---
title: Spiking Graph Neural Networks
url: https://www.emergentmind.com/topics/spiking-graph-neural-networks-sgnns
type: topic
---

# Spiking Graph Neural Networks

Spiking Graph Neural Networks (SGNNs) are graph learning models that implement the core ideas of Graph Neural Networks—message passing, neighborhood aggregation, and representation learning—using spiking neural networks as the computational substrate. Across the recent literature, SGNNs are described as combining graph-structured inductive bias with event-driven, temporally dynamic computation: node states are realized as membrane potentials and spike trains, edges define synaptic connectivity or graph-constrained aggregation, and learning may proceed through surrogate-gradient backpropagation, probabilistic variational objectives, or local plasticity rules such as STDP and R-STDP [2107.06865], [2403.17040], [2211.01952], [2404.01897].

## 1. Conceptual foundations

SGNNs inherit two distinct modeling commitments. From GNNs they inherit graph-based inductive bias, adjacency-constrained aggregation, and relational message passing; from SNNs they inherit discrete spike events, membrane dynamics, thresholding, reset, and sparse event-driven communication. A generic spiking graph layer can therefore be written as a graph aggregation followed by a spiking state update. In one explicit formulation, the input current to node \(i\) at time \(t\) is
\[
I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),
\]
and the membrane potential evolves according to a leaky integrate-and-fire update before generating a binary spike through a Heaviside threshold [2304.07655].

Several papers define SGNNs almost identically: node features are encoded as spike trains, graph connectivity constrains synaptic interactions, and node-update functions are implemented by spiking neurons rather than continuous activations [2107.06865], [2410.17941]. In the general Graph SNN framework, the layerwise update is written as
\[
\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),
\]
which makes the dependence on graph propagation, trainable weights, and prior temporal state explicit [2107.06865].

This perspective also clarifies what SGNNs are not. They are not restricted to ANN-to-SNN conversion, and they are not uniformly tied to static Euclidean embeddings. The literature already includes spike-based graph convolution, graph attention, graph transformers, variational graph auto-encoders, continuous-time graph ODEs, knowledge-graph reasoning systems, and manifold-valued models [2403.15480], [2404.01897], [2410.17941].

## 2. Neuron models, encodings, and spike-based propagation

The dominant neuron model in SGNNs is the Leaky Integrate-and-Fire neuron. In one continuous-time form used by attention-driven SGNNs,
\[
\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),
\]
with binary firing and reset determined by a threshold \(u_{\text{th}}\) [2403.17040]. A discrete-time formulation used in graph spiking architectures writes
\[
V^{n,i}_{t+1}
= \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big)
+ \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big),
\qquad
\widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),
\]
which explicitly couples graph filtering and spike generation [2107.06865].

Input encoding varies substantially across tasks. S-VGAE converts node features into spike trains by Poisson rate encoding, producing \(X^{1:T}\in\mathbb{R}^{N\times C_0\times T}\) for a spiking encoder over \(T\) time steps [2211.01952]. SpikeGraphormer linearly embeds static node features, repeats them over \(T\) time steps, and then applies a spiking neuron layer to obtain binary spike tensors \(S_0\in\mathbb{R}^{T\times N\times D}\) [2403.15480]. Signal-SGN uses the temporal dimension of a skeleton sequence itself as the spiking time axis, avoiding an additional artificial time dimension [2408.01701]. In transductive neuromorphic citation classification on Loihi 2, a single spike is injected into the paper neuron under evaluation at \(t=0\), and subsequent spike propagation through the citation graph performs the classification computation [2404.17048].

Propagation is likewise heterogeneous. In attention-driven SGNNs, neighbor contributions are weighted by graph attention coefficients \(\alpha_{ij}^{(k)}\) and injected as currents into LIF neurons, yielding spike-based multi-head message passing [2403.17040]. In S-VGAE, propagation and transformation are explicitly decoupled into two stacked spiking layers so that fixed topology-based diffusion and trainable synaptic transformation are both implemented with spiking neurons, reducing multiply–accumulate operations [2211.01952]. In continuous formulations such as COS-GNN, spike trains over an internal latency axis are compressed into spike representations and then coupled to first- or second-order graph ODEs [2404.01897].

