Denoising the Future: Context-Aware Spectral Diffusion for Temporal Knowledge Graph Extrapolation

Extrapolative temporal knowledge graph reasoning (TKGR) predicts future facts from historical snapshots. Most existing methods train once on an early prefix of the timeline and then use a frozen model for all future timestamps. We argue that this fixed-prefix protocol is misaligned with extrapolation. It learns from a static prefix, whereas the target stream is non-stationary: new entities and facts emerge, temporal dependencies shift across regimes, and recurring historical signals must be refreshed online. As a result, models trained only on early snapshots become outdated and degrade over long horizons. We address this mismatch by formulating extrapolative TKGR as continual learning over streaming snapshots. Under this view, effective extrapolation must jointly handle current dynamics, stable knowledge, and recurring historical evidence. Based on these requirements, we propose History-enhanced Two-Step Continual Learning (HiTS-CL), a backbone-agnostic continual learning framework for extrapolative TKGR. HiTS-CL tracks current dynamics via continual fine-tuning, preserves stable knowledge via multi-teacher adaptive distillation, and retains recurring historical evidence via a selective memory of recent and frequent facts. We integrate HiTS-CL into five representative TKGR backbones and evaluate it on four benchmark datasets. HiTS-CL consistently improves extrapolation accuracy, reduces long-horizon degradation, and outperforms strong continual-learning baselines, including a recent method for temporal knowledge graphs. Source code and data are available at https://github.com/liuyansong98/HiTS-CL.

Temporal knowledge graph (TKG) extrapolation is an important task that aims to predict future facts through historical interaction information within KG snapshots. A key challenge for most existing TKG extrapolation models is handling entities with sparse historical interaction. The ontological knowledge is beneficial for alleviating this sparsity issue by enabling these entities to inherit behavioral patterns from other entities with the same concept, which is ignored by previous studies. In this paper, we propose a novel encoder-decoder framework OntoTKGE that leverages the ontological knowledge from the ontology-view KG (i.e., a KG modeling hierarchical relations among abstract concepts as well as the connections between concepts and entities) to guide the TKG extrapolation model's learning process through the effective integration of the ontological and temporal knowledge, thereby enhancing entity embeddings. OntoTKGE is flexible enough to adapt to many TKG extrapolation models. Extensive experiments on five data sets demonstrate that OntoTKGE not only significantly improves the performance of many TKG extrapolation models but also surpasses many state-of-the-art(SOTA) baseline methods.

Temporal knowledge graph (TKG) reasoning aims to infer future facts at unseen timestamps from temporally evolving entities and relations. Despite recent progress, existing approaches still suffer from inherent limitations due to their inductive biases, as they predominantly rely on time-invariant or weakly time-dependent structures and overlook the evolutionary dynamics. To overcome this limitation, we propose a novel collaborative learning framework for TKGR (dubbed CID-TKG) that integrates evolutionary dynamics and historical invariance semantics as an effective inductive bias for reasoning. Specifically, CID-TKG constructs a historical invariance graph to capture long-term structural regularities and an evolutionary dynamics graph to model short-term temporal transitions. Dedicated encoders are then employed to learn representations from each structure. To alleviate semantic discrepancies across the two structures, we decompose relations into view-specific representations and align view-specific query representations via a contrastive objective, which promotes cross-view consistency while suppressing view-specific noise. Extensive experiments verify that our CID-TKG achieves state-of-the-art performance under extrapolation settings.