Graph classification is a critical task in analyzing graph data, with applications across various domains. While graph neural networks (GNNs) have achieved remarkable results, their ability to generalize across graphs of varying scales remains a challenge. Conventional models often perform well on large-scale graphs but struggle with distributions that are skewed towards small scales. Conversely, models tailored to address scale imbalances frequently prioritize small-scale graphs, leading to diminished performance in more balanced scenarios. To overcome these limitations, we introduce a Unbalanced-Balanced Representation Converter (U2B), which exhibits no explicit bias toward graph scales. U2B employs a two-step workflow: a distillation phase to extract base features from both node-level and graph-level representations, followed by a refinement phase to generate unbiased representations for improved balance. In the distillation phase, a static constraint guides node-level adjustments, improving the representation of nodes in small graphs. Simultaneously, a dynamic constraint in the graph-level process mitigates biases toward features from large graphs. To ensure harmony between the representations, a consistency alignment loss is introduced, aligning node-level and graph-level features to create more cohesive and balanced graph representations. Extensive experiments on multiple datasets show that U2B achieves competitive performance.

Due to the profound impact of air pollution on human health, livelihoods, and economic development, air quality forecasting is of paramount significance. Initially, we employ the causal graph method to scrutinize the constraints of existing research in comprehensively modeling the causal relationships between the air quality index (AQI) and meteorological features. In order to enhance prediction accuracy, we introduce a novel air quality forecasting model, AirCade, which incorporates a causal decoupling approach. AirCade leverages a spatiotemporal module in conjunction with knowledge embedding techniques to capture the internal dynamics of AQI. Subsequently, a causal decoupling module is proposed to disentangle synchronous causality from past AQI and meteorological features, followed by the dissemination of acquired knowledge to future time steps to enhance performance. Additionally, we introduce a causal intervention mechanism to explicitly represent the uncertainty of future meteorological features, thereby bolstering the model’s robustness. Our evaluation of AirCade on an open-source air quality dataset demonstrates over 20% relative improvement over state-of-the-art models. Our source code is available at https://github.com/PoorOtterBob/AirCade.

Recently, spatiotemporal graph convolutional networks have achieved dominant performance in spatiotemporal prediction tasks. However, most models relying on node-to-node messaging interaction exhibit sensitivity to spatiotemporal shifts, encountering out-of-distribution (OOD) challenges. To address these issues, we introduce \textbf{\underline{S}}patio-\textbf{\underline{T}}emporal \textbf{\underline{O}}OD \textbf{\underline{P}}rocessor (STOP), which employs a centralized messaging mechanism along with a message perturbation mechanism to facilitate robust spatiotemporal interactions. Specifically, the centralized messaging mechanism integrates Context-Aware Units for coarse-grained spatiotemporal feature interactions with nodes, effectively blocking traditional node-to-node messages. We also implement a message perturbation mechanism to disrupt this messaging process, compelling the model to extract generalizable contextual features from generated variant environments. Finally, we customize a spatiotemporal distributionally robust optimization approach that exposes the model to challenging environments, thereby further enhancing its generalization capabilities. Compared with 14 baselines across six datasets, STOP achieves up to \textbf{17.01\%} improvement in generalization performance and \textbf{18.44\%} improvement in inductive learning performance. The code is available at https://github.com/PoorOtterBob/STOP.

Air quality prediction plays a crucial role in the development of smart cities, garnering significant attention from both academia and industry. Current air quality prediction models encounter two major limitations: their high computational complexity limits scalability to nationwide datasets, and they often regard weather covariates as optional auxiliary information. In reality, weather covariates can have a substantial impact on air quality indices (AQI), exhibiting a significant causal association. In this paper, we first present a nationwide air quality dataset to address the lack of open-source, large-scale datasets in this field. Then we propose a causal learning model, CauAir, for air quality prediction that harnesses the powerful representation capabilities of the Transformer to explicitly model the causal association between weather covariates and AQI. To address the high complexity of traditional Transformers, we design CachLormer, which features two key innovations: a simplified architecture with redundant components removed, and a cache-attention mechanism that employs learnable embeddings for perceiving causal association between AQI and weather covariates in a coarsegrained perspective. We use information theory to illustrate the superiority of the proposed model. Finally, experimental results on three datasets with 28 as the baseline demonstrate that our model achieves competitive performance, while maintaining high training efficiency and low memory consumption. The source code is available at CauAir Official Repository.

The stable periodic patterns present in the time series data serve as the foundation for long-term forecasting. However, existing models suffer from limitations such as continuous and chaotic input partitioning, as well as weak inductive biases, which restrict their ability to capture such recurring structures. In this paper, we propose MoFo, which interprets periodicity as both the correlation of period-aligned time steps and the trend of period-offset time steps. We first design period-structured patches—2D tensors generated through discrete sampling—where each row contains only period-aligned time steps, enabling direct modeling of periodic correlations. Period-offset time steps within a period are aligned in columns. To capture trends across these offset time steps, we introduce a period-aware modulator. This modulator introduces an adaptive strong inductive bias through a regulated relaxation function, encouraging the model to generate attention coefficients that align with periodic trends. This function is end-to-end trainable, enabling the model to adaptively capture the distinct periodic patterns across diverse datasets. Extensive empirical results on widely used benchmark datasets demonstrate that MoFo achieves competitive performance while maintaining high memory efficiency and fast training speed.

