Recently introduced prior-encoding deep generative models (e.g., PriorVAE, $\pi$VAE, and PriorCVAE) have emerged as powerful tools for scalable Bayesian inference by emulating complex stochastic processes like Gaussian processes (GPs). However, these methods remain largely a proof-of-concept and inaccessible to practitioners. We propose DeepRV, a lightweight, decoder-only approach that accelerates training, and enhances real-world applicability in comparison to current VAE-based prior encoding approaches. Leveraging probabilistic programming frameworks (e.g., NumPyro) for inference, DeepRV achieves significant speedups while also improving the quality of parameter inference, closely matching full MCMC sampling. We showcase its effectiveness in process emulation and spatial analysis of the UK using simulated data, gender-wise cancer mortality rates for individuals under 50, and HIV prevalence in Zimbabwe. To bridge the gap between theory and practice, we provide a user-friendly API, enabling scalable and efficient Bayesian inference.

-- Monitoring flowers over time is essential for precision robotic pollination in agriculture. T o accomplish this, a continuous spatial-temporal observation of plant growth can be done using stationary RGB-D cameras. However, image registration becomes a serious challenge due to changes in the visual appearance of the plant caused by the pollination process and occlusions from growth and camera angles. Plants flower in a manner that produces distinct clusters on branches. This paper presents a method for matching flower clusters using descriptors generated from RGB-D data and considers allowing for spatial uncertainty within the cluster . The proposed approach leverages the Unscented Transform to efficiently estimate plant descriptor uncertainty tolerances, enabling a robust image-registration process despite temporal changes. The Unscented Transform is used to handle the nonlinear transformations by propagating the uncertainty of flower positions to determine the variations in the descriptor domain. A Monte Carlo simulation is used to validate the Unscented Transform results, confirming our method's effectiveness for flower cluster matching. Therefore, it can facilitate improved robotics pollination in dynamic environments. Although global agriculture relies heavily on pollination, evidence has shown that the population of natural pollinators is decreasing, raising concerns about food and the economy [1].

Existing solutions to the hotspot prediction problem in the field of geographic information remain at a relatively preliminary stage. This study presents a novel approach for detecting and predicting geographical hotspots, utilizing point cloud-voxel-community partition clustering. By analyzing high-dimensional data, we represent spatial information through point clouds, which are then subdivided into multiple voxels to enhance analytical efficiency. Our method identifies spatial voxels with similar characteristics through community partitioning, thereby revealing underlying patterns in hotspot distributions. Experimental results indicate that when applied to a dataset of archaeological sites in Turkey, our approach achieves a 19.31% increase in processing speed, with an accuracy loss of merely 6%, outperforming traditional clustering methods. This method not only provides a fresh perspective for hotspot prediction but also serves as an effective tool for high-dimensional data analysis.

Hail nowcasting is a considerable contributor to meteorological disasters and there is a great need to mitigate its socioeconomic effects through precise forecast that has high resolution, long lead times and local details with large landscapes. Existing medium-range weather forecasting methods primarily rely on changes in upper air currents and cloud layers to predict precipitation events, such as heavy rainfall, which are unsuitable for hail nowcasting since it is mainly caused by low-altitude local strong convection associated with terrains. Additionally, radar captures the status of low cloud layers, such as water vapor, droplets, and ice crystals, providing rich signals suitable for hail nowcasting. To this end, we introduce a Spatial-Temporal gEnerAtive Model called SteamCast for hail nowcasting with radar echo extrapolation, it is a deep probabilistic diffusion model based on spatial-temporal representations including radar echoes as well as their position/time embeddings, which we trained on historical reanalysis archive from Yan'an Meteorological Bureau in China, where the crop yield like apple suffers greatly from hail damage. Considering the short-term nature of hail, SteamCast provides 30-minute nowcasts at 6-minute intervals for a single radar reflectivity variable, across 9 different vertical angles, on a latitude-longitude grid with approximately 1 km * 1 km resolution per pixel in Yan'an City, China. By successfully fusing the spatial-temporal features of radar echoes, SteamCast delivers competitive, and in some cases superior, results compared to other deep learning-based models such as PredRNN and VMRNN.

Vision-Language Models (VLMs) have recently emerged as powerful tools, excelling in tasks that integrate visual and textual comprehension, such as image captioning, visual question answering, and image-text retrieval. However, existing benchmarks for VLMs include spatial components, which often fail to isolate spatial reasoning from related tasks such as object detection or semantic comprehension. In this paper, we address these deficiencies with a multi-faceted approach towards understanding spatial reasoning. Informed by the diverse and multi-dimensional nature of human spatial reasoning abilities, we present a detailed analysis that first delineates the core elements of spatial reasoning: spatial relations, orientation and navigation, mental rotation, and spatial visualization, and then assesses the performance of these models in both synthetic and real-world images, bridging controlled and naturalistic contexts. W e analyze 13 state-of-the-art Vision-Language Models, uncovering pivotal insights into their spatial reasoning performance. Our results reveal profound shortcomings in current VLMs, with average accuracy across the 13 models approximating random chance, highlighting spatial reasoning as a persistent obstacle. This work not only exposes the pressing need to advance spatial reasoning within VLMs but also establishes a solid platform for future exploration.

