The rapid evolution of large language models (LLMs) holds promise for reforming the methodology of spatio-temporal data mining. However, current works for evaluating the spatio-temporal understanding capability of LLMs are somewhat limited and biased. These works either fail to incorporate the latest language models or only focus on assessing the memorized spatio-temporal knowledge. To address this gap, this paper dissects LLMs' capability of spatio-temporal data into four distinct dimensions: knowledge comprehension, spatio-temporal reasoning, accurate computation, and downstream applications. We curate several natural language question-answer tasks for each category and build the benchmark dataset, namely STBench, containing 13 distinct tasks and over 60,000 QA pairs. Moreover, we have assessed the capabilities of 13 LLMs, such as GPT-4o, Gemma and Mistral. Experimental results reveal that existing LLMs show remarkable performance on knowledge comprehension and spatio-temporal reasoning tasks, with potential for further enhancement on other tasks through in-context learning, chain-of-though prompting, and fine-tuning. The code and datasets of STBench are released on https://github.com/LwbXc/STBench.

Reasoning about time is essential for Large Language Models (LLMs) to understand the world. Previous works focus on solving specific tasks, primarily on time-sensitive question answering. While these methods have proven effective, they cannot generalize to a wider spectrum of temporal reasoning tasks. Therefore, we propose a crucial question: Can we build a universal framework to handle a variety of temporal reasoning tasks? To that end, we systematically study 38 temporal reasoning tasks. Based on the observation that 19 tasks are directly related to mathematics, we first leverage the available mathematical dataset to set a solid foundation for temporal reasoning. However, the in-depth study indicates that focusing solely on mathematical enhancement falls short of addressing pure temporal reasoning tasks. To mitigate this limitation, we propose a simple but effective self-critic temporal optimization method to enhance the model's temporal reasoning capabilities without sacrificing general task abilities. Finally, we develop Timo, a model designed to excel in temporal reasoning at the 7B and 13B scales. Notably, Timo outperforms the counterpart LLMs by 10.0 and 7.6 in average accuracy scores and achieves the new state-of-the-art (SOTA) performance of comparable size. Extensive experiments further validate our framework's effectiveness and its generalization across diverse temporal tasks. The code is available at https://github.com/zhaochen0110/Timo.

Multi-relational temporal graphs are powerful tools for modeling real-world data, capturing the evolving and interconnected nature of entities over time. Recently, many novel models are proposed for ML on such graphs intensifying the need for robust evaluation and standardized benchmark datasets. However, the availability of such resources remains scarce and evaluation faces added complexity due to reproducibility issues in experimental protocols. To address these challenges, we introduce Temporal Graph Benchmark 2.0 (TGB 2.0), a novel benchmarking framework tailored for evaluating methods for predicting future links on Temporal Knowledge Graphs and Temporal Heterogeneous Graphs with a focus on large-scale datasets, extending the Temporal Graph Benchmark. TGB 2.0 facilitates comprehensive evaluations by presenting eight novel datasets spanning five domains with up to 53 million edges. TGB 2.0 datasets are significantly larger than existing datasets in terms of number of nodes, edges, or timestamps. In addition, TGB 2.0 provides a reproducible and realistic evaluation pipeline for multi-relational temporal graphs. Through extensive experimentation, we observe that 1) leveraging edge-type information is crucial to obtain high performance, 2) simple heuristic baselines are often competitive with more complex methods, 3) most methods fail to run on our largest datasets, highlighting the need for research on more scalable methods.

Temporal reasoning is fundamental for large language models (LLMs) to comprehend the world. Current temporal reasoning datasets are limited to questions about single or isolated events, falling short in mirroring the realistic temporal characteristics involving concurrent nature and intricate temporal interconnections. In this paper, we introduce CoTempQA, a comprehensive co-temporal Question Answering (QA) benchmark containing four co-temporal scenarios (Equal, Overlap, During, Mix) with 4,748 samples for evaluating the co-temporal comprehension and reasoning abilities of LLMs. Our extensive experiments reveal a significant gap between the performance of current LLMs and human-level reasoning on CoTempQA tasks. Even when enhanced with Chain of Thought (CoT) methodologies, models consistently struggle with our task. In our preliminary exploration, we discovered that mathematical reasoning plays a significant role in handling co-temporal events and proposed a strategy to boost LLMs' co-temporal reasoning from a mathematical perspective. We hope that our CoTempQA datasets will encourage further advancements in improving the co-temporal reasoning capabilities of LLMs. Our code is available at https://github.com/zhaochen0110/Cotempqa.

Temporal knowledge graph (TKG) reasoning has two settings: interpolation reasoning and extrapolation reasoning. Both of them draw plenty of research interest and have great significance. Methods of the former de-emphasize the temporal correlations among facts sequences, while methods of the latter require strict chronological order of knowledge and ignore inferring clues provided by missing facts of the past. These limit the practicability of TKG applications as almost all of the existing TKG reasoning methods are designed specifically to address either one setting. To this end, this paper proposes an original Temporal PAth-based Reasoning (TPAR) model for both the interpolation and extrapolation reasoning. TPAR performs a neural-driven symbolic reasoning fashion that is robust to ambiguous and noisy temporal data and with fine interpretability as well. Comprehensive experiments show that TPAR outperforms SOTA methods on the link prediction task for both the interpolation and the extrapolation settings. A novel pipeline experimental setting is designed to evaluate the performances of SOTA combinations and the proposed TPAR towards interpolation and extrapolation reasoning. More diverse experiments are conducted to show the robustness and interpretability of TPAR.

Traditional traffic prediction, limited by the scope of sensor data, falls short in comprehensive traffic management. Mobile networks offer a promising alternative using network activity counts, but these lack crucial directionality. Thus, we present the TeltoMob dataset, featuring undirected telecom counts and corresponding directional flows, to predict directional mobility flows on roadways. To address this, we propose a two-stage spatio-temporal graph neural network (STGNN) framework. The first stage uses a pre-trained STGNN to process telecom data, while the second stage integrates directional and geographic insights for accurate prediction. Our experiments demonstrate the framework's compatibility with various STGNN models and confirm its effectiveness. We also show how to incorporate the framework into real-world transportation systems, enhancing sustainable urban mobility.

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.