Temporal Knowledge Graphs (TKGs) have been developed and used in many different areas. Reasoning on TKGs that predicts potential facts (events) in the future brings great challenges to existing models. When facing a prediction task, human beings usually search useful historical information (i.e., clues) in their memories and then reason for future meticulously. Inspired by this mechanism, we propose CluSTeR to predict future facts in a two-stage manner, Clue Searching and Temporal Reasoning, accordingly. Specifically, at the clue searching stage, CluSTeR learns a beam search policy via reinforcement learning (RL) to induce multiple clues from historical facts. At the temporal reasoning stage, it adopts a graph convolution network based sequence method to deduce answers from clues. Experiments on four datasets demonstrate the substantial advantages of CluSTeR compared with the state-of-the-art methods. Moreover, the clues found by CluSTeR further provide interpretability for the results.

Reasoning in a temporal knowledge graph (TKG) is a critical task for information retrieval and semantic search. It is particularly challenging when the TKG is updated frequently. The model has to adapt to changes in the TKG for efficient training and inference while preserving its performance on historical knowledge. Recent work approaches TKG completion (TKGC) by augmenting the encoder-decoder framework with a time-aware encoding function. However, naively fine-tuning the model at every time step using these methods does not address the problems of 1) catastrophic forgetting, 2) the model's inability to identify the change of facts (e.g., the change of the political affiliation and end of a marriage), and 3) the lack of training efficiency. To address these challenges, we present the Time-aware Incremental Embedding (TIE) framework, which combines TKG representation learning, experience replay, and temporal regularization. We introduce a set of metrics that characterizes the intransigence of the model and propose a constraint that associates the deleted facts with negative labels. Experimental results on Wikidata12k and YAGO11k datasets demonstrate that the proposed TIE framework reduces training time by about ten times and improves on the proposed metrics compared to vanilla full-batch training. It comes without a significant loss in performance for any traditional measures. Extensive ablation studies reveal performance trade-offs among different evaluation metrics, which is essential for decision-making around real-world TKG applications.

Knowledge Graph (KG) reasoning that predicts missing facts for incomplete KGs has been widely explored. However, reasoning over Temporal KG (TKG) that predicts facts in the future is still far from resolved. The key to predict future facts is to thoroughly understand the historical facts. A TKG is actually a sequence of KGs corresponding to different timestamps, where all concurrent facts in each KG exhibit structural dependencies and temporally adjacent facts carry informative sequential patterns. To capture these properties effectively and efficiently, we propose a novel Recurrent Evolution network based on Graph Convolution Network (GCN), called RE-GCN, which learns the evolutional representations of entities and relations at each timestamp by modeling the KG sequence recurrently. Specifically, for the evolution unit, a relation-aware GCN is leveraged to capture the structural dependencies within the KG at each timestamp. In order to capture the sequential patterns of all facts in parallel, the historical KG sequence is modeled auto-regressively by the gate recurrent components. Moreover, the static properties of entities such as entity types, are also incorporated via a static graph constraint component to obtain better entity representations. Fact prediction at future timestamps can then be realized based on the evolutional entity and relation representations. Extensive experiments demonstrate that the RE-GCN model obtains substantial performance and efficiency improvement for the temporal reasoning tasks on six benchmark datasets. Especially, it achieves up to 11.46\% improvement in MRR for entity prediction with up to 82 times speedup comparing to the state-of-the-art baseline.

Spatial-temporal reasoning is a challenging task in Artificial Intelligence (AI) due to its demanding but unique nature: a theoretic requirement on representing and reasoning based on spatial-temporal knowledge in mind, and an applied requirement on a high-level cognitive system capable of navigating and acting in space and time. Recent works have focused on an abstract reasoning task of this kind -- Raven's Progressive Matrices (RPM). Despite the encouraging progress on RPM that achieves human-level performance in terms of accuracy, modern approaches have neither a treatment of human-like reasoning on generalization, nor a potential to generate answers. To fill in this gap, we propose a neuro-symbolic Probabilistic Abduction and Execution (PrAE) learner; central to the PrAE learner is the process of probabilistic abduction and execution on a probabilistic scene representation, akin to the mental manipulation of objects. Specifically, we disentangle perception and reasoning from a monolithic model. The neural visual perception frontend predicts objects' attributes, later aggregated by a scene inference engine to produce a probabilistic scene representation. In the symbolic logical reasoning backend, the PrAE learner uses the representation to abduce the hidden rules. An answer is predicted by executing the rules on the probabilistic representation. The entire system is trained end-to-end in an analysis-by-synthesis manner without any visual attribute annotations. Extensive experiments demonstrate that the PrAE learner improves cross-configuration generalization and is capable of rendering an answer, in contrast to prior works that merely make a categorical choice from candidates.

Learning node representation on dynamically-evolving, multi-relational graph data has gained great research interest. However, most of the existing models for temporal knowledge graph forecasting use Recurrent Neural Network (RNN) with discrete depth to capture temporal information, while time is a continuous variable. Inspired by Neural Ordinary Differential Equation (NODE), we extend the idea of continuum-depth models to time-evolving multi-relational graph data, and propose a novel Temporal Knowledge Graph Forecasting model with NODE. Our model captures temporal information through NODE and structural information through a Graph Neural Network (GNN). Thus, our graph ODE model achieves a continuous model in time and efficiently learns node representation for future prediction. We evaluate our model on six temporal knowledge graph datasets by performing link forecasting. Experiment results show the superiority of our model.