## 3. Architectural families

The recent SGNN literature contains several relatively distinct architectural families.

| Family / model | Core mechanism | Primary task |
|---|---|---|
| Graph SNN, GC-SNN, GA-SNN [2107.06865] | graph convolution filters inside spiking dynamics; Spatial-Temporal Feature Normalization | node classification |
| SpikingGAT [2403.17040] | multi-head attention in a spiking message-passing framework with LIF neurons | node, edge, and graph classification |
| S-VGAE [2211.01952] | spiking GNN encoder, Bernoulli latent variables, weighted inner product decoder | link prediction |
| SpikeGraphormer [2403.15480] | Spiking Graph Attention and a dual-branch architecture with all-pair node interactions | node classification |
| COS-GNN [2404.01897] | spike representations integrated into first- and second-order graph ODEs | node and graph classification |
| MSG and GSG [2410.17941], [2508.06793] | manifold-valued spiking layers, curvature-aware aggregation, Riemannian optimization | node classification and link prediction |
| KRR-GSNN, SpikE, spiking relational GNN [2207.05561], [2104.13398], [2208.02576] | population or spike-time encoding of symbolic entities and relations | reasoning and link prediction |

The early general framework of graph convolution SNNs and graph attention SNNs established that graph filters can be unfolded in space and time and then trained end-to-end with spike dynamics and a graph-specific normalization scheme [2107.06865]. SpikingGAT pushed this line further by defining a spike-based counterpart of GAT with multi-head attention, attention-weighted synaptic currents, and LIF dynamics over a discrete time window \(T=8\) [2403.17040].

A second line replaces not only activations but the graph learning objective itself. S-VGAE is described as the first SNN-based deep generative graph model for multi-node tasks. Its encoder is a spiking GCN, its latent variables are Bernoulli spike trains, and its decoder reconstructs edges through a weighted inner product on sparse binary spikes [2211.01952].

A third line targets global interaction. SpikeGraphormer introduces Spiking Graph Attention, replaces matrix multiplication by sparse addition and mask operations, and couples a sparse GNN branch with an SGA-driven graph transformer branch. The model is explicitly designed to retain all-pair node interactions with training complexity \(O(N+E)\) and 10–20× lower GPU memory than vanilla self-attention [2403.15480].

A fourth line introduces continuous or geometric dynamics. COS-GNN couples an SNN latency axis with a continuous graph-time ODE and provides first- and second-order formulations intended to preserve information and mitigate exploding and vanishing gradients [2404.01897]. MSG moves SGNNs to geodesically complete Riemannian manifolds and replaces surrogate-gradient BPTT with Differentiation via Manifold, while GSG generalizes this direction with mixed-curvature manifolds, curvature-based attention, and a manifold learning objective trained by Riemannian SGD [2410.17941], [2508.06793].

Knowledge-graph and neuro-symbolic variants depart even further from standard message passing. KRR-GSNN maps entities and relations to sparse neuron populations and encodes triples through STDP-shaped synapses between populations [2207.05561]. SpikE encodes entities as vectors of single spike times and relations as spike-time differences [2104.13398]. A spiking relational graph neural network extends this by implementing relational graph convolution directly in spike time and synaptic kernel space [2208.02576].

## 4. Learning paradigms and optimization

Most SGNNs are trained end-to-end with standard optimizers and surrogate-gradient approximations to the spike derivative. In citation and multi-graph benchmarks, spiking graph attention uses Adam, cross-entropy loss, backpropagation through time over \(T=8\), and surrogate gradients to handle the non-differentiable spike function [2403.17040]. The general Graph SNN framework follows the same pattern and adds Spatial-Temporal Feature Normalization, which normalizes pre-synaptic membrane potentials across time and feature dimensions for each node to accelerate convergence [2107.06865]. SpikeGraphormer likewise uses surrogate gradients for the Heaviside function and trains with Adam under BCE or NLL losses [2403.15480].

