Temporal Knowledge Graph (TKG) reasoning focuses on predicting events through historical information within snapshots distributed on a timeline. Existing studies mainly concentrate on two perspectives of leveraging the history of TKGs, including capturing evolution of each recent snapshot or correlations among global historical facts. Despite the achieved significant accomplishments, these models still fall short of (1) investigating the influences of multi-granularity interactions across recent snapshots and (2) harnessing the expressive semantics of significant links accorded with queries throughout the entire history, especially events exerting a profound impact on the future. These inadequacies restrict representation ability to reflect historical dependencies and future trends thoroughly. To overcome these drawbacks, we propose an innovative TKG reasoning approach towards \textbf{His}torically \textbf{R}elevant \textbf{E}vents \textbf{S}tructuring ($\mathsf{HisRES}$). Concretely, $\mathsf{HisRES}$ comprises two distinctive modules excelling in structuring historically relevant events within TKGs, including a multi-granularity evolutionary encoder that captures structural and temporal dependencies of the most recent snapshots, and a global relevance encoder that concentrates on crucial correlations among events relevant to queries from the entire history. Furthermore, $\mathsf{HisRES}$ incorporates a self-gating mechanism for adaptively merging multi-granularity recent and historically relevant structuring representations. Extensive experiments on four event-based benchmarks demonstrate the state-of-the-art performance of $\mathsf{HisRES}$ and indicate the superiority and effectiveness of structuring historical relevance for TKG reasoning.

Temporal knowledge graphs (TKGs) can effectively model the ever-evolving nature of real-world knowledge, and their completeness and enhancement can be achieved by reasoning new events from existing ones. However, reasoning accuracy is adversely impacted due to an imbalance between new and recurring events in the datasets. To achieve more accurate TKG reasoning, we propose an attention masking-based contrastive event network (AMCEN) with local-global temporal patterns for the two-stage prediction of future events. In the network, historical and non-historical attention mask vectors are designed to control the attention bias towards historical and non-historical entities, acting as the key to alleviating the imbalance. A local-global message-passing module is proposed to comprehensively consider and capture multi-hop structural dependencies and local-global temporal evolution for the in-depth exploration of latent impact factors of different event types. A contrastive event classifier is used to classify events more accurately by incorporating local-global temporal patterns into contrastive learning. Therefore, AMCEN refines the prediction scope with the results of the contrastive event classification, followed by utilizing attention masking-based decoders to finalize the specific outcomes. The results of our experiments on four benchmark datasets highlight the superiority of AMCEN. Especially, the considerable improvements in Hits@1 prove that AMCEN can make more precise predictions about future occurrences.

Distinguished from traditional knowledge graphs (KGs), temporal knowledge graphs (TKGs) must explore and reason over temporally evolving facts adequately. However, existing TKG approaches still face two main challenges, i.e., the limited capability to model arbitrary timestamps continuously and the lack of rich inference patterns under temporal constraints. In this paper, we propose an innovative TKGE method (PTBox) via polynomial decomposition-based temporal representation and box embedding-based entity representation to tackle the above-mentioned problems. Specifically, we decompose time information by polynomials and then enhance the model's capability to represent arbitrary timestamps flexibly by incorporating the learnable temporal basis tensor. In addition, we model every entity as a hyperrectangle box and define each relation as a transformation on the head and tail entity boxes. The entity boxes can capture complex geometric structures and learn robust representations, improving the model's inductive capability for rich inference patterns. Theoretically, our PTBox can encode arbitrary time information or even unseen timestamps while capturing rich inference patterns and higher-arity relations of the knowledge base. Extensive experiments on real-world datasets demonstrate the effectiveness of our method.

Temporal Knowledge Graph (TKG) reasoning often involves completing missing factual elements along the timeline. Although existing methods can learn good embeddings for each factual element in quadruples by integrating temporal information, they often fail to infer the evolution of temporal facts. This is mainly because of (1) insufficiently exploring the internal structure and semantic relationships within individual quadruples and (2) inadequately learning a unified representation of the contextual and temporal correlations among different quadruples. To overcome these limitations, we propose a novel Transformer-based reasoning model (dubbed ECEformer) for TKG to learn the Evolutionary Chain of Events (ECE). Specifically, we unfold the neighborhood subgraph of an entity node in chronological order, forming an evolutionary chain of events as the input for our model. Subsequently, we utilize a Transformer encoder to learn the embeddings of intra-quadruples for ECE. We then craft a mixed-context reasoning module based on the multi-layer perceptron (MLP) to learn the unified representations of inter-quadruples for ECE while accomplishing temporal knowledge reasoning. In addition, to enhance the timeliness of the events, we devise an additional time prediction task to complete effective temporal information within the learned unified representation. Extensive experiments on six benchmark datasets verify the state-of-the-art performance and the effectiveness of our method.

Temporal Knowledge Graph (TKG) Forecasting aims at predicting links in Knowledge Graphs for future timesteps based on a history of Knowledge Graphs. To this day, standardized evaluation protocols and rigorous comparison across TKG models are available, but the importance of simple baselines is often neglected in the evaluation, which prevents researchers from discerning actual and fictitious progress. We propose to close this gap by designing an intuitive baseline for TKG Forecasting based on predicting recurring facts. Compared to most TKG models, it requires little hyperparameter tuning and no iterative training. Further, it can help to identify failure modes in existing approaches. The empirical findings are quite unexpected: compared to 11 methods on five datasets, our baseline ranks first or third in three of them, painting a radically different picture of the predictive quality of the state of the art.

