Spiking Graph Neural Networks

• Spiking Graph Neural Networks are models that integrate graph-based message passing with spiking neural dynamics to capture temporal and spatial patterns.
• They implement key SNN mechanisms, such as membrane potential updates and discrete spike events, enabling efficient temporal computation on graph data.
• SGNNs employ diverse architectures and training paradigms—including convolution, attention, and geometric dynamics—to address various graph learning applications.

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 (Xu et al., 2021, Yin et al., 2024, Yang et al., 2022, Yin et al., 2024).

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 (Chen et al., 2023).

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 (Xu et al., 2021, Sun et al., 2024). 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 (Xu et al., 2021).

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 (Sun et al., 2024, Yin et al., 2024, Sun et al., 2024).

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 $u_{\text{th}}$ (Yin et al., 2024). 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 (Xu et al., 2021).

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 (Yang et al., 2022). SpikeGraphormer linearly embeds static node features, repeats them over $T$ time steps, and then applies a spiking neuron layer to obtain binary spike tensors $t$0 (Sun et al., 2024). Signal-SGN uses the temporal dimension of a skeleton sequence itself as the spiking time axis, avoiding an additional artificial time dimension (Zheng et al., 2024). In transductive neuromorphic citation classification on Loihi 2, a single spike is injected into the paper neuron under evaluation at $t$1, and subsequent spike propagation through the citation graph performs the classification computation (Snyder et al., 2024).

Propagation is likewise heterogeneous. In attention-driven SGNNs, neighbor contributions are weighted by graph attention coefficients $t$2 and injected as currents into LIF neurons, yielding spike-based multi-head message passing (Yin et al., 2024). 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 (Yang et al., 2022). 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 (Yin et al., 2024).

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 (Xu et al., 2021)	graph convolution filters inside spiking dynamics; Spatial-Temporal Feature Normalization	node classification
SpikingGAT (Yin et al., 2024)	multi-head attention in a spiking message-passing framework with LIF neurons	node, edge, and graph classification
S-VGAE (Yang et al., 2022)	spiking GNN encoder, Bernoulli latent variables, weighted inner product decoder	link prediction
SpikeGraphormer (Sun et al., 2024)	Spiking Graph Attention and a dual-branch architecture with all-pair node interactions	node classification
COS-GNN (Yin et al., 2024)	spike representations integrated into first- and second-order graph ODEs	node and graph classification
MSG and GSG (Sun et al., 2024, Zhang et al., 9 Aug 2025)	manifold-valued spiking layers, curvature-aware aggregation, Riemannian optimization	node classification and link prediction
KRR-GSNN, SpikE, spiking relational GNN (Fang et al., 2022, Dold et al., 2021, Dold et al., 2022)	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 (Xu et al., 2021). 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$3 (Yin et al., 2024).

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 (Yang et al., 2022).

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 $t$4 and 10–20× lower GPU memory than vanilla self-attention (Sun et al., 2024).

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 (Yin et al., 2024). 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 (Sun et al., 2024, Zhang et al., 9 Aug 2025).

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 (Fang et al., 2022). SpikE encodes entities as vectors of single spike times and relations as spike-time differences (Dold et al., 2021). A spiking relational graph neural network extends this by implementing relational graph convolution directly in spike time and synaptic kernel space (Dold et al., 2022).

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$5, and surrogate gradients to handle the non-differentiable spike function (Yin et al., 2024). 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 (Xu et al., 2021). SpikeGraphormer likewise uses surrogate gradients for the Heaviside function and trains with Adam under BCE or NLL losses (Sun et al., 2024).

Variational and probabilistic objectives introduce a different training regime. S-VGAE minimizes a negative ELBO composed of edge reconstruction and Bernoulli KL divergence,

$t$6

with binary latent spike codes sampled by probabilistic LIF neurons (Yang et al., 2022). 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 (Li et al., 2023).

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 (Fang et al., 2022, Snyder et al., 2024). 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 (Fang et al., 2022). The Loihi-compatible citation classifier learns val/test-to-topic synapses by integer STDP and tunes hyperparameters through Lava Bayesian Optimization (Snyder et al., 2024). SDGN combines local STDP updates for dynamic graph estimation with global likelihood-based optimization of multivariate point-process intensities (Chakraborty et al., 1 Apr 2025).

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 (Wang et al., 2024).

5. Empirical regimes and applications

On standard citation graphs, SpikingGAT was evaluated on Cora, Citeseer, and Pubmed with 20 labels per class, $t$7, $t$8, and eight attention heads. Reported accuracies were $t$9% on Cora, $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$0% on Citeseer, and $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$1% on Pubmed, versus $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$2%, $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$3%, and $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$4% for GAT. On MNIST graphs, SpikingGAT reached $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$5% versus $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$6% for GAT, and on SBM CLUSTER and TSP it consistently outperformed SpikingGCN (Yin et al., 2024).

