Reasoning over Temporal Knowledge Graphs (TKGs) aims to predict future facts based on given history. One of the key challenges for prediction is to learn the evolution of facts. Most existing works focus on exploring evolutionary information in history to obtain effective temporal embeddings for entities and relations, but they ignore the variation in evolution patterns of facts, which makes them struggle to adapt to future data with different evolution patterns. Moreover, new entities continue to emerge along with the evolution of facts over time. Since existing models highly rely on historical information to learn embeddings for entities, they perform poorly on such entities with little historical information. To tackle these issues, we propose a novel Temporal Meta-learning framework for TKG reasoning, MetaTKG for brevity. Specifically, our method regards TKG prediction as many temporal meta-tasks, and utilizes the designed Temporal Meta-learner to learn evolutionary meta-knowledge from these meta-tasks. The proposed method aims to guide the backbones to learn to adapt quickly to future data and deal with entities with little historical information by the learned meta-knowledge. Specially, in temporal meta-learner, we design a Gating Integration module to adaptively establish temporal correlations between meta-tasks. Extensive experiments on four widely-used datasets and three backbones demonstrate that our method can greatly improve the performance.

Knowledge about space and time is necessary to solve problems in the physical world: An AI agent situated in the physical world and interacting with objects often needs to reason about positions of and relations between objects; and as soon as the agent plans its actions to solve a task, it needs to consider the temporal aspect (e.g., what actions to perform over time). Spatio-temporal knowledge, however, is required beyond interacting with the physical world, and is also often transferred to the abstract world of concepts through analogies and metaphors (e.g., "a threat that is hanging over our heads"). As spatial and temporal reasoning is ubiquitous, different attempts have been made to integrate this into AI systems. In the area of knowledge representation, spatial and temporal reasoning has been largely limited to modeling objects and relations and developing reasoning methods to verify statements about objects and relations. On the other hand, neural network researchers have tried to teach models to learn spatial relations from data with limited reasoning capabilities. Bridging the gap between these two approaches in a mutually beneficial way could allow us to tackle many complex real-world problems, such as natural language processing, visual question answering, and semantic image segmentation. In this chapter, we view this integration problem from the perspective of Neuro-Symbolic AI. Specifically, we propose a synergy between logical reasoning and machine learning that will be grounded on spatial and temporal knowledge. Describing some successful applications, remaining challenges, and evaluation datasets pertaining to this direction is the main topic of this contribution.

Temporal knowledge graph, serving as an effective way to store and model dynamic relations, shows promising prospects in event forecasting. However, most temporal knowledge graph reasoning methods are highly dependent on the recurrence or periodicity of events, which brings challenges to inferring future events related to entities that lack historical interaction. In fact, the current moment is often the combined effect of a small part of historical information and those unobserved underlying factors. To this end, we propose a new event forecasting model called Contrastive Event Network (CENET), based on a novel training framework of historical contrastive learning. CENET learns both the historical and non-historical dependency to distinguish the most potential entities that can best match the given query. Simultaneously, it trains representations of queries to investigate whether the current moment depends more on historical or non-historical events by launching contrastive learning. The representations further help train a binary classifier whose output is a boolean mask to indicate related entities in the search space. During the inference process, CENET employs a mask-based strategy to generate the final results. We evaluate our proposed model on five benchmark graphs. The results demonstrate that CENET significantly outperforms all existing methods in most metrics, achieving at least $8.3\%$ relative improvement of Hits@1 over previous state-of-the-art baselines on event-based datasets.

Predicting the impact of publications in science and technology has become an important research area, which is useful in various real world scenarios such as technology investment, research direction selection, and technology policymaking. Citation trajectory prediction is one of the most popular tasks in this area. Existing approaches mainly rely on mining temporal and graph data from academic articles. Some recent methods are capable of handling cold-start prediction by aggregating metadata features of new publications. However, the implicit factors causing citations and the richer information from handling temporal and attribute features still need to be explored. In this paper, we propose CTPIR, a new citation trajectory prediction framework that is able to represent the influence (the momentum of citation) of either new or existing publications using the history information of all their attributes. Our framework is composed of three modules: difference-preserved graph embedding, fine-grained influence representation, and learning-based trajectory calculation. To test the effectiveness of our framework in more situations, we collect and construct a new temporal knowledge graph dataset from the real world, named AIPatent, which stems from global patents in the field of artificial intelligence. Experiments are conducted on both the APS academic dataset and our contributed AIPatent dataset. The results demonstrate the strengths of our approach in the citation trajectory prediction task.

Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an operator-based approach for spatiotemporal analysis. Our approach combines three components that are often considered separately: (i) manifold learning for building operators representing the geometry of the variables, (ii) Riemannian geometry of symmetric positive-definite matrices for multiscale composition of operators corresponding to different time samples, and (iii) spectral analysis of the composite operators for extracting different dynamic modes. We propose a method that is analogous to the classical wavelet analysis, which we term Riemannian multi-resolution analysis (RMRA). We provide some theoretical results on the spectral analysis of the composite operators, and we demonstrate the proposed method on simulations and on real data.

