We train all models in link prediction tasks in a self-supervised approach.

Temporal graph networks (TGNs) have gained prominence as models for embedding dynamic interactions, but little is known about their theoretical underpinnings.

Temporal Graph Networks (TGNs) have demonstrated significant success in dynamic graph tasks such as link prediction and node classification. Both tasks comprise transductive settings, where the model predicts links among known nodes, and in inductive settings, where it generalises learned patterns to previously unseen nodes. Existing TGN designs face a dilemma under these dual scenarios. Anonymous TGNs, which rely solely on temporal and structural information, offer strong inductive generalisation but struggle to distinguish known nodes. In contrast, non-anonymous TGNs leverage node features to excel in transductive tasks yet fail to adapt to new nodes. To address this challenge, we propose Trajectory Encoding TGN (TETGN). Our approach introduces automatically expandable node identifiers (IDs) as learnable temporal positional features and performs message passing over these IDs to capture each node's historical context. By integrating this trajectory-aware module with a standard TGN using multi-head attention, TETGN effectively balances transductive accuracy with inductive generalisation. Experimental results on three real-world datasets show that TETGN significantly outperforms strong baselines on both link prediction and node classification tasks, demonstrating its ability to unify the advantages of anonymous and non-anonymous models for dynamic graph learning.

Temporal graph networks (TGNs) have gained prominence as models for embedding dynamic interactions, but little is known about their theoretical underpinnings. We establish fundamental results about the representational power and limits of the two main categories of TGNs: those that aggregate temporal walks (WA-TGNs), and those that augment local message passing with recurrent memory modules (MP-TGNs). Specifically, novel constructions reveal the inadequacy of MP-TGNs and WA-TGNs, proving that neither category subsumes the other. We extend the 1-WL (Weisfeiler-Leman) test to temporal graphs, and show that the most powerful MP-TGNs should use injective updates, as in this case they become as expressive as the temporal WL. Also, we show that sufficiently deep MP-TGNs cannot benefit from memory, and MP/WA-TGNs fail to compute graph properties such as girth. These theoretical insights lead us to PINT -- a novel architecture that leverages injective temporal message passing and relative positional features. Importantly, PINT is provably more expressive than both MP-TGNs and WA-TGNs. PINT significantly outperforms existing TGNs on several real-world benchmarks.