Spatio-Temporal Correlations

Generative models like Diffusion Models and Flow Matching have demonstrated remarkable capabilities in synthesizing high-fidelity driving videos, but are severely constrained by high inference latency due to the requirement of extensive sampling steps. We argue that this inefficiency stems from the prevailing reliance on a standard Gaussian source distribution, where consecutive frames are initialized as independent Gaussian noise. This paradigm disregards the rich spatiotemporal correlations inherent in driving videos, compelling the model to regenerate deterministic scene structures existing in previous frames from noise, which is both computationally redundant and prone to geometric inconsistency. To address this problem, we propose GeoFlow, a novel framework designed to achieve efficient driving video generation by harnessing explicit geometric priors. Instead of sampling from standard Gaussian noise, we leverage multi-view geometry and spatially-adaptive noise injection to construct a Geometry-Aligned Prior (GAP) distribution as starting point. This initialization bridges the gap between source distribution and data distribution, yielding a significantly straighter and shorter sampling trajectory. Extensive experiments demonstrate that GeoFlow can achieve remarkable efficiency of both training and inference: merely several hours of fine-tuning on baseline models can significantly boost few-step generation quality, while fully converged training drastically reduces number of inference steps required for state-of-the-art video generation.

Existing active reconstruction systems with Gaussian-splatting maps select observations greedily, optimizing a single next-best-view (NBV) at each step and connecting the chosen views by short-horizon path planning. This greedy decoupling disregards the global structure of scene information, producing inefficient trajectories that waste sensing capacity in transit between selected views. In this work, we study active reconstruction as an ergodic coverage problem: the time-averaged spatial statistics of the sensor trajectory should match a target information distribution induced by the current map. Our approach derives this target distribution online from uncertainty and visibility, and calculates ergodic trajectories via a kernel-ergodic horizon planner with gradient flow and footprint depletion, closing the loop between mapping and trajectory optimization. We thoroughly evaluate TRACE on the Replica dataset against the Next-Best-View (NBV) baselines, improving PSNR by 1.5 dB. Code: https://github.com/spikelab-jhu/trace-active-reconstruction.

Predicting traffic flow is crucial to optimizing transportation systems and improving urban mobility. Many graph convolution-based models have been proposed to extract spatial-temporal features and predict traffic flow. However, most focus on spatial-temporal and semantic correlation in topological relationships. There are two primary problems to address. Firstly, the convolutional structure in the model focuses on utilizing static spatial dependencies and spatial-temporal relationships in topological structures, while neglecting the different information propagation delays between adjacent nodes in the convolution. Secondly, these methods often stack a large number of complex structures, resulting in a substantial increase in computational time during the model training phase, thereby disregarding the model's requirements for timeliness. In this paper, we propose a novel network called the Attention-Based Spatial-Temporal Fusion Graph Convolution Network (A-STFGCN). We design a spatial-temporal fusion block to extract the spatial-temporal feature correlations with propagation delay errors removed and to capture both long-term and short-term temporal characteristics of the data within a multi-head self-attention mechanism based on a mask matrix. Extensive experiments on five real-world datasets demonstrate that our method achieves the best overall performance while having good computation and data utilization efficiency compared with the eight baseline methods.

We propose a novel measure of the discrepancy between two probability distributions $f$ and $g$ on a graph - which we call the diffusion distance - that measures the rate of convergence of $f$ to $g$ under a graph-constrained Markov chain with stationary distribution $g$. As a default choice for this Markov chain, we use the Metropolis-Hastings transition matrix targeting $g$ with proposals given by a random walk on the graph. Our primary case of interest is when the second distribution $g$ is uniform, in which case the diffusion distance becomes a measure of spatial clustering in $f$. Used in this way, (Metropolis-Hastings) diffusion distance to uniformity extends Moran's $I$-type measures of spatial autocorrelation by incorporating global graph geometry rather than just local patterns. Indeed, Moran's $I$, the most well-known measure of spatial autocorrelation, can be viewed as a one-step heuristic for diffusion distance, so long as specific spatial weights are used. We establish theoretical bounds and a stability result for our measure, connecting it to graph spectra and optimal transport. We then turn our attention to outlining a statistical test for spatial clustering using diffusion distance. Under permutation null models, we derive high-probability bounds on diffusion distance underpinned by exact spectral formulas for convergence of distributions, enabling an efficient statistical test for spatial clustering on large datasets. We empirically compare diffusion distance to Moran's $I$ both as a numerical measure and as a statistical test. We show that diffusion distance exhibits higher power on synthetic data using a stochastic block model. Empirical analysis of Black population distributions for 100 U.S. cities shows that diffusion distance detects subtle differences in urban segregation patterns that Moran's $I$ does not.