Conventional static knowledge graphs model entities in relational data as nodes, connected by edges of specific relation types. However, information and knowledge evolve continuously, and temporal dynamics emerge, which are expected to influence future situations. In temporal knowledge graphs, time information is integrated into the graph by equipping each edge with a timestamp or a time range. Embedding-based methods have been introduced for link prediction on temporal knowledge graphs, but they mostly lack explainability and comprehensible reasoning chains. Particularly, they are usually not designed to deal with link forecasting -- event prediction involving future timestamps. We address the task of link forecasting on temporal knowledge graphs and introduce TLogic, an explainable framework that is based on temporal logical rules extracted via temporal random walks. We compare TLogic with state-of-the-art baselines on three benchmark datasets and show better overall performance while our method also provides explanations that preserve time consistency. Furthermore, in contrast to most state-of-the-art embedding-based methods, TLogic works well in the inductive setting where already learned rules are transferred to related datasets with a common vocabulary.

While knowledge graphs contain rich semantic knowledge of various entities and the relational information among them, temporal knowledge graphs (TKGs) further indicate the interactions of the entities over time. To study how to better model TKGs, automatic temporal knowledge graph completion (TKGC) has gained great interest. Recent TKGC methods aim to integrate advanced deep learning techniques, e.g., attention mechanism and Transformer, to boost model performance. However, we find that compared to adopting various kinds of complex modules, it is more beneficial to better utilize the whole amount of temporal information along the time axis. In this paper, we propose a simple but powerful graph encoder TARGCN for TKGC. TARGCN is parameter-efficient, and it extensively utilizes the information from the whole temporal context. We perform experiments on three benchmark datasets. Our model can achieve a more than 42% relative improvement on GDELT dataset compared with the state-of-the-art model. Meanwhile, it outperforms the strongest baseline on ICEWS05-15 dataset with around 18.5% fewer parameters.

In knowledge graph reasoning, we observe a trend to analyze temporal data evolving over time. The additional temporal dimension is attached to facts in a knowledge base resulting in quadruples between entities such as (Nintendo, released, Super Mario, Sep-13-1985), where the relation between two entities is associated to a specific time interval or point in time. Multi-hop reasoning on inferred subgraphs connecting entities within a knowledge graph can be formulated as a reinforcement learning task where the agent sequentially performs inference upon the explored subgraph. The task in this work is to infer the predicate between a subject and an object entity, i.e., (subject, ?, object, time), being valid at a certain timestamp or time interval. Given query entities, our agent starts to gather temporal relevant information about the neighborhood of the subject and object. The encoding of information about the explored graph structures is referred to as fingerprints. Subsequently, we use the two fingerprints as input to a Q-Network. Our agent decides sequentially which relational type needs to be explored next expanding the local subgraphs of the query entities in order to find promising paths between them. The evaluation shows that the proposed method not only yields results being in line with state-of-the-art embedding algorithms for temporal Knowledge Graphs (tKG), but we also gain information about the relevant structures between subjects and objects.

Temporal knowledge graph (TKG) reasoning is a crucial task that has gained increasing research interest in recent years. Most existing methods focus on reasoning at past timestamps to complete the missing facts, and there are only a few works of reasoning on known TKGs to forecast future facts. Compared with the completion task, the forecasting task is more difficult that faces two main challenges: (1) how to effectively model the time information to handle future timestamps? (2) how to make inductive inference to handle previously unseen entities that emerge over time? To address these challenges, we propose the first reinforcement learning method for forecasting. Specifically, the agent travels on historical knowledge graph snapshots to search for the answer. Our method defines a relative time encoding function to capture the timespan information, and we design a novel time-shaped reward based on Dirichlet distribution to guide the model learning. Furthermore, we propose a novel representation method for unseen entities to improve the inductive inference ability of the model. We evaluate our method for this link prediction task at future timestamps. Extensive experiments on four benchmark datasets demonstrate substantial performance improvement meanwhile with higher explainability, less calculation, and fewer parameters when compared with existing state-of-the-art methods.

Completion through the embedding representation of the knowledge graph (KGE) has been a research hotspot in recent years. Realistic knowledge graphs are mostly related to time, while most of the existing KGE algorithms ignore the time information. A few existing methods directly or indirectly encode the time information, ignoring the balance of timestamp distribution, which greatly limits the performance of temporal knowledge graph completion (KGC). In this paper, a temporal KGC method is proposed based on the direct encoding time information framework, and a given time slice is treated as the finest granularity for balanced timestamp distribution. A large number of experiments on temporal knowledge graph datasets extracted from the real world demonstrate the effectiveness of our method.