Variational and probabilistic objectives introduce a different training regime. S-VGAE minimizes a negative ELBO composed of edge reconstruction and Bernoulli KL divergence,
\[
\mathcal{L}
=
-\sum_{n,m}\mathbb{E}_q[\log p(y_{nm}\mid z_n^{1:T},z_m^{1:T})]
+
\frac{1}{T}\sum_{n,t}\mathrm{KL}\big[q(z_n^t\mid X^{1:t})\Vert p(z_n^t)\big],
\]
with binary latent spike codes sampled by probabilistic LIF neurons [2211.01952]. Contrastive self-supervision also appears: SpikeGCL learns 1-bit spike representations for graphs within a graph contrastive learning pipeline and reports nearly 32× representation storage compression [2305.19306].

Not all SGNNs depend on surrogate-gradient BPTT. KRR-GSNN and the Loihi transductive SGNN use local spike-timing rules rather than global error backpropagation [2207.05561], [2404.17048]. KRR-GSNN employs STDP and reward-modulated STDP with eligibility traces and global reward signals to learn commonsense reasoning circuits in a ConceptNet-derived graph [2207.05561]. The Loihi-compatible citation classifier learns val/test-to-topic synapses by integer STDP and tunes hyperparameters through Lava Bayesian Optimization [2404.17048]. SDGN combines local STDP updates for dynamic graph estimation with global likelihood-based optimization of multivariate point-process intensities [2504.01246].

Domain-shifted training has also entered the SGNN literature. DeSGDA couples degree-aware threshold adaptation with adversarial alignment of source and target spiking representations and a pseudo-label distillation mechanism defined across shallow and deep spiking feature spaces [2410.06883].

## 5. Empirical regimes and applications

On standard citation graphs, SpikingGAT was evaluated on Cora, Citeseer, and Pubmed with 20 labels per class, \(T=8\), \(u_{\text{th}}=0.25\), and eight attention heads. Reported accuracies were \(79.9 \pm 0.9\)% on Cora, \(68.4 \pm 0.5\)% on Citeseer, and \(78.0 \pm 0.5\)% on Pubmed, versus \(83.0 \pm 0.7\)%, \(72.5 \pm 0.7\)%, and \(79.0 \pm 0.3\)% for GAT. On MNIST graphs, SpikingGAT reached \(95.483 \pm 0.002\)% versus \(95.535 \pm 0.205\)% for GAT, and on SBM CLUSTER and TSP it consistently outperformed SpikingGCN [2403.17040].

For link prediction, S-VGAE reported on Cora an AUC of 92.6 versus 91.4 for VGAE while reducing floating-point energy from \(92.70\) to \(4.23\) and integer energy from \(64.49\) to \(0.47\) in units of \(\times 10^4\) pJ per link prediction. On the same dataset, removing its decoupling mechanism raised \(E^F\) from \(4.23\) to \(13.36\) and \(E^I\) from \(0.47\) to \(7.74\) [2211.01952].

For large-scale node classification and graph transformers, SpikeGraphormer reported \(84.8 \pm 0.7\)% on Cora, \(44.8 \pm 4.2\)% on Chameleon, \(42.6 \pm 2.4\)% on Squirrel, \(79.62 \pm 0.90\) ROC-AUC on OGB-Proteins, and \(88.12 \pm 0.06\)% on Amazon2M. Runtime measurements on an RTX-4090 showed \(92.8\) MB GPU memory on Cora and \(132\) MB on Squirrel, versus \(238.95\) MB and \(4159.99\) MB for Nodeformer; the paper states 10–20× lower GPU memory than vanilla self-attention [2403.15480].

Geometric SGNNs show another empirical pattern. MSG achieved \(93.11\)% node classification accuracy on Photo, outperforming SpikeNet at \(92.90\)% and SpikeGCN at \(92.60\)%, while on the CS dataset its reported energy was \(0.026\) mJ versus \(0.128\) mJ for SpikeGCL and \(0.218\) mJ for SpikeNet [2410.17941]. GSG reported \(90.11\)% on Computers, \(93.62\)% on Photo, \(93.01\)% on CS, and \(96.27\)% on Physics, with corresponding energies of \(0.096\), \(0.079\), and \(0.051\) mJ on Computers, Photo, and CS [2508.06793].

