Temporal link prediction, aiming at predicting future interactions among entities based on historical interactions, is crucial for a series of real-world applications. Although previous methods have demonstrated the importance of relative encodings for effective temporal link prediction, computational efficiency remains a major concern in constructing these encodings. Moreover, existing relative encodings are usually constructed based on structural connectivity, where temporal information is seldom considered. To address the aforementioned issues, we first analyze existing relative encodings and unify them as a function of temporal walk matrices. This unification establishes a connection between relative encodings and temporal walk matrices, providing a more principled way for analyzing and designing relative encodings. Based on this analysis, we propose a new temporal graph neural network called TPNet, which introduces a temporal walk matrix that incorporates the time decay effect to simultaneously consider both temporal and structural information. Moreover, TPNet designs a random feature propagation mechanism with theoretical guarantees to implicitly maintain the temporal walk matrices, which improves the computation and storage efficiency. Experimental results on 13 benchmark datasets verify the effectiveness and efficiency of TPNet, where TPNet outperforms other baselines on most datasets and achieves a maximum speedup of $33.3 \times$ compared to the SOTA baseline. Our code can be found at \url{https://github.com/lxd99/TPNet}.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

Robust multi-agent reinforcement learning (MARL) necessitates resilience to uncertain or worst-case actions by unknown allies. Existing max-min optimization techniques in robust MARL seek to enhance resilience by training agents against worst-case adversaries, but this becomes intractable as the number of agents grows, leading to exponentially increasing worst-case scenarios. Attempts to simplify this complexity often yield overly pessimistic policies, inadequate robustness across scenarios and high computational demands. Unlike these approaches, humans naturally learn adaptive and resilient behaviors without the necessity of preparing for every conceivable worst-case scenario. Motivated by this, we propose MIR2, which trains policy in routine scenarios and minimize Mutual Information as Robust Regularization. Theoretically, we frame robustness as an inference problem and prove that minimizing mutual information between histories and actions implicitly maximizes a lower bound on robustness under certain assumptions. Further analysis reveals that our proposed approach prevents agents from overreacting to others through an information bottleneck and aligns the policy with a robust action prior. Empirically, our MIR2 displays even greater resilience against worst-case adversaries than max-min optimization in StarCraft II, Multi-agent Mujoco and rendezvous. Our superiority is consistent when deployed in challenging real-world robot swarm control scenario. See code and demo videos in Supplementary Materials.

We propose DyGFormer, a new Transformer-based architecture for dynamic graph learning. DyGFormer is conceptually simple and only needs to learn from nodes' historical first-hop interactions by: (1) a neighbor co-occurrence encoding scheme that explores the correlations of the source node and destination node based on their historical sequences; (2) a patching technique that divides each sequence into multiple patches and feeds them to Transformer, allowing the model to effectively and efficiently benefit from longer histories. We also introduce DyGLib, a unified library with standard training pipelines, extensible coding interfaces, and comprehensive evaluating protocols to promote reproducible, scalable, and credible dynamic graph learning research. By performing exhaustive experiments on thirteen datasets for dynamic link prediction and dynamic node classification tasks, we find that DyGFormer achieves state-of-the-art performance on most of the datasets, demonstrating its effectiveness in capturing nodes' correlations and long-term temporal dependencies. Moreover, some results of baselines are inconsistent with previous reports, which may be caused by their diverse but less rigorous implementations, showing the importance of DyGLib. All the used resources are publicly available at https://github.com/yule-BUAA/DyGLib.

Given a sequence of sets, where each set has a timestamp and contains an arbitrary number of elements, temporal sets prediction aims to predict the elements in the subsequent set. Previous studies for temporal sets prediction mainly focus on the modelling of elements and implicitly represent each user's preference based on his/her interacted elements. However, user preferences are often continuously evolving and the evolutionary trend cannot be fully captured with the indirect learning paradigm of user preferences. To this end, we propose a continuous-time user preference modelling framework for temporal sets prediction, which explicitly models the evolving preference of each user by maintaining a memory bank to store the states of all the users and elements. Specifically, we first construct a universal sequence by arranging all the user-set interactions in a non-descending temporal order, and then chronologically learn from each user-set interaction. For each interaction, we continuously update the memories of the related user and elements based on their currently encoded messages and past memories. Moreover, we present a personalized user behavior learning module to discover user-specific characteristics based on each user's historical sequence, which aggregates the previously interacted elements from dual perspectives according to the user and elements. Finally, we develop a set-batch algorithm to improve the model efficiency, which can create time-consistent batches in advance and achieve 3.5x and 3.0x speedups in the training and evaluation process on average. Experiments on four real-world datasets demonstrate the superiority of our approach over state-of-the-arts under both transductive and inductive settings. The good interpretability of our method is also shown.

