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.

Owing to the capability for reliable and all-weather long-range sensing, the fusion of LiDAR and Radar has been widely applied to autonomous vehicles for robust perception. In practical operation, well manually calibrated extrinsic parameters, which are crucial for the fusion of multi-modal sensors, may drift due to the vibration. To address this issue, we present a novel targetless calibration approach, termed LiRaCo, for the extrinsic 6DoF calibration of LiDAR and Radar sensors. Although both types of sensors can obtain geometric information, bridging the geometric correspondences between multi-modal data without any clues of explicit artificial markers is nontrivial, mainly due to the low vertical resolution of scanning Radar. To achieve the targetless calibration, LiRaCo leverages a spatial occupancy consistency between LiDAR point clouds and Radar scans in a common cylindrical representation, considering the increasing data sparsity with distance for both sensors. Specifically, LiRaCo expands the valid Radar scanned pixels into 3D occupancy grids to constrain LiDAR point clouds based on spatial consistency. Consequently, a cost function involving extrinsic calibration parameters is formulated based on the spatial overlap of 3D grids and LiDAR points. Extrinsic parameters are finally estimated by optimizing the cost function. Comprehensive quantitative and qualitative experiments on two real outdoor datasets with different LiDAR sensors demonstrate the feasibility and accuracy of the proposed method. The source code will be publicly available.

Advancements in vision and language foundation models have inspired the development of geo-foundation models (GeoFMs), enhancing performance across diverse geospatial tasks. However, many existing GeoFMs primarily focus on overhead remote sensing (RS) data while neglecting other data modalities such as ground-level imagery. A key challenge in multimodal GeoFM development is to explicitly model geospatial relationships across modalities, which enables generalizability across tasks, spatial scales, and temporal contexts. To address these limitations, we propose GAIR, a novel multimodal GeoFM architecture integrating overhead RS data, street view (SV) imagery, and their geolocation metadata. We utilize three factorized neural encoders to project an SV image, its geolocation, and an RS image into the embedding space. The SV image needs to be located within the RS image's spatial footprint but does not need to be at its geographic center. In order to geographically align the SV image and RS image, we propose a novel implicit neural representations (INR) module that learns a continuous RS image representation and looks up the RS embedding at the SV image's geolocation. Next, these geographically aligned SV embedding, RS embedding, and location embedding are trained with contrastive learning objectives from unlabeled data. We evaluate GAIR across 10 geospatial tasks spanning RS image-based, SV image-based, and location embedding-based benchmarks. Experimental results demonstrate that GAIR outperforms state-of-the-art GeoFMs and other strong baselines, highlighting its effectiveness in learning generalizable and transferable geospatial representations.

Urban traffic forecasting is a commonly encountered problem, with wide-ranging applications in fields such as urban planning, civil engineering and transport. In this paper, we study the enhancement of traffic forecasting with pre-training, focusing on spatio-temporal graph methods. While various machine learning methods to solve traffic forecasting problems have been explored and extensively studied, there is a gap of a more contextual approach: studying how relevant non-traffic data can improve prediction performance on traffic forecasting problems. We call this data spatial context. We introduce a novel method of combining road and traffic information through the notion of a traffic quotient graph, a quotient graph formed from road geometry and traffic sensors. We also define a way to encode this relationship in the form of a geometric encoder, pre-trained using contrastive learning methods and enhanced with OpenStreetMap data. We introduce and discuss ways to integrate this geometric encoder with existing graph neural network (GNN)-based traffic forecasting models, using a contrastive pre-training paradigm. We demonstrate the potential for this hybrid model to improve generalisation and performance with zero additional traffic data. Code for this paper is available at https://github.com/mattchrlw/forecasting-on-new-roads.

Efficient material logistics play a critical role in controlling costs and schedules in the construction industry. However, manual material handling remains prone to inefficiencies, delays, and safety risks. Autonomous forklifts offer a promising solution to streamline on-site logistics, reducing reliance on human operators and mitigating labor shortages. This paper presents the development and evaluation of the Autonomous Dynamic All-terrain Pallet Transporter (ADAPT), a fully autonomous off-road forklift designed for construction environments. Unlike structured warehouse settings, construction sites pose significant challenges, including dynamic obstacles, unstructured terrain, and varying weather conditions. To address these challenges, our system integrates AI-driven perception techniques with traditional approaches for decision making, planning, and control, enabling reliable operation in complex environments. We validate the system through extensive real-world testing, comparing its long-term performance against an experienced human operator across various weather conditions. We also provide a comprehensive analysis of challenges and key lessons learned, contributing to the advancement of autonomous heavy machinery. Our findings demonstrate that autonomous outdoor forklifts can operate near human-level performance, offering a viable path toward safer and more efficient construction logistics.