 6×66\times 62.4620.4315.7 ×\times2.512.0×10−112.0\times 10^{-11}
0.002, 7×77\times 71.7470.3515.0 ×\times2.651.1×10−111.1\times 10^{-11}
0.003, 4×44\times 411.8440.93312.7 ×\times2.417.3×10−117.3\times 10^{-11}
Table 4: Runtime benefit of exact incremental hyperedge updates.
Figure 6: Incremental update speedup. Labels also report the average number AA of affected source hyperedges, illustrating why locality is valuable.
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