The effectiveness of Spatiotemporal Graph Neural Networks (STGNNs) critically hinges on the quality of the underlying graph topology. While end-to-end adaptive graph learning methods have demonstrated promising results in capturing latent spatiotemporal dependencies, they often suffer from high computational complexity and limited expressive capacity. In this paper, we propose MAGE for efficient spatiotemporal forecasting. We first conduct a theoretical analysis demonstrating that the ReLU activation function employed in existing methods amplifies edge-level noise during graph topology learning, thereby compromising the fidelity of the learned graph structures. To enhance model expressiveness, we introduce a sparse yet balanced mixture-of-experts strategy, where each expert perceives the unique underlying graph through kernel-based functions and operates with linear complexity relative to the number of nodes. The sparsity mechanism ensures that each node interacts exclusively with compatible experts, while the balancing mechanism promotes uniform activation across all experts, enabling diverse and adaptive graph representations. Furthermore, we theoretically establish that a single graph convolution using the learned graph in MAGE is mathematically equivalent to multiple convolutional steps under conventional graphs. We evaluate MAGE against advanced baselines on multiple real-world spatiotemporal datasets. MAGE achieves competitive performance while maintaining strong computational efficiency.

In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering original data with dimension $d$, we prove that, under some mild conditions, the perfect recovery of the cluster membership assignments of the convex clustering model, if exists, can be preserved by the randomly projected convex clustering model with embedding dimension $m = O(\epsilon^{-2}\log(n))$, where $\epsilon > 0$ is some given parameter. We further prove that the embedding dimension can be improved to be $O(\epsilon^{-2}\log(K))$, which is independent of the number of data points. We also establish the recovery guarantees of our proposed model with uniform weights for clustering a mixture of spherical Gaussians. Extensive numerical results demonstrate the robustness and superior performance of the randomly projected convex clustering model. The numerical results will also demonstrate that the randomly projected convex clustering model can outperform other popular clustering models on the dimension-reduced data, including the randomly projected K-means model.

While existing spatiotemporal prediction models have shown promising performance, they often rely on the assumption of input-label spatiotemporal consistency, and their high complexity raises concerns about scalability. To enhance both efficiency and performance, we integrate label information into the learning process and propose a spatiotemporal dynamic theory that outlines a bi-directional learning paradigm. Building on this paradigm, we design BiST, a lightweight yet effective Bi -directional S patio -T emporal prediction model. BiST incorporates two key processes: a forward spatiotemporal learning process and a backward correction process. The forward process utilizes MLP layers exclusively to model input correlations and generate base prediction. In the backward process, we implement a spatiotemporal decoupling module, which can learn the residual modeling deviation between input and label representations from a decoupled perspective. After smoothing the residual with a diffusion module, we can obtain the correction term to correct the base predictions. This innovative design enables BiST to achieve competitive performance while remaining lightweight. We evaluate BiST against 26 baselines across 13 datasets, including a large-scale dataset with ten thousand nodes and a longrange dataset spanning 20 years. An impressive experimental result demonstrates that BiST achieves a 8.13% improvement in performance compared to state-of-the-art models while consuming only 1.86% of the training time and 7.36% of the memory usage.

Understanding mobile traffic data and predicting future trends are essential for wireless operators and service providers to allocate resources efficiently and manage energy effectively. Despite the strong performance of existing models, accurately forecasting mobile traffic remains a challenge due to limited spatial and temporal modeling capabilities and high computational complexity. This paper introduces MobiMixer, a lightweight and efficient multi-scale spatiotemporal mixing model. Its core concept is to integrate multi-scale information from both spatial and temporal dimensions to improve performance on mobile traffic data. We develop a hierarchical interaction module that incorporates super nodes to enable global high-level feature interactions among nodes with common patterns. Additionally, we employ a dynamic time warping strategy to decouple mobile traffic sequences into stable and seasonal components, which are then modeled at different scales using a multi-scale temporal mixing module. We conduct extensive experiments on mobile traffic datasets collected from four international cities. Compared with 21 state-of-the-art benchmark models, MobiMixer demonstrates highly competitive performance, achieving a maximum improvement of 48.49% on the Milan mobile dataset. The model achieves an improvement in training efficiency of up to 10.69 times and reduces memory usage by 33.01%. The source code is available athttps://github.com/PoorOtterBob/Submitted_Code.

Traffic prediction is a crucial task in the Intelligent Transportation System (ITS), receiving significant attention from both industry and academia. Numerous spatio-temporal graph convolutional networks have emerged for traffic prediction and achieved remarkable success. However, these models have limitations in terms of generalization and scalability when dealing with Out-of-Distribution (OOD) graph data with both structural and temporal shifts. To tackle the challenges of spatio-temporal shift, we propose a framework called STONE by learning invariable node dependencies, which achieve stable performance in variable environments. STONE initially employs gated-transformers to extract spatial and temporal semantic graphs. These two kinds of graphs represent spatial and temporal dependencies, respectively. Then we design three techniques to address spatio-temporal shifts. Firstly, we introduce a Fréchet embedding method that is insensitive to structural shifts, and this embedding space can integrate loose position dependencies of nodes within the graph. Secondly, we propose a graph intervention mechanism to generate multiple variant environments by perturbing two kinds of semantic graphs without any data augmentations, and STONE can explore invariant node representation from environments. Finally, we further introduce an explore-to-extrapolate risk objective to enhance the variety of generated environments. We conduct experiments on multiple traffic datasets, and the results demonstrate that our proposed model exhibits competitive performance in terms of generalization and scalability.