Video diffusion transformers (vDiTs) generate high quality video but introduce extremely high compute cost due to the long diffusion timesteps and self attention computation. As diffusion timesteps are reduced, the computation cost of self attention becomes the dominant bottleneck. Existing acceleration approaches largely inherit sparse attention techniques from large language models, which fail to consider the unique spatiotemporal correlation of video data. This paper presents Kaleido, an algorithm hardware codesign that accelerates all operations in vDiTs by exploiting channel-wise spatiotemporal correlations in latent space. Based on this insight, we propose a lightweight channelwise reuse algorithm that skips redundant computations by reusing partial results while preserving higher generative quality than prior methods (>17 dB). To efficiently support this algorithm, we design a systolic array like accelerator with reconfigurable processing elements and a lightweight data dispatcher to mitigate irregular sparsity and data access patterns introduced by our reuse algorithm. Evaluations across three mainstream vDiT models show that Kaleido achieves up to 5.9x speedup and 16.0x energy savings over state of the art accelerators.

Fine-scale rainfall reconstruction is critical for urban flood modeling, but real rainfall sensing systems observe the field through incompatible spatial supports: gauges measure points, microwave links measure paths, and radar/satellite products measure gridded areas. These differences in measurement support impose geometrically distinct constraints on the rainfall field, yet existing heterogeneous graph approaches reconcile such sources in feature space, giving each its own embedding while discarding the geometry of its support. We propose a geometry-aware multi-support heterogeneous graph neural network that represents each observation according to its support type (0D point, 1D line, or 2D grid) as a distinct node layer, and fuses them through cross-support message passing into a point-support prediction layer from which the field is reconstructed. An inductive masked-node formulation decouples prediction resolution from sensing resolution, allowing the same trained model to reconstruct the field at user-defined target locations or display grids. On Singapore data, the proposed method reduces RMSE by 23.2% over the classical interpolation baseline, inverse-distance weighting, and consistently outperforms other neural architectures such as convolutional fusion and support-agnostic heterogeneous graph baselines. A generalization study using data from Sydney, Australia lets us characterize when multi-support fusion helps: the available skill appears to depend on gauge spacing relative to the spatial correlation length of the field, so fusion delivers the largest gains where the field is under-sampled relative to its correlation length and little when it is already resolved. Code and models will be open-sourced upon paper acceptance.

Light Field Super-Resolution (LFSR) necessitates accurate modeling of spatial-angular correlations while preserving intrinsic 4D ray coherence. However, maintaining such high-dimensional consistency remains challenging, primarily due to two inherent limitations in prevailing modeling paradigms. First, spatial and angular dimensions are often modeled in a decoupled manner, restricting early cross-dimensional interaction and leading to geometric inconsistencies. Moreover, although continuous sequence modeling paradigms show promise in representing epipolar structures, their rigid scanning mechanisms fundamentally conflict with epipolar geometry, limiting geometry-aware feature aggregation. To address these challenges, we propose a hybrid light field super-resolution network, termed SMART, which integrates a Slope-Guided Mamba and an Angular-Refined Transformer to effectively overcome these limitations. Specifically, we introduce an angular-modulated spatial module to bridge the decoupling gap, incorporating angular priors to strengthen spatial-angular correlation modeling. To mitigate the scan-geometry mismatch, we propose a manifold-aligned trajectory module that enables geometry-consistent sequence modeling along epipolar structures. Experiments on five benchmarks demonstrate that SMART achieves state-of-the-art performance, surpassing previous methods by 0.42 dB (PSNR) with significantly reduced artifacts.