Designing new molecules is essential for drug discovery and material science. Recently, deep generative models that aim to model molecule distribution have made promising progress in narrowing down the chemical research space and generating high-fidelity molecules. However, current generative models only focus on modeling either 2D bonding graphs or 3D geometries, which are two complementary descriptors for molecules. The lack of ability to jointly model both limits the improvement of generation quality and further downstream applications. In this paper, we propose a new joint 2D and 3D diffusion model (JODO) that generates complete molecules with atom types, formal charges, bond information, and 3D coordinates. To capture the correlation between molecular graphs and geometries in the diffusion process, we develop a Diffusion Graph Transformer to parameterize the data prediction model that recovers the original data from noisy data. The Diffusion Graph Transformer interacts node and edge representations based on our relational attention mechanism, while simultaneously propagating and updating scalar features and geometric vectors. Our model can also be extended for inverse molecular design targeting single or multiple quantum properties. In our comprehensive evaluation pipeline for unconditional joint generation, the results of the experiment show that JODO remarkably outperforms the baselines on the QM9 and GEOM-Drugs datasets. Furthermore, our model excels in few-step fast sampling, as well as in inverse molecule design and molecular graph generation. Our code is provided in https://github.com/GRAPH-0/JODO.

Learning the underlying distribution of molecular graphs and generating high-fidelity samples is a fundamental research problem in drug discovery and material science. However, accurately modeling distribution and rapidly generating novel molecular graphs remain crucial and challenging goals. To accomplish these goals, we propose a novel Conditional Diffusion model based on discrete Graph Structures (CDGS) for molecular graph generation. Specifically, we construct a forward graph diffusion process on both graph structures and inherent features through stochastic differential equations (SDE) and derive discrete graph structures as the condition for reverse generative processes. We present a specialized hybrid graph noise prediction model that extracts the global context and the local node-edge dependency from intermediate graph states. We further utilize ordinary differential equation (ODE) solvers for efficient graph sampling, based on the semi-linear structure of the probability flow ODE. Experiments on diverse datasets validate the effectiveness of our framework. Particularly, the proposed method still generates high-quality molecular graphs in a limited number of steps. Our code is provided in https://github.com/GRAPH-0/CDGS.

We consider a K-armed bandit problem in general graphs where agents are arbitrarily connected and each of them has limited memorizing capabilities and communication bandwidth. The goal is to let each of the agents eventually learn the best arm. It is assumed in these studies that the communication graph should be complete or well-structured, whereas such an assumption is not always valid in practice. Furthermore, limited memorization and communication bandwidth also restrict the collaborations of the agents, since the agents memorize and communicate very few experiences. Additionally, an agent may be corrupted to share falsified experiences to its peers, while the resource limit in terms of memorization and communication may considerably restrict the reliability of the learning process. To address the above issues, we propose a three-staged collaborative learning algorithm. In each step, the agents share their latest experiences with each other through light-weight random walks in a general communication graph, and then make decisions on which arms to pull according to the recommendations received from their peers. The agents finally update their adoptions (i.e., preferences to the arms) based on the reward obtained by pulling the arms. Our theoretical analysis shows that, when there are a sufficient number of agents participating in the collaborative learning process, all the agents eventually learn the best arm with high probability, even with limited memorizing capabilities and light-weight communications. We also reveal in our theoretical analysis the upper bound on the number of corrupted agents our algorithm can tolerate. The efficacy of our proposed three-staged collaborative learning algorithm is finally verified by extensive experiments on both synthetic and real datasets.

Graph Neural Networks (GNNs) have been widely applied in the semi-supervised node classification task, where a key point lies in how to sufficiently leverage the limited but valuable label information. Most of the classical GNNs solely use the known labels for computing the classification loss at the output. In recent years, several methods have been designed to additionally utilize the labels at the input. One part of the methods augment the node features via concatenating or adding them with the one-hot encodings of labels, while other methods optimize the graph structure by assuming neighboring nodes tend to have the same label. To bring into full play the rich information of labels, in this paper, we present a label-enhanced learning framework for GNNs, which first models each label as a virtual center for intra-class nodes and then jointly learns the representations of both nodes and labels. Our approach could not only smooth the representations of nodes belonging to the same class, but also explicitly encode the label semantics into the learning process of GNNs. Moreover, a training node selection technique is provided to eliminate the potential label leakage issue and guarantee the model generalization ability. Finally, an adaptive self-training strategy is proposed to iteratively enlarge the training set with more reliable pseudo labels and distinguish the importance of each pseudo-labeled node during the model training process. Experimental results on both real-world and synthetic datasets demonstrate our approach can not only consistently outperform the state-of-the-arts, but also effectively smooth the representations of intra-class nodes.

Graph generative models have broad applications in biology, chemistry and social science. However, modelling and understanding the generative process of graphs is challenging due to the discrete and high-dimensional nature of graphs, as well as permutation invariance to node orderings in underlying graph distributions. Current leading autoregressive models fail to capture the permutation invariance nature of graphs for the reliance on generation ordering and have high time complexity. Here, we propose a continuous-time generative diffusion process for permutation invariant graph generation to mitigate these issues. Specifically, we first construct a forward diffusion process defined by a stochastic differential equation (SDE), which smoothly converts graphs within the complex distribution to random graphs that follow a known edge probability. Solving the corresponding reverse-time SDE, graphs can be generated from newly sampled random graphs. To facilitate the reverse-time SDE, we newly design a position-enhanced graph score network, capturing the evolving structure and position information from perturbed graphs for permutation equivariant score estimation. Under the evaluation of comprehensive metrics, our proposed generative diffusion process achieves competitive performance in graph distribution learning. Experimental results also show that GraphGDP can generate high-quality graphs in only 24 function evaluations, much faster than previous autoregressive models.