Multi-step spatial reasoning entails understanding and reasoning about spatial relationships across multiple sequential steps, which is crucial for tackling complex real-world applications, such as robotic manipulation, autonomous navigation, and automated assembly. To assess how well current Multimodal Large Language Models (MLLMs) have acquired this fundamental capability, we introduce \textbf{LEGO-Puzzles}, a scalable benchmark designed to evaluate both \textbf{spatial understanding} and \textbf{sequential reasoning} in MLLMs through LEGO-based tasks. LEGO-Puzzles consists of 1,100 carefully curated visual question-answering (VQA) samples spanning 11 distinct tasks, ranging from basic spatial understanding to complex multi-step reasoning. Based on LEGO-Puzzles, we conduct a comprehensive evaluation of state-of-the-art MLLMs and uncover significant limitations in their spatial reasoning capabilities: even the most powerful MLLMs can answer only about half of the test cases, whereas human participants achieve over 90\% accuracy. In addition to VQA tasks, we evaluate MLLMs' abilities to generate LEGO images following assembly illustrations. Our experiments show that only Gemini-2.0-Flash and GPT-4o exhibit a limited ability to follow these instructions, while other MLLMs either replicate the input image or generate completely irrelevant outputs. Overall, LEGO-Puzzles exposes critical deficiencies in existing MLLMs' spatial understanding and sequential reasoning capabilities, and underscores the need for further advancements in multimodal spatial reasoning.

We present MetaSpatial, the first reinforcement learning (RL)-based framework designed to enhance 3D spatial reasoning in vision-language models (VLMs), enabling real-time 3D scene generation without the need for hard-coded optimizations. MetaSpatial addresses two core challenges: (i) the lack of internalized 3D spatial reasoning in VLMs, which limits their ability to generate realistic layouts, and (ii) the inefficiency of traditional supervised fine-tuning (SFT) for layout generation tasks, as perfect ground truth annotations are unavailable. Our key innovation is a multi-turn RL-based optimization mechanism that integrates physics-aware constraints and rendered image evaluations, ensuring generated 3D layouts are coherent, physically plausible, and aesthetically consistent. Methodologically, MetaSpatial introduces an adaptive, iterative reasoning process, where the VLM refines spatial arrangements over multiple turns by analyzing rendered outputs, improving scene coherence progressively. Empirical evaluations demonstrate that MetaSpatial significantly enhances the spatial consistency and formatting stability of various scale models. Post-training, object placements are more realistic, aligned, and functionally coherent, validating the effectiveness of RL for 3D spatial reasoning in metaverse, AR/VR, digital twins, and game development applications.

This paper presents AlphaSpace, a novel methodology designed to enhance the spatial reasoning capabilities of language models for robotic manipulation in 3D Cartesian space. AlphaSpace employs a hierarchical semanticsbased tokenization strategy that encodes spatial information at both coarse and fine-grained levels. Our approach represents objects with their attributes, positions, and height information through structured tokens, enabling precise spatial reasoning without relying on traditional vision-based embeddings. This approach enables LLMs to accurately manipulate objects by positioning them at specific [x, y, z] coordinates. Experimental results demonstrate that AlphaSpace significantly outperforms existing models on manipulation subtasks, achieving a total accuracy of 66.67%, compared to 37.5% for GPT-4o and 29.17% for Claude 3.5 Sonnet.

Human mobility data is crucial for understanding patterns of movement across geographical regions, with applications spanning urban planning[1], transportation systems design[2], infectious disease modeling and control [3, 4], and social dynamics studies [5]. Traditionally, mobility data has been represented using flow networks[6, 7] or colocation matrices [8], where the primary representation is via pairwise interactions. In flow networks, this means directed edges represent the movement of individuals between two locations; colocation matrices measure the probability that a random individual from a region is colocated with a random individual from another region at the same location. These data types and their pairwise representation structure have been used to identify the spatial scales and regularity of human mobility, but have inherent limitations in their capacity to capture more complex patterns of human movement involving higher-order interactions between locations - that is, group of locations that are frequently visited by many individuals within a period of time (e.g., a week) and revisited regularly over time. Higher-order interactions between locations can contain crucial information under certain scenarios.

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as an efficient approach for solving these PDE problems. By using parametrization in the frequency domain, FNOs can efficiently capture global patterns. However, this approach inherently overlooks the critical role of local spatial features, as frequency-domain parameterized convolutions primarily emphasize global interactions without encoding comprehensive localized spatial dependencies. Although several studies have attempted to address this limitation, their extracted Local Spatial Features (LSFs) remain insufficient, and computational efficiency is often compromised. To address this limitation, we introduce a convolutional neural network (CNN) preprocessor to extract LSFs directly from input data, resulting in a hybrid architecture termed \textit{Conv-FNO}. Furthermore, we introduce two novel resizing schemes to make our Conv-FNO resolution invariant. In this work, we focus on demonstrating the effectiveness of incorporating LSFs into FNOs by conducting both a theoretical analysis and extensive numerical experiments. Our findings show that this simple yet impactful modification enhances the representational capacity of FNOs and significantly improves performance on challenging PDE benchmarks.