Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

Temporal signed networks (TSNs) model the time evolution of cooperative and adversarial relationships that arise in applications such as social media analysis, trust and reputation systems, and financial transaction networks. While graph neural networks (GNNs) perform well for static or unsigned link prediction, effective learning in temporal signed graphs remains challenging due to the interaction of signed relations, evolving structure, and balance-theoretic constraints. To address this gap, we propose a \emph{modular} temporal enhancement framework for signed GNNs that integrates historical context into otherwise static architectures. The framework introduces a Historical Context Integration Module (HCIM) that combines learnable recency-aware temporal weighting, LSTM-based embedding trajectory modeling, and multi-head temporal attention to capture both short- and long-term signed interaction dynamics. Historical information is fused with current node representations using either global or node-adaptive weighting, allowing the architecture-agnostic framework to accommodate heterogeneous temporal behaviors. We instantiate the approach on the Self-Explainable Signed Graph Transformer (SE-SGformer), preserving interpretability while extending it with temporal awareness. Experiments on real-world and synthetic TSNs, including Bitcoin OTC, Bitcoin Alpha, Reddit, and small-world network models, demonstrate consistent and statistically significant improvements over the static baseline.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. \emph{Temporal-first} approaches build per-node temporal embeddings and only afterwards perform spatial aggregation, whereas \emph{Spatial-first} approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; concretely, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's \emph{past} trajectory. This paper introduces \textbf{SiST-GNN} (\textbf{Si}multaneous \textbf{S}patial-\textbf{T}emporal \textbf{GNN}), which fuses the two signals inside a single message-passing operation rather than chaining them. Concretely, at each snapshot we maintain a recurrent hidden state per node that summarises its history, pair it with the node's current feature vector, and treat the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. Our empirical study spans nine public baselines and fourteen model-dataset combinations, covering both fixed-split and live-update evaluation regimes. Across every public benchmark, SiST-GNN sets a new state of the art in link prediction task over the strongest prior method by $109$--$277\%$ in the fixed-split setting and by $68$--$194\%$ in the live-update setting. We additionally construct three dynamic node-classification tasks by discretising the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by $7$--$22\%$ and matches continuous-time (CTDG) methods that consume the raw events directly.

Aggregating temporal signals from historic interactions is a key step in future link prediction on dynamic graphs. However, incorporating long histories is resource-intensive. Hence, temporal graph neural networks (TGNNs) often rely on historical neighbors sampling heuristics such as uniform sampling or recent neighbors selection. These heuristics are static and fail to adapt to the underlying graph structure. We introduce FLASH, a learnable and graph-adaptive neighborhood selection mechanism that generalizes existing heuristics. FLASH integrates seamlessly into TGNNs and is trained end-to-end using a self-supervised ranking loss. We provide theoretical evidence that commonly used heuristics hinder TGNNs performance, motivating our design. Extensive experiments across multiple benchmarks demonstrate consistent and significant performance improvements for TGNNs equipped with FLASH.