Unsupervised pre-training on large-scale datasets has demonstrated significant potential for improving the sample efficiency and performance of Reinforcement Learning (RL). Given the large-scale action-free internet videos, existing methods utilize single-step transition prediction and image reconstruction to learn representations. However, these methods prefer to preserve large-proportion stationary information in the pixel space, neglecting small but crucial information. To preserve enough information in the representation, it is essential to pay equal attention to each element in videos. Specifically, we propose a temporal correlation space to distinguish each element. For implementation, we introduce the Multi-scale Temporal Contrastive Learning (MTCL) method to model multi-scale temporal correlations separately. This approach can balance the attention of different elements and yield more informative representations, effectively supporting policy learning in various downstream tasks. Experimental results demonstrate that our method improves sample efficiency and asymptotic performance across various downstream tasks.

The integration of multiple thematic data layers into a single composite map, known as the cartographic synthesis problem, is typically addressed through expert-driven weighting schemes. This study presents a multi-objective formulation of cartographic synthesis grounded in spatial autocorrelation structure. We develop a bi-objective evolutionary framework, GIS-moGA, that estimates layer weights by simultaneously maximizing global spatial structure, measured by Global Moran's I, and minimizing local spatial heterogeneity, measured by the variance of Local Indicators of Spatial Association (LISA). Because naive evaluation of spatial relationships requires O(N^2) operations, direct computation becomes impractical for larger datasets. We address this challenge by exploiting the 97.7% sparsity of queen contiguity matrices, reducing effective complexity to O(N k) and enabling scalable municipal-level analysis. The framework is evaluated on a high-dimensional spatial epidemiology dataset with N = 523 units from Araraquara, Brazil. A 64-scenario experimental design is used to examine evolutionary behavior across parameter settings. Results show that higher mutation rates are important for maintaining population diversity and preventing premature convergence in spatially autocorrelated fitness landscapes, where crossover operators can disrupt geographically coherent structures. Compared with expert-derived Analytic Hierarchy Process baselines, the resulting Pareto fronts show substantial hypervolume gains and significant improvements in spatial coherence (p < 0.001, Cliff's delta = 0.87). These findings provide a systematic and scalable framework for data-driven geographic multi-criteria decision analysis.

Autoregressive (AR) models have demonstrated remarkable performance in generating high-fidelity images. However, their inherently sequential next-token prediction leads to significantly slower inference. Recent studies have introduced Jacobi-style decoding to accelerate autoregressive image generation. Extending the draft sequence initially improves efficiency, yet the acceleration quickly saturates as error propagation in the one-dimensional sequence hinders convergence. Observing that images exhibit strong local spatial correlations, we propose Parallel Jacobi Decoding (PJD), a training-free decoding approach that expands draft tokens in the two-dimensional spatial domain to enable efficient spatially parallel refinement. PJD adjusts the attention mask to mitigate error accumulation and improve convergence stability. Extensive experiments on diverse datasets show that PJD achieves 4.8x-6.4x acceleration across multiple autoregressive image generation models while maintaining competitive generation quality.

Physical systems do not merely add noise to search processes; they impose constraints that generate structured correlations. We propose a principle of constraint-enhanced physical search in which temporal correlations in exploration are matched to constraint-induced spatial correlations in the update dynamics. Using a minimal tug-of-war bandit model (TOW), we show that a conservation law converts local observations into differential evidence across alternatives, while a temporally correlated drive controls the order of exploration. Search efficiency is improved not by stronger randomness or by maximal anti-correlation, but by matching the temporal correlation to the physical update scale that converts feedback into evidence. A scaling estimate identifies the update-noise-to-contrast ratio as the leading parameter that limits how strongly temporal anti-correlation can be used. The results suggest a general organizing principle for physical search: constraints and fluctuations can generate structured spatiotemporal correlations, and efficient exploration emerges when these correlations are matched to the update dynamics.

Geometric partitioning has attracted increasing attention by its remarkable motion field description capability in the hybrid video coding framework. However, the existing geometric partitioning (GEO) scheme in Versatile Video Coding (VVC) causes a non-negligible burden for signaling the side information. Consequently, the coding efficiency is limited. In view of this, we propose a spatio-temporal correlation guided geometric partitioning (STGEO) scheme to efficiently describe the object information in the motion field of video coding. The proposed method can economize the bits consumed for side information signaling, including the partitioning mode and motion information. We firstly analyze the characteristics of partitioning mode decision and motion vector selection in a statistically-sound way. Based on the observed spatio-temporal correlation, we design a mode prediction and coding method to reduce the overhead for representing the above mentioned side information. The main idea is to predict the STGEO modes and motion candidates that have higher selection possibilities, which can guide the entropy coding, i.e., representing the predicted high-probability modes and motion candidates with fewer bits. In particular, the high-probability STGEO modes are predicted based on the edge information and history modes of adjacent STGEO-coded blocks. The corresponding motion information is represented by the index in a merge candidate list, which is adaptively inferred based on the off-line trained merge candidate selection probability. Simulation results show that the proposed approach achieves 0.95% and 1.98% bit-rate savings on average compared to VTM-8.0 without GEO for Random Access and Low-Delay B configurations, respectively.