Application-specific SGNNs broaden the empirical landscape. EEGSN reports a \(\times 20\) reduction in inference computational complexity compared to state-of-the-art SNNs while achieving comparable accuracy on motor execution classification tasks [2304.07655]. Signal-SGN reaches \(80.5\)% / \(87.7\)% on NTU RGB+D for one-stream Bone and \(86.1\)% / \(93.1\)% for a four-stream ensemble, with reported energy \(0.372\) mJ and \(1.288\) mJ respectively [2408.01701]. On Loihi-oriented citation classification, the fixed-precision Lava implementation obtained \(63.57\)% validation accuracy at \(T_s=14\), delay \(=0\), and Bayesian optimization found a best configuration with \(62.86\)% validation accuracy and \(3.58\)% improvement over the original NEST parameter set when ported to fixed-precision Lava [2404.17048]. In dynamic event modeling, SDGN reported lower prediction errors than Poisson, Hawkes, THP, and GRTPP on NYC Taxi, Reddit, Stack Overflow, Earthquake, and 911 datasets [2504.01246].

Knowledge-graph and commonsense-reasoning systems show that SGNNs are not limited to conventional benchmark graphs. KRR-GSNN encodes roughly 2.5 million triples, roughly 800,000 entities, and 17 relation types as populations and synapses, and on a transitivity reasoning task it achieves comparable final accuracy to GCN with faster convergence [2207.05561]. Spike-time embeddings in SpikE reach test MRR \(0.645 \pm 0.009\) on an industrial KG, versus \(0.671 \pm 0.003\) for TransE, while enabling event-based anomaly detection and low-latency plausibility scoring [2104.13398].

## 6. Limitations, misconceptions, and open problems

Several recurring limitations cut across the literature. First, many SGNNs still rely on explicit time unrolling, surrogate gradients, and BPTT. This raises computational cost, complicates training, and can slow scaling to deeper networks or larger graphs [2403.17040], [2107.06865]. Second, many empirical studies remain on static graphs even when the models have temporal machinery. This suggests that the temporal expressivity of spikes is often used as a computational substrate rather than being fully matched to time-evolving topology [2403.15480], [2403.17040]. Third, energy-efficiency claims are frequently inferred from sparsity, operation counts, or GPU measurements rather than validated on deployed neuromorphic hardware [2403.15480], [2508.06793].

A common misconception is that “spiking” alone guarantees neuromorphic realism or local learning. In practice, a substantial part of the SGNN literature trains with Adam, cross-entropy, and surrogate gradients on conventional hardware [2403.17040], [2403.15480]. Conversely, another misconception is that SGNNs are just GNNs with thresholded activations. Models such as S-VGAE, SpikeGraphormer, MSG, COS-GNN, and KRR-GSNN alter the graph learning objective, the propagation rule, the geometry, or the learning rule itself rather than merely binarizing activations [2211.01952], [2410.17941], [2404.01897], [2207.05561].

Open problems are now relatively well defined. Scalability to very large graphs, dense graphs, and dynamic graphs remains difficult; SDGN explicitly notes limitations on dense graphs and certain non-Gaussian dependencies [2504.01246]. Hardware realization remains uneven: the Loihi work shows that fixed-precision, Loihi 2 compatible SGNNs can perform citation graph classification with comparable accuracy to floating-point implementations, but it also notes capacity limits, the absence of node features in the present implementation, and substantial toolchain overhead [2404.17048]. Geometry-aware models raise further questions about manifold selection, Jacobian cost, and deployment of log/exp-map operations on neuromorphic substrates [2410.17941], [2508.06793]. Domain-shifted SGNNs, as shown by DeSGDA, introduce additional issues of threshold transfer, unseen degree values, and adaptation guarantees [2410.06883].

Taken together, the literature suggests that SGNNs have moved from proof-of-concept spike-based graph convolutions to a broader research program encompassing attention, transformers, generative modeling, continuous dynamics, manifold geometry, knowledge representation, domain adaptation, and neuromorphic deployment. A plausible implication is that the next stage will not be a single “unified SGNN framework,” but a stratified family of graph-spiking models tailored to distinct regimes: message-passing SGNNs for sparse relational learning, generative SGNNs for link prediction, transformer-style SGNNs for global interaction, and continuous or geometric SGNNs for structure-rich non-Euclidean graphs.

Source: https://www.emergentmind.com/topics/spiking-graph-neural-networks-sgnns