CTDG-THOR: Query-Side Second-Order Temporal History Routing for Continuous-Time Dynamic Graphs

Events in a continuous-time dynamic graph (CTDG) arrive as a stream of timestamps and messages. Most CTDG encoders build a node representation from that node’s own events, so a neighbor’s trajectory reaches a link score only when the model routes it across nodes. We present CTDG-THOR, which isolates candidate-independent routing of second-order temporal history from the query side. The model combines a TGN-style memory, history-conditioned attention, and pair-level aggregation of first-hop contexts for the query’s neighbors. It expands second-order context only for the query, so the negative candidate set does not multiply path computation. We formalize an incident-only endpoint and a one-hop endpoint, and prove a witness separation: exponentially many event streams that the incident-only endpoint cannot distinguish become separable once second-order history is routed. Under matched seeds and a shared backbone, CTDG-THOR improves test MRR by +0.0653 on tgbl-wiki and +0.0368 on tgbl-enron. Fixed-checkpoint interventions also indicate that the trained predictor uses this route. Under the fixed-negative TGB-v1 protocol, it reaches test MRR 0.6416 ± 0.0123, 0.2478 ± 0.0255, and 0.1223 ± 0.0084 on these three datasets. The second-order route adds one scalar and a mean aggregation over the one-hop control and keeps peak memory below 90 MB. The comparisons show that where cross-node history is routed affects prediction in memory-based CTDGs.