Investigating spatial-temporal correlations, specifically how spatial points vary over time, is crucial for understanding point cloud videos. Traditional methods, particularly flow-based techniques, struggle with these correlations due to the unordered spatial arrangement of sequential point cloud data. To address this challenge, we propose a novel approach that regularizes spatial-temporal correlation learning by formulating the problem as a solvable Partial Differential Equation (PDE). While PDEs have long been effective in the physical domain, their application to novel sequential data like point cloud video remains underexplored. Inspired by fluid analysis, we construct a simplified PDE, and the process of solving PDE is guided and refined by a contrastive learning structure between the temporal embeddings and the spatial embeddings. With this extra supervision, our method, named MotionPDE, serves as an effective, plug-and-play enhancement module for existing backbone models, adding minimal computational overhead and parameters. Capitalizing on the contrastive learning process, we delve deeper into the self-supervised capabilities of MotionPDE, yielding promising results that underscore its utility and adaptability in point cloud video data interpretation. The code repo with trained checkpoints will be available at https://github.com/zhh6425/motionpde.git for facilitating future research.

Predicting spatial gene expression from routine H&E enables large-scale molecular profiling, yet current models treat this as isolated pointwise tasks, thereby overlooking essential biological structures like gene coordination and spatial distribution. To preserve these relationships, we introduce \textbf{FLAG}, a diffusion-based framework that redefines this task as structured distribution modeling. At the same time, we identify the critical \textbf{Gene Dimension Curse}, where joint modeling gene expression and their spatial interactions fail in high-dimensional spaces, and FLAG solves this challenge by integrating a spatial graph encoder for topological consistency and utilizing Gene Foundation Model (GFM) alignment for gene-gene fidelity in the generation process. To rigorously assess model performance, we propose a set of novel structural evaluation metrics, including Gene Structural Correlation (\textbf{GSC}) and Spatial Structural Correlation (\textbf{SSC}). Our experiments demonstrate that FLAG is highly competitive in traditional accuracy (PCC/MSE) while achieving significantly enhanced structural fidelity in capturing both gene-gene and gene-spatial relationships. The code is available at https://github.com/darkflash03/FLAG.

Traffic forecasting is a significant part of intelligent transportation systems. One of the critical challenges of traffic forecasting is to find spatio-temporal correlations. In recent years, graph convolutional networks and graph attention networks have replaced traditional statistical models to predict future traffic. However, it is complicated for both of them to allow vertices to have far different characters. To address this, we propose the Global-Local Graph Attention Network (GLGAT) with pairwise encoding and the event-based adjacency matrix. The GLGAT allows vertices to have a global attention matrix set for the whole graph and assigns local attention matrix sets to each vertex. Experiments on two real-world traffic datasets show that GLGAT can effectively capture spatio-temporal correlations and has competitive performance against other state-of-the-art baselines.

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN training still suffers from high-dimensional non-convex loss landscapes, imbalanced multiobjective constraints, and ineffective information propagation. Existing curriculum learning and causality-guided strategies improve training stability, but mainly focus on temporal or parametric progression, lacking explicit treatment of spatial information propagation and inter-region consistency. Moreover, they are not directly applicable to boundary value problems (BVPs) with strong spatial coupling. To address this issue, we propose a spatially correlated curriculum learning framework for PINNs. To the best of our knowledge, this is the first work to address PINN training difficulties from the perspective of spatial coupling among subregions. First, spatial causal weights guide information from near-boundary regions inward, reducing optimization failures and spurious convergence. Second, a low-frequency information bridge enforces pseudo-label-based consistency across spatially separated regions, suppressing global low-frequency drift. Third, a region-adaptive reweighting strategy adjusts subregion losses to reduce local residuals and recover high-frequency details. Experiments on PDE benchmarks show that, under comparable computational cost, the proposed method alleviates training failures and improves solution accuracy. The code is available at https://github.com/pigofmomo/CurriculumLearningPINN.