For link prediction, S-VGAE reported on Cora an AUC of 92.6 versus 91.4 for VGAE while reducing floating-point energy from $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$7 to $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$8 and integer energy from $$I_i^{(l)}(t) = \sum_j A_{ij}\, w_{ij}^{(l)}\, s_j^{(l-1)}(t),$$9 to $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$0 in units of $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$1 pJ per link prediction. On the same dataset, removing its decoupling mechanism raised $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$2 from $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$3 to $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$4 and $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$5 from $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$6 to $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$7 (Yang et al., 2022).

For large-scale node classification and graph transformers, SpikeGraphormer reported $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$8% on Cora, $$\widetilde{H}_t^{n} = \Phi\big(\mathcal{G}_c(A, \widetilde{H}_t^{n-1}) W^{n}, \widetilde{H}_{t-1}^{n}\big),$$9% on Chameleon, $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$0% on Squirrel, $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$1 ROC-AUC on OGB-Proteins, and $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$2% on Amazon2M. Runtime measurements on an RTX-4090 showed $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$3 MB GPU memory on Cora and $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$4 MB on Squirrel, versus $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$5 MB and $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$6 MB for Nodeformer; the paper states 10–20× lower GPU memory than vanilla self-attention (Sun et al., 2024).

Geometric SGNNs show another empirical pattern. MSG achieved $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$7% node classification accuracy on Photo, outperforming SpikeNet at $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$8% and SpikeGCN at $$\tau \frac{du(t)}{dt} = -\big[u(t) - U_{\text{rest}}\big] + R I(t),$$9%, while on the CS dataset its reported energy was $u_{\text{th}}$0 mJ versus $u_{\text{th}}$1 mJ for SpikeGCL and $u_{\text{th}}$2 mJ for SpikeNet (Sun et al., 2024). GSG reported $u_{\text{th}}$3% on Computers, $u_{\text{th}}$4% on Photo, $u_{\text{th}}$5% on CS, and $u_{\text{th}}$6% on Physics, with corresponding energies of $u_{\text{th}}$7, $u_{\text{th}}$8, and $u_{\text{th}}$9 mJ on Computers, Photo, and CS (Zhang et al., 9 Aug 2025).

Application-specific SGNNs broaden the empirical landscape. EEGSN reports a $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$0 reduction in inference computational complexity compared to state-of-the-art SNNs while achieving comparable accuracy on motor execution classification tasks (Chen et al., 2023). Signal-SGN reaches $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$1% / $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$2% on NTU RGB+D for one-stream Bone and $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$3% / $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$4% for a four-stream ensemble, with reported energy $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$5 mJ and $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$6 mJ respectively (Zheng et al., 2024). On Loihi-oriented citation classification, the fixed-precision Lava implementation obtained $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$7% validation accuracy at $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$8, delay $$V^{n,i}_{t+1} = \kappa V^{n,i}_t \big(1-\widetilde{H}^{n,i}_t\big) + \sum_j W^{n,ij}\mathcal{G}_c\big(A,\widetilde{H}^{n-1,j}_{t+1}\big), \qquad \widetilde{H}^{n,i}_{t+1}=g\big(V^{n,i}_{t+1}-V_{th}\big),$$9, and Bayesian optimization found a best configuration with $X^{1:T}\in\mathbb{R}^{N\times C_0\times T}$0% validation accuracy and $X^{1:T}\in\mathbb{R}^{N\times C_0\times T}$1% improvement over the original NEST parameter set when ported to fixed-precision Lava (Snyder et al., 2024). 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 (Chakraborty et al., 1 Apr 2025).

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 (Fang et al., 2022). Spike-time embeddings in SpikE reach test MRR $X^{1:T}\in\mathbb{R}^{N\times C_0\times T}$2 on an industrial KG, versus $X^{1:T}\in\mathbb{R}^{N\times C_0\times T}$3 for TransE, while enabling event-based anomaly detection and low-latency plausibility scoring (Dold et al., 2021).

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 (Yin et al., 2024, Xu et al., 2021). 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 (Sun et al., 2024, Yin et al., 2024). Third, energy-efficiency claims are frequently inferred from sparsity, operation counts, or GPU measurements rather than validated on deployed neuromorphic hardware (Sun et al., 2024, Zhang et al., 9 Aug 2025).

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 (Yin et al., 2024, Sun et al., 2024). 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 (Yang et al., 2022, Sun et al., 2024, Yin et al., 2024, Fang et al., 2022).

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 (Chakraborty et al., 1 Apr 2025). 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 (Snyder et al., 2024). Geometry-aware models raise further questions about manifold selection, Jacobian cost, and deployment of log/exp-map operations on neuromorphic substrates (Sun et al., 2024, Zhang et al., 9 Aug 2025). Domain-shifted SGNNs, as shown by DeSGDA, introduce additional issues of threshold transfer, unseen degree values, and adaptation guarantees (Wang et al., 2024).

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.