Temporal knowledge graphs (TKGs) inherently reflect the transient nature of real-world knowledge, as opposed to static knowledge graphs. Naturally, automatic TKG completion has drawn much research interests for a more realistic modeling of relational reasoning. However, most of the existing mod-els for TKG completion extend static KG embeddings that donot fully exploit TKG structure, thus lacking in 1) account-ing for temporally relevant events already residing in the lo-cal neighborhood of a query, and 2) path-based inference that facilitates multi-hop reasoning and better interpretability. In this paper, we propose T-GAP, a novel model for TKG completion that maximally utilizes both temporal information and graph structure in its encoder and decoder. T-GAP encodes query-specific substructure of TKG by focusing on the temporal displacement between each event and the query times-tamp, and performs path-based inference by propagating attention through the graph. Our empirical experiments demonstrate that T-GAP not only achieves superior performance against state-of-the-art baselines, but also competently generalizes to queries with unseen timestamps. Through extensive qualitative analyses, we also show that T-GAP enjoys from transparent interpretability, and follows human intuition in its reasoning process.

Large knowledge graphs often grow to store temporal facts that model the dynamic relations or interactions of entities along the timeline. Since such temporal knowledge graphs often suffer from incompleteness, it is important to develop time-aware representation learning models that help to infer the missing temporal facts. While the temporal facts are typically evolving, it is observed that many facts often show a repeated pattern along the timeline, such as economic crises and diplomatic activities. This observation indicates that a model could potentially learn much from the known facts appeared in history. To this end, we propose a new representation learning model for temporal knowledge graphs, namely CyGNet, based on a novel timeaware copy-generation mechanism. CyGNet is not only able to predict future facts from the whole entity vocabulary, but also capable of identifying facts with repetition and accordingly predicting such future facts with reference to the known facts in the past. We evaluate the proposed method on the knowledge graph completion task using five benchmark datasets. Extensive experiments demonstrate the effectiveness of CyGNet for predicting future facts with repetition as well as de novo fact prediction.

There has recently been increasing interest in learning representations of temporal knowledge graphs (KGs), which record the dynamic relationships between entities over time. Temporal KGs often exhibit multiple simultaneous non-Euclidean structures, such as hierarchical and cyclic structures. However, existing embedding approaches for temporal KGs typically learn entity representations and their dynamic evolution in the Euclidean space, which might not capture such intrinsic structures very well. To this end, we propose Dy- ERNIE, a non-Euclidean embedding approach that learns evolving entity representations in a product of Riemannian manifolds, where the composed spaces are estimated from the sectional curvatures of underlying data. Product manifolds enable our approach to better reflect a wide variety of geometric structures on temporal KGs. Besides, to capture the evolutionary dynamics of temporal KGs, we let the entity representations evolve according to a velocity vector defined in the tangent space at each timestamp. We analyze in detail the contribution of geometric spaces to representation learning of temporal KGs and evaluate our model on temporal knowledge graph completion tasks. Extensive experiments on three real-world datasets demonstrate significantly improved performance, indicating that the dynamics of multi-relational graph data can be more properly modeled by the evolution of embeddings on Riemannian manifolds.

Most real-world knowledge graphs are characterized by a long-tail relation frequency distribution where a significant fraction of relations occurs only a handful of times. This observation has given rise to recent interest in low-shot learning methods that are able to generalize from only a few examples. The existing approaches, however, are tailored to static knowledge graphs and not easily generalized to temporal settings, where data scarcity poses even bigger problems, e.g., due to occurrence of new, previously unseen relations. We address this shortcoming by proposing a one-shot learning framework for link prediction in temporal knowledge graphs. Our proposed method employs a self-attention mechanism to effectively encode temporal interactions between entities, and a network to compute a similarity score between a given query and a (one-shot) example. Our experiments show that the proposed algorithm outperforms the state of the art baselines for two well-studied benchmarks while achieving significantly better performance for sparse relations.

In recent years, many efforts have been made to complete knowledge graphs (KGs) by various graph embedding methods, most of which only focus on static KGs (SKGs) without considering the time dependency of facts. However, KGs in reality are dynamic and there exists correlations between facts with different timestamps. Due to the sparsity of temporal KGs (TKGs), SKG embedding methods cannot be directly applied to TKGs. And existing methods of TKG embedding suffer from two issues: (1) they follow the pattern of SKG embedding where all facts need to be retrained when a new timestamp appears; (2) they don't provide a general way to transplant SKG embedding methods to TKGs and therefore lack extensibility. In this paper, we propose a novel Recursive Temporal Fact Embedding Framework (RTFE) to transplant translation-based or graph neural network-based SKG embedding methods to TKGs. In the recursive way, timestamp parameters provide a good starting point for the next future timestamp. And existing SKG embedding models can be used as components. Experiments on TKGs show that our proposed framework (1) outperforms the state-of-the-art baseline model in the entity prediction task on fact datasets; (2) achieves similar performance compared with the state-of-the-art baseline model in relation prediction task on fact datasets; and (3) shows performance in the entity prediction task on event datasets.