T3former: Temporal Graph Classification with Topological Machine Learning

TL;DR

The paper tackles temporal graph classification where edges carry timestamps, a setting where preserving temporal fidelity is essential. It introduces T3Former, a Topological Temporal Transformer that fuses sliding-window topological descriptors (Betti numbers) and spectral DoS vectors with a global GraphSAGE encoder through a Descriptor-Attention fusion mechanism. The authors provide stability guarantees for the topological and spectral descriptors under perturbations, introduce new temporal-graph classification datasets, and demonstrate state-of-the-art results across social, brain, and traffic benchmarks. The work showcases robust, scalable temporal graph learning by integrating global structure with mesoscopic topological and spectral signatures through a principled multi-view fusion framework.

Abstract

Temporal graph classification plays a critical role in applications such as cybersecurity, brain connectivity analysis, social dynamics, and traffic monitoring. Despite its significance, this problem remains underexplored compared to temporal link prediction or node forecasting. Existing methods often rely on snapshot-based or recurrent architectures that either lose fine-grained temporal information or struggle with long-range dependencies. Moreover, local message-passing approaches suffer from oversmoothing and oversquashing, limiting their ability to capture complex temporal structures. We introduce T3former, a novel Topological Temporal Transformer that leverages sliding-window topological and spectral descriptors as first-class tokens, integrated via a specialized Descriptor-Attention mechanism. This design preserves temporal fidelity, enhances robustness, and enables principled cross-modal fusion without rigid discretization. T3former achieves state-of-the-art performance across multiple benchmarks, including dynamic social networks, brain functional connectivity datasets, and traffic networks. It also offers theoretical guarantees of stability under temporal and structural perturbations. Our results highlight the power of combining topological and spectral insights for advancing the frontier of temporal graph learning.

Figures (8)

• Figure 1: Graph Filtration. For $\mathcal{G}=\mathcal{G}_3$ in both examples, the top figure illustrates a superlevel filtration using the node degree function with thresholds $3>2>1$, where nodes of degree 3 are activated first, followed by those of lower degrees. Similarly, the bottom figure illustrates a sublevel filtration based on edge weights with thresholds $1.5< 1.8< 2.1$.
• Figure 2: Sliding window construction. DoS and Betti vectors $\{\mathcal{X}_i\}$) are extracted for each induced subgraph $\mathcal{G}_t=\mathcal{G}_{[t,t+\delta]}$.
• Figure 3: T3Former Flowchart. Given a temporal graph $\mathcal{G}=(\mathcal{V},\mathcal{E},\tau)$, GraphSAGE generates time-aware structural embeddings. In parallel, a sliding-window module extracts topological (Betti) and spectral (density of states) vectors. These sequential features are processed through a Transformer to capture temporal dependencies. An attention-based fusion module merges the multi-view representations, which are then passed through a final neural layer for graph property prediction.
• Figure 4: Sliding‐window Subgraphs: Given a temporal graph $\mathcal{G}$, the sliding window approach generates a sequence of subgraphs ($\mathcal{G}_{[1,3]}, \mathcal{G}_{[2,4]}, \mathcal{G}_{[3,5]}$ above), where each subgraph $\mathcal{G}_{[a,b]}$ includes only the edges active within the time interval $[a,b]$, i.e., edges $e$ such that $t_e \in [a,b]$.
• Figure 5: PEMS04 (2) tSNE Visualizations. t-SNE plots of individual embedding representations from T3former components on the PEMS04 traffic dataset with two classes.

Theorems & Definitions (6)

• Theorem 3.1: Stability of Topological Descriptors
• Theorem 3.2: Stability of Spectral Descriptors
• Lemma A.1
• Lemma A.2
• proof
• proof