Sample-efficient diffusion-based control of complex nonlinear systems

Complex nonlinear system control faces challenges in achieving sample-efficient, reliable performance. While diffusion-based methods have demonstrated advantages over classical and reinforcement learning approaches in long-term control performance, they are limited by sample efficiency. This paper presents SEDC (Sample-Efficient Diffusion-based Control), a novel diffusion-based control framework addressing three core challenges: high-dimensional state-action spaces, nonlinear system dynamics, and the gap between non-optimal training data and near-optimal control solutions. Through three innovations - Decoupled State Diffusion, Dual-Mode Decomposition, and Guided Self-finetuning - SEDC achieves 39.5\%-49.4\% better control accuracy than baselines while using only 10\% of the training samples, as validated across three complex nonlinear dynamic systems. Our approach represents a significant advancement in sample-efficient control of complex nonlinear systems. The implementation of the code can be found at https://anonymous.4open.science/r/DIFOCON-C019.

Structure-prior Informed Diffusion Model for Graph Source Localization with Limited Data

The source localization problem in graph information propagation is crucial for managing various network disruptions, from misinformation spread to infrastructure failures. While recent deep generative approaches have shown promise in this domain, their effectiveness is limited by the scarcity of real-world propagation data. This paper introduces SIDSL (\textbf{S}tructure-prior \textbf{I}nformed \textbf{D}iffusion model for \textbf{S}ource \textbf{L}ocalization), a novel framework that addresses three key challenges in limited-data scenarios: unknown propagation patterns, complex topology-propagation relationships, and class imbalance between source and non-source nodes. SIDSL incorporates topology-aware priors through graph label propagation and employs a propagation-enhanced conditional denoiser with a GNN-parameterized label propagation module (GNN-LP). Additionally, we propose a structure-prior biased denoising scheme that initializes from structure-based source estimations rather than random noise, effectively countering class imbalance issues. Experimental results across four real-world datasets demonstrate SIDSL's superior performance, achieving 7.5-13.3% improvements in F1 scores compared to state-of-the-art methods. Notably, when pretrained with simulation data of synthetic patterns, SIDSL maintains robust performance with only 10% of training data, surpassing baselines by more than 18.8%. These results highlight SIDSL's effectiveness in real-world applications where labeled data is scarce.

Unveiling the Power of Noise Priors: Enhancing Diffusion Models for Mobile Traffic Prediction

Accurate prediction of mobile traffic, \textit{i.e.,} network traffic from cellular base stations, is crucial for optimizing network performance and supporting urban development. However, the non-stationary nature of mobile traffic, driven by human activity and environmental changes, leads to both regular patterns and abrupt variations. Diffusion models excel in capturing such complex temporal dynamics due to their ability to capture the inherent uncertainties. Most existing approaches prioritize designing novel denoising networks but often neglect the critical role of noise itself, potentially leading to sub-optimal performance. In this paper, we introduce a novel perspective by emphasizing the role of noise in the denoising process. Our analysis reveals that noise fundamentally shapes mobile traffic predictions, exhibiting distinct and consistent patterns. We propose NPDiff, a framework that decomposes noise into \textit{prior} and \textit{residual} components, with the \textit{prior} derived from data dynamics, enhancing the model's ability to capture both regular and abrupt variations. NPDiff can seamlessly integrate with various diffusion-based prediction models, delivering predictions that are effective, efficient, and robust. Extensive experiments demonstrate that it achieves superior performance with an improvement over 30\%, offering a new perspective on leveraging diffusion models in this domain.

