Embodied world models aim to predict and interact with the physical world through visual observations and actions. However, existing models struggle to accurately translate low-level actions (e.g., joint positions) into precise robotic movements in predicted frames, leading to inconsistencies with real-world physical interactions. To address these limitations, we propose MTV-World, an embodied world model that introduces Multi-view Trajectory-Video control for precise visuomotor prediction. Specifically, instead of directly using low-level actions for control, we employ trajectory videos obtained through camera intrinsic and extrinsic parameters and Cartesian-space transformation as control signals. However, projecting 3D raw actions onto 2D images inevitably causes a loss of spatial information, making a single view insufficient for accurate interaction modeling. To overcome this, we introduce a multi-view framework that compensates for spatial information loss and ensures high-consistency with physical world. MTV-World forecasts future frames based on multi-view trajectory videos as input and conditioning on an initial frame per view. Furthermore, to systematically evaluate both robotic motion precision and object interaction accuracy, we develop an auto-evaluation pipeline leveraging multimodal large models and referring video object segmentation models. To measure spatial consistency, we formulate it as an object location matching problem and adopt the Jaccard Index as the evaluation metric. Extensive experiments demonstrate that MTV-World achieves precise control execution and accurate physical interaction modeling in complex dual-arm scenarios.

Spatial intelligence spans a rich suite of abilities, including visualising and transforming shapes, mentally rotating objects, judging relational positions and containment, and estimating numerosity. However, it still remains a critical unresolved challenge for Multimodal Large Language Models (MLLMs). To fill this gap, we propose to treat Euclidean geometry problem-solving as a surrogate task. Specifically, we meticulously constructed a curated multimodal dataset, called Euclid30K, comprising approximately 30K plane and solid geometry problems. Furthermore, to enable the model to learn and apply Euclidean principles from these geometry problems, we fine-tuned seven model variants (spanning 3--72B parameters) from the Qwen2.5VL, Qwen3VL, and RoboBrain2.0 families using Group Relative Policy Optimization (GRPO), inspiring the models to identify shapes, count, and relate entities, and perform multi-step deductive reasoning using Euclidean principles. Our experiments demonstrate that the resulting models achieve substantial zero-shot gains across four spatial reasoning benchmarks (Super-CLEVR, Omni3DBench, VSI-Bench, and MindCube) without any task-specific adaptations. Notably, after training on the Euclid30K, the mean VSI-Bench accuracy rose from 36.6\% to 41.8\% (+5.2\%), and the mean MindCube accuracy rose from 31.4\% to 38.1\% (+6.7\%). To our knowledge, this is the first systematic study showing that geometry-centric fine-tuning can confer vision-language models with broadly transferable spatial skills. Code and Euclid30K dataset can be found in \href{https://zgca-ai4edu.github.io/Euclids_Gift}{this}.

Vision--language--action (VLA) models have recently shown promising performance on a variety of embodied tasks, yet they still fall short in reliability and generalization, especially when deployed across different embodiments or real-world environments. In this work, we introduce NORA-1.5, a VLA model built from the pre-trained NORA backbone by adding to it a flow-matching-based action expert. This architectural enhancement alone yields substantial performance gains, enabling NORA-1.5 to outperform NORA and several state-of-the-art VLA models across both simulated and real-world benchmarks. To further improve robustness and task success, we develop a set of reward models for post-training VLA policies. Our rewards combine (i) an action-conditioned world model (WM) that evaluates whether generated actions lead toward the desired goal, and (ii) a deviation-from-ground-truth heuristic that distinguishes good actions from poor ones. Using these reward signals, we construct preference datasets and adapt NORA-1.5 to target embodiments through direct preference optimization (DPO). Extensive evaluations show that reward-driven post-training consistently improves performance in both simulation and real-robot settings, demonstrating significant VLA model-reliability gains through simple yet effective reward models. Our findings highlight NORA-1.5 and reward-guided post-training as a viable path toward more dependable embodied agents suitable for real-world deployment.

Place recognition--the process of an animal, person or robot recognizing a familiar location in the world--has attracted significant attention across multiple disciplines. In animals, this capability has evolved over millions of years through sophisticated neural mechanisms: hippocampal place cells fire at specific spatial locations (1), entorhinal grid cells provide spatial coordinates through hexagonal firing patterns (2), while diverse species demonstrate remarkable navigation--from desert ants using celestial cues and visual panoramas (3) to migratory birds returning to precise breeding sites across hemispheric distances (4). Humans extend these biological foundations with unique cognitive abilities, recognizing places not only through sensory perception but also through semantic meaning, emotional associations, and cultural context--enabling us to identify familiar locations from descriptions, memories, or even fictional narratives (5). In artificial systems, place recognition underpins core robotics functions such as localization, mapping, and long-term autonomy, developing into a mature field that, while sometimes inspired by biological principles, often diverges significantly in implementation to optimize for computational efficiency and metric accuracy. As research has grown in the area, so too has a rich landscape of surveys and reviews that reflect the field's evolution and diversification.

Large language models (LLMs) and vision language models (VLMs), such as DeepSeek R1,OpenAI o3, and Gemini 2.5 Pro, have demonstrated remarkable reasoning capabilities across logical inference, problem solving, and decision making. However, spatial reasoning:a fundamental component of human cognition that includes mental rotation, navigation, and spatial relationship comprehension remains a significant challenge for current advanced VLMs. We hypothesize that imagination, the internal simulation of spatial states, is the dominant reasoning mechanism within a spatial world model. To test this hypothesis and systematically probe current VLM spatial reasoning mechanisms, we introduce SpatiaLite, a fully synthetic benchmark that jointly measures spatial reasoning accuracy and reasoning efficiency. Comprehensive experiments reveal three key findings. First, advanced VLMs predominantly rely on linguistic representations for reasoning and imagination, resulting in significant deficiencies on visual centric tasks that demand perceptual spatial relations and 3D geometry transformations such as mental rotation or projection prediction. Second, advanced VLMs exhibit severe inefficiency in their current spatial reasoning mechanisms, with token usage growing rapidly as transformation complexity increases. Third, we propose an Imagery Driven Framework (IDF) for data synthesis and training, which can implicitly construct an internal world model that is critical for spatial reasoning in VLMs. Building on SpatiaLite, this work delineates the spatial reasoning limits and patterns of advanced VLMs, identifies key shortcomings, and informs future advances

Trajectory representation learning (TRL) maps trajectories to vector embeddings and facