We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch, and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shapes using Square Root Velocity Function Trees (SRVFT). By solving the spatial registration in the SRVFT space, which is equipped with an L2 metric, 4D tree-shaped structures become time-parameterized trajectories in this space. This reduces the problem of modeling and analyzing 4D tree-like shapes to that of modeling and analyzing elastic trajectories in the SRVFT space, where elasticity refers to time warping. In this paper, we propose a novel mathematical representation of the shape space of such trajectories, a Riemannian metric on that space, and computational tools for fast and accurate spatiotemporal registration and geodesics computation between 4D tree-shaped structures. Leveraging these building blocks, we develop a full framework for modelling the spatiotemporal variability using statistical models and generating novel 4D tree-like structures from a set of exemplars. We demonstrate and validate the proposed framework using real 4D plant data.

Temporal knowledge graph reasoning (TKGR) is increasingly gaining attention for its ability to extrapolate new events from historical data, thereby enriching the inherently incomplete temporal knowledge graphs. Existing graph-based representation learning frameworks have made significant strides in developing evolving representations for both entities and relational embeddings. Despite these achievements, there's a notable tendency in these models to inadvertently learn biased data representations and mine spurious correlations, consequently failing to discern the causal relationships between events. This often leads to incorrect predictions based on these false correlations. To address this, we propose an innovative causal enhanced graph representation learning framework for TKGR (named CEGRL-TKGR). This framework introduces causal structures in graph-based representation learning to unveil the essential causal relationships between events, ultimately enhancing task performance. Specifically, we first disentangle the evolutionary representations of entities and relations in a temporal graph sequence into two distinct components, namely causal representations and confounding representations. Then, drawing on causal intervention theory, we advocate the utilization of causal representations for predictions, aiming to mitigate the effects of erroneous correlations caused by confounding features, thus achieving more robust and accurate predictions. Finally, extensive experimental results on six benchmark datasets demonstrate the superior performance of our model in the link prediction task.

Temporal knowledge graph completion aims to infer the missing facts in temporal knowledge graphs. Current approaches usually embed factual knowledge into continuous vector space and apply geometric operations to learn potential patterns in temporal knowledge graphs. However, these methods only adopt a single operation, which may have limitations in capturing the complex temporal dynamics present in temporal knowledge graphs. Therefore, we propose a simple but effective method, i.e. TCompoundE, which is specially designed with two geometric operations, including time-specific and relation-specific operations. We provide mathematical proofs to demonstrate the ability of TCompoundE to encode various relation patterns. Experimental results show that our proposed model significantly outperforms existing temporal knowledge graph embedding models. Our code is available at https://github.com/nk-ruiying/TCompoundE.

Knowledge Base Question Answering (KBQA) has been a long-standing field to answer questions based on knowledge bases. Recently, the evolving dynamics of knowledge have attracted a growing interest in Temporal Knowledge Graph Question Answering (TKGQA), an emerging task to answer temporal questions. However, this field grapples with ambiguities in defining temporal questions and lacks a systematic categorization of existing methods for TKGQA. In response, this paper provides a thorough survey from two perspectives: the taxonomy of temporal questions and the methodological categorization for TKGQA. Specifically, we first establish a detailed taxonomy of temporal questions engaged in prior studies. Subsequently, we provide a comprehensive review of TKGQA techniques of two categories: semantic parsing-based and TKG embedding-based. Building on this review, the paper outlines potential research directions aimed at advancing the field of TKGQA. This work aims to serve as a comprehensive reference for TKGQA and to stimulate further research.

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.