A Diffusive Data Augmentation Framework for Reconstruction of Complex Network Evolutionary History

The evolutionary processes of complex systems contain critical information regarding their functional characteristics. The generation time of edges provides insights into the historical evolution of various networked complex systems, such as protein-protein interaction networks, ecosystems, and social networks. Recovering these evolutionary processes holds significant scientific value, including aiding in the interpretation of the evolution of protein-protein interaction networks. However, existing methods are capable of predicting the generation times of remaining edges given a partial temporal network but often perform poorly in cross-network prediction tasks. These methods frequently fail in edge generation time recovery tasks for static networks that lack timestamps. In this work, we adopt a comparative paradigm-based framework that fuses multiple networks for training, enabling cross-network learning of the relationship between network structure and edge generation times. Compared to separate training, this approach yields an average accuracy improvement of 16.98%. Furthermore, given the difficulty in collecting temporal networks, we propose a novel diffusion-model-based generation method to produce a large number of temporal networks. By combining real temporal networks with generated ones for training, we achieve an additional average accuracy improvement of 5.46% through joint training.

Noise Matters: Diffusion Model-based Urban Mobility Generation with Collaborative Noise Priors

With global urbanization, the focus on sustainable cities has largely grown, driving research into equity, resilience, and urban planning, which often relies on mobility data. The rise of web-based apps and mobile devices has provided valuable user data for mobility-related research. However, real-world mobility data is costly and raises privacy concerns. To protect privacy while retaining key features of real-world movement, the demand for synthetic data has steadily increased. Recent advances in diffusion models have shown great potential for mobility trajectory generation due to their ability to model randomness and uncertainty. However, existing approaches often directly apply identically distributed (i.i.d.) noise sampling from image generation techniques, which fail to account for the spatiotemporal correlations and social interactions that shape urban mobility patterns. In this paper, we propose CoDiffMob, a diffusion method for urban mobility generation with collaborative noise priors, we emphasize the critical role of noise in diffusion models for generating mobility data. By leveraging both individual movement characteristics and population-wide dynamics, we construct novel collaborative noise priors that provide richer and more informative guidance throughout the generation process. Extensive experiments demonstrate the superiority of our method, with generated data accurately capturing both individual preferences and collective patterns, achieving an improvement of over 32\%. Furthermore, it can effectively replace web-derived mobility data to better support downstream applications, while safeguarding user privacy and fostering a more secure and ethical web. This highlights its tremendous potential for applications in sustainable city-related research.

Understanding World or Predicting Future? A Comprehensive Survey of World Models

The concept of world models has garnered significant attention due to advancements in multimodal large language models such as GPT-4 and video generation models such as Sora, which are central to the pursuit of artificial general intelligence. This survey offers a comprehensive review of the literature on world models. Generally, world models are regarded as tools for either understanding the present state of the world or predicting its future dynamics. This review presents a systematic categorization of world models, emphasizing two primary functions: (1) constructing internal representations to understand the mechanisms of the world, and (2) predicting future states to simulate and guide decision-making. Initially, we examine the current progress in these two categories. We then explore the application of world models in key domains, including autonomous driving, robotics, and social simulacra, with a focus on how each domain utilizes these aspects. Finally, we outline key challenges and provide insights into potential future research directions.

A Foundation Model for Unified Urban Spatio-Temporal Flow Prediction

Urban spatio-temporal flow prediction, encompassing traffic flows and crowd flows, is crucial for optimizing city infrastructure and managing traffic and emergency responses. Traditional approaches have relied on separate models tailored to either grid-based data, representing cities as uniform cells, or graph-based data, modeling cities as networks of nodes and edges. In this paper, we build UniFlow, a foundational model for general urban flow prediction that unifies both grid-based and graphbased data. We first design a multi-view spatio-temporal patching mechanism to standardize different data into a consistent sequential format and then introduce a spatio-temporal transformer architecture to capture complex correlations and dynamics. To leverage shared spatio-temporal patterns across different data types and facilitate effective cross-learning, we propose SpatioTemporal Memory Retrieval Augmentation (ST-MRA). By creating structured memory modules to store shared spatio-temporal patterns, ST-MRA enhances predictions through adaptive memory retrieval. Extensive experiments demonstrate that UniFlow outperforms existing models in both grid-based and graph-based flow prediction, excelling particularly in scenarios with limited data availability, showcasing its superior performance and broad applicability. The datasets and code implementation have been released on https://github.com/YuanYuan98/UniFlow.

