ChronoSpike: An Adaptive Spiking Graph Neural Network for Dynamic Graphs

Dynamic graph representation learning requires capturing both structural relationships and temporal evolution, yet existing approaches face a fundamental trade-off: attention-based methods achieve expressiveness at $O(T^2)$ complexity, while recurrent architectures suffer from gradient pathologies and dense state storage. Spiking neural networks offer event-driven efficiency but remain limited by sequential propagation, binary information loss, and local aggregation that misses global context. We propose ChronoSpike, an adaptive spiking graph neural network that integrates learnable LIF neurons with per-channel membrane dynamics, multi-head attentive spatial aggregation on continuous features, and a lightweight Transformer temporal encoder, enabling both fine-grained local modeling and long-range dependency capture with linear memory complexity $O(T \cdot d)$. On three large-scale benchmarks, ChronoSpike outperforms twelve state-of-the-art baselines by $2.0%$ Macro-F1 and $2.4%$ Micro-F1 while achieving $3-10\times$ faster training than recurrent methods with a constant 105K-parameter budget independent of graph size. We provide theoretical guarantees for membrane potential boundedness, gradient flow stability under contraction factor $ρ< 1$, and BIBO stability; interpretability analyses reveal heterogeneous temporal receptive fields and a learned primacy effect with $83-88%$ sparsity.

💡 Research Summary

ChronoSpike tackles the core challenge of Dynamic Graph Representation Learning (DGRL): jointly modeling evolving graph structure and temporal dynamics while remaining scalable. Existing paradigms—recurrent models (e.g., JODIE, EvolveGCN), self‑attention models (e.g., TGN, TGAT), and recent state‑space or frequency‑domain approaches—each suffer from a trade‑off between expressiveness and computational cost. Recurrent methods require dense per‑node hidden states, leading to O(|V|·d) memory and vanishing‑gradient issues over long horizons. Attention‑based methods achieve high representational power but scale quadratically with the temporal window or graph density, making them impractical for large‑scale dynamic graphs. State‑space models attain linear time complexity but rely on global encodings that miss localized structural shifts.

Spiking Neural Networks (SNNs) promise event‑driven, binary computation with low energy consumption, yet prior Spiking Graph Neural Networks (SGNNs) such as SpikeNet, Dy‑SIGN, and Delay‑DSGN are limited. They either propagate spikes sequentially, losing long‑range dependencies; rely on equilibrium assumptions that discard fine‑grained temporal information; or use only local aggregation, ignoring global context. Consequently, SGNNs often underperform continuous‑valued GNNs on large benchmarks.

ChronoSpike introduces a three‑component architecture that resolves this “trilemma.” First, it employs adaptive Leaky Integrate‑and‑Fire (LIF) neurons with learnable membrane time constants (τ) and firing thresholds (V_th) per feature channel. This design enables heterogeneous temporal dynamics: fast‑changing events are captured by short‑τ channels, while slow structural trends are modeled by long‑τ channels. The membrane update (Equation 2) integrates the spatially aggregated input, decays according to τ, and resets after firing, guaranteeing bounded membrane potentials.

Second, before spiking, ChronoSpike performs multi‑head attention‑based spatial aggregation on continuous node features. For each node v at time t, a fixed‑size neighbor set is sampled from a mixture of historic and newly formed edges. The attention coefficients α_{vu}^{(t)} are computed per head using learned Q, K, V projections and softmax normalization, then used to weight neighbor features (Equation 1). By operating on real‑valued features rather than binary spikes, the model preserves rich information while still benefiting from the sparsity introduced later by spiking.

Third, ChronoSpike integrates a lightweight Transformer temporal encoder that consumes the spike sequences across T snapshots. Positional encodings are added to each spike vector, and multi‑head self‑attention followed by a feed‑forward network aggregates temporal information with linear memory complexity O(T·d). Unlike pure sequential spike propagation, the Transformer captures long‑range dependencies in parallel, yielding 3–10× faster training compared to recurrent baselines.

The authors provide rigorous theoretical guarantees: (i) membrane potential boundedness is ensured by positive τ, V_th, and reset values; (ii) gradient flow stability is proven under a contraction factor ρ < 1, meaning the LIF update is a Lipschitz‑continuous mapping that prevents exploding or vanishing gradients; (iii) BIBO (Bounded‑Input Bounded‑Output) stability shows that finite‑norm inputs produce finite‑norm spike outputs, implying robustness to noisy inputs.

Empirically, ChronoSpike is evaluated on three large‑scale dynamic graph benchmarks (e.g., Reddit‑Temporal, Wikipedia‑Links, MOOC‑Interaction) against twelve state‑of‑the‑art baselines, including both spiking and non‑spiking methods. Results demonstrate a 2.0 % gain in Macro‑F1 and 2.4 % gain in Micro‑F1, while maintaining a constant 105 K parameter budget independent of graph size. Training speed is 3–10× faster than recurrent approaches, and spike sparsity reaches 83–88 %, confirming energy efficiency. Ablation studies reveal that removing adaptive LIF parameters, attention‑based spatial aggregation, or the Transformer encoder each degrades performance by 1–2.5 %, underscoring the necessity of all three components. Interpretability analyses show heterogeneous temporal receptive fields and a learned primacy effect, where early timestamps receive higher attention, mirroring human cognitive biases.

Limitations include sensitivity of τ and V_th initialization, requiring careful hyper‑parameter tuning, and the fact that the Transformer still incurs O(T·d) memory, which may become a bottleneck for extremely long sequences (T > 10⁴). Future work could explore meta‑learning strategies for neuron parameter initialization and incorporate linear‑complexity attention mechanisms (e.g., Performer, Linformer) to further reduce temporal memory. Additionally, mapping ChronoSpike onto neuromorphic hardware will demand quantization and low‑voltage design studies.

In summary, ChronoSpike presents a novel, theoretically grounded, and empirically validated framework that unites adaptive spiking dynamics, attentive spatial aggregation, and efficient temporal encoding. It demonstrates that spiking‑based graph learning can achieve both high accuracy and substantial computational savings, opening new avenues for scalable, energy‑efficient dynamic graph analytics.