The success of deep learning in high-dimensional settings is often attributed to the presence of low-dimensional structure in real-world data. While standard theoretical models typically assume that this structure lies in the target function, projecting unstructured inputs onto a low-dimensional subspace, data such as images, text or genomic sequences exhibit strong spatial correlations within the input space itself. In this paper, we propose a tractable model to study how these correlations affect the sample complexity of learning with gradient descent on shallow neural networks. Specifically, we consider targets that depend on a small number of latent Boolean variables, and input features grouped into clusters and correlated with the latent variables. Under an identifiability assumption, we show that for a layerwise gradient-descent variant, the sample complexity scales with the number of hidden variables and, when the signal-to-noise ratio is sufficiently high, is independent of the input dimension, up to logarithmic terms. We empirically test our theoretical findings on both synthetic and real data.

We study how temporal correlations in the data can make certain sparse learning problems efficiently learnable by gradient-based methods. Our focus is on Boolean k-juntas, a canonical sparse learning problem known to pose barriers for gradient-based methods under independent uniform samples. We show that this picture changes when the samples are generated by a lazy random walk on the hypercube. In this setting, the temporal dependencies can be exploited by a two-layer ReLU network trained using stylized-SGD with a temporal-difference loss, which compares target and predicted increments across consecutive samples. For every fixed k, the resulting sample complexity is essentially linear in the ambient dimension d. By contrast, we show that for large-batch gradient methods using standard convex pointwise losses, temporal correlations do not provide the same advantage.

Speech-preserving facial expression manipulation (SPFEM) aims to modify facial emotions while meticulously maintaining the mouth animation associated with spoken content. Current works depend on inaccessible paired training samples for the person, where two aligned frames exhibit the same speech content yet differ in emotional expression, limiting the SPFEM applications in real-world scenarios. In this work, we discover that speakers who convey the same content with different emotions exhibit highly correlated local facial animations in both spatial and temporal spaces, providing valuable supervision for SPFEM. To capitalize on this insight, we propose a novel spatial-temporal coherent correlation learning (STCCL) algorithm, which models the aforementioned correlations as explicit metrics and integrates the metrics to supervise manipulating facial expression and meanwhile better preserving the facial animation of spoken content. To this end, it first learns a spatial coherent correlation metric, ensuring that the visual correlations of adjacent local regions within an image linked to a specific emotion closely resemble those of corresponding regions in an image linked to a different emotion. Simultaneously, it develops a temporal coherent correlation metric, ensuring that the visual correlations of specific regions across adjacent image frames associated with one emotion are similar to those in the corresponding regions of frames associated with another emotion. Recognizing that visual correlations are not uniform across all regions, we have also crafted a correlation-aware adaptive strategy that prioritizes regions that present greater challenges. During SPFEM model training, we construct the spatial-temporal coherent correlation metric between corresponding local regions of the input and output image frames as an additional loss to supervise the generation process.

DINO models provide rich patch-level representations that have recently enabled strong performance in unsupervised anomaly detection (UAD). Most existing methods extract patch embeddings from normal images and model them independently, ignoring spatial and neighborhood relationships between patches. This implicitly assumes that self-attention and positional encodings sufficiently encode contextual information within each patch embedding. In addition, the normative distribution is often modeled as memory banks or prototype-based representations, which require storing large numbers of features and performing costly comparisons at inference time, leading to substantial memory and computational overhead. In this work, we explicitly model spatial and contextual dependencies between patch embeddings using a 2D autoregressive (AR) model, allowing us to use a simple and efficient model for normative modeling. Instead of storing embeddings or clustering prototypes, our approach learns a compact parametric model of the normative distribution via an AR convolutional neural network (CNN). At test time, anomaly detection reduces to a single forward pass through the network and enables fast and memory-efficient inference. We evaluate our method on the BMAD benchmark, comprising three medical imaging datasets, and the VisA dataset, comprising 12 industrial object categories, and compare it against existing methods, including recent DINO-based approaches. Experimental results demonstrate that explicitly modeling spatial dependencies achieves competitive anomaly detection performance while substantially reducing inference time and memory requirements. Code is available at the project page: https://eerdil.github.io/spatial-ar-dinov3-uad/