UrbanDiT: A Foundation Model for Open-World Urban Spatio-Temporal Learning

The urban environment is characterized by complex spatio-temporal dynamics arising from diverse human activities and interactions. Effectively modeling these dynamics is essential for understanding and optimizing urban systems In this work, we introduce UrbanDiT, a foundation model for open-world urban spatio-temporal learning that successfully scale up diffusion transformers in this field. UrbanDiT pioneers a unified model that integrates diverse spatio-temporal data sources and types while learning universal spatio-temporal patterns across different cities and scenarios. This allows the model to unify both multi-data and multi-task learning, and effectively support a wide range of spatio-temporal applications. Its key innovation lies in the elaborated prompt learning framework, which adaptively generates both data-driven and task-specific prompts, guiding the model to deliver superior performance across various urban applications. UrbanDiT offers three primary advantages: 1) It unifies diverse data types, such as grid-based and graph-based data, into a sequential format, allowing to capture spatio-temporal dynamics across diverse scenarios of different cities; 2) With masking strategies and task-specific prompts, it supports a wide range of tasks, including bi-directional spatio-temporal prediction, temporal interpolation, spatial extrapolation, and spatio-temporal imputation; and 3) It generalizes effectively to open-world scenarios, with its powerful zero-shot capabilities outperforming nearly all baselines with training data. These features allow UrbanDiT to achieves state-of-the-art performance in different domains such as transportation traffic, crowd flows, taxi demand, bike usage, and cellular traffic, across multiple cities and tasks. UrbanDiT sets up a new benchmark for foundation models in the urban spatio-temporal domain.

Generalizing Hyperedge Expansion for Hyper-relational Knowledge Graph Modeling

By representing knowledge in a primary triple associated with additional attribute-value qualifiers, hyper-relational knowledge graph (HKG) that generalizes triple-based knowledge graph (KG) has been attracting research attention recently. Compared with KG, HKG is enriched with the semantic qualifiers as well as the hyper-relational graph structure. However, to model HKG, existing studies mainly focus on either semantic information or structural information therein, which however fail to capture both simultaneously. To tackle this issue, in this paper, we generalize the hyperedge expansion in hypergraph learning and propose an equivalent transformation for HKG modeling, referred to as TransEQ. Specifically, the equivalent transformation transforms a HKG to a KG, which considers both semantic and structural characteristics. Then an encoder-decoder framework is developed to bridge the modeling research between KG and HKG. In the encoder part, KG-based graph neural networks are leveraged for structural modeling; while in the decoder part, various HKG-based scoring functions are exploited for semantic modeling. Especially, we design the sharing embedding mechanism in the encoder-decoder framework with semantic relatedness captured. We further theoretically prove that TransEQ preserves complete information in the equivalent transformation, and also achieves full expressivity. Finally, extensive experiments on three benchmarks demonstrate the superior performance of TransEQ in terms of both effectiveness and efficiency. On the largest benchmark WikiPeople, TransEQ significantly improves the state-of-the-art models by 15\% on MRR.

Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length

Symbolic regression, a task discovering the formula best fitting the given data, is typically based on the heuristical search. These methods usually update candidate formulas to obtain new ones with lower prediction errors iteratively. However, since formulas with similar function shapes may have completely different symbolic forms, the prediction error does not decrease monotonously as the search approaches the target formula, causing the low recovery rate of existing methods. To solve this problem, we propose a novel search objective based on the minimum description length, which reflects the distance from the target and decreases monotonically as the search approaches the correct form of the target formula. To estimate the minimum description length of any input data, we design a neural network, MDLformer, which enables robust and scalable estimation through large-scale training. With the MDLformer's output as the search objective, we implement a symbolic regression method, SR4MDL, that can effectively recover the correct mathematical form of the formula. Extensive experiments illustrate its excellent performance in recovering formulas from data. Our method successfully recovers around 50 formulas across two benchmark datasets comprising 133 problems, outperforming state-of-the-art methods by 43.92%.