Temporal Knowledge Graph (TKG), which characterizes temporally evolving facts in the form of (subject, relation, object, timestamp), has attracted much attention recently. TKG reasoning aims to predict future facts based on given historical ones. However, existing TKG reasoning models are unable to abstain from predictions they are uncertain, which will inevitably bring risks in real-world applications. Thus, in this paper, we propose an abstention mechanism for TKG reasoning, which helps the existing models make selective, instead of indiscriminate, predictions. Specifically, we develop a confidence estimator, called Confidence Estimator with History (CEHis), to enable the existing TKG reasoning models to first estimate their confidence in making predictions, and then abstain from those with low confidence. To do so, CEHis takes two kinds of information into consideration, namely, the certainty of the current prediction and the accuracy of historical predictions. Experiments with representative TKG reasoning models on two benchmark datasets demonstrate the effectiveness of the proposed CEHis.

Temporal Knowledge Graph Question Answering (TKGQA) aims to answer questions with temporal intent over Temporal Knowledge Graphs (TKGs). The core challenge of this task lies in understanding the complex semantic information regarding multiple types of time constraints (e.g., before, first) in questions. Existing end-to-end methods implicitly model the time constraints by learning time-aware embeddings of questions and candidate answers, which is far from understanding the question comprehensively. Motivated by semantic-parsing-based approaches that explicitly model constraints in questions by generating logical forms with symbolic operators, we design fundamental temporal operators for time constraints and introduce a novel self-improvement Programming method for TKGQA (Prog-TQA). Specifically, Prog-TQA leverages the in-context learning ability of Large Language Models (LLMs) to understand the combinatory time constraints in the questions and generate corresponding program drafts with a few examples given. Then, it aligns these drafts to TKGs with the linking module and subsequently executes them to generate the answers. To enhance the ability to understand questions, Prog-TQA is further equipped with a self-improvement strategy to effectively bootstrap LLMs using high-quality self-generated drafts. Extensive experiments demonstrate the superiority of the proposed Prog-TQA on MultiTQ and CronQuestions datasets, especially in the Hits@1 metric.

Temporal Knowledge Graph (TKG) reasoning is based on historical information to predict the future. Therefore, parsing and mining historical information is key to predicting the future. Most existing methods fail to concurrently address and comprehend historical information from both global and local perspectives. Neglecting the global view might result in overlooking macroscopic trends and patterns, while ignoring the local view can lead to missing critical detailed information. Additionally, some methods do not focus on learning from high-frequency repeating events, which means they may not fully grasp frequently occurring historical events. To this end, we propose the \textbf{R}epetitive-\textbf{L}ocal-\textbf{G}lobal History \textbf{Net}work(RLGNet). We utilize a global history encoder to capture the overarching nature of historical information. Subsequently, the local history encoder provides information related to the query timestamp. Finally, we employ the repeating history encoder to identify and learn from frequently occurring historical events. In the evaluation on six benchmark datasets, our approach generally outperforms existing TKG reasoning models in multi-step and single-step reasoning tasks.

Temporal Knowledge Graphs (TKGs) incorporate a temporal dimension, allowing for a precise capture of the evolution of knowledge and reflecting the dynamic nature of the real world. Typically, TKGs contain complex geometric structures, with various geometric structures interwoven. However, existing Temporal Knowledge Graph Completion (TKGC) methods either model TKGs in a single space or neglect the heterogeneity of different curvature spaces, thus constraining their capacity to capture these intricate geometric structures. In this paper, we propose a novel Integrating Multi-curvature shared and specific Embedding (IME) model for TKGC tasks. Concretely, IME models TKGs into multi-curvature spaces, including hyperspherical, hyperbolic, and Euclidean spaces. Subsequently, IME incorporates two key properties, namely space-shared property and space-specific property. The space-shared property facilitates the learning of commonalities across different curvature spaces and alleviates the spatial gap caused by the heterogeneous nature of multi-curvature spaces, while the space-specific property captures characteristic features. Meanwhile, IME proposes an Adjustable Multi-curvature Pooling (AMP) approach to effectively retain important information. Furthermore, IME innovatively designs similarity, difference, and structure loss functions to attain the stated objective. Experimental results clearly demonstrate the superior performance of IME over existing state-of-the-art TKGC models.

Temporal Knowledge Graph Reasoning (TKGR) is the task of inferring missing facts for incomplete TKGs in complex scenarios (e.g., transductive and inductive settings), which has been gaining increasing attention. Recently, to mitigate dependence on structured connections in TKGs, text-based methods have been developed to utilize rich linguistic information from entity descriptions. However, suffering from the enormous parameters and inflexibility of pre-trained language models, existing text-based methods struggle to balance the textual knowledge and temporal information with computationally expensive purpose-built training strategies. To tap the potential of text-based models for TKGR in various complex scenarios, we propose ChapTER, a Contrastive historical modeling framework with prefix-tuning for TEmporal Reasoning. ChapTER feeds history-contextualized text into the pseudo-Siamese encoders to strike a textual-temporal balance via contrastive estimation between queries and candidates. By introducing virtual time prefix tokens, it applies a prefix-based tuning method to facilitate the frozen PLM capable for TKGR tasks under different settings. We evaluate ChapTER on four transductive and three few-shot inductive TKGR benchmarks, and experimental results demonstrate that ChapTER achieves superior performance compared to competitive baselines with only 0.17% tuned parameters. We conduct thorough analysis to verify the effectiveness, flexibility and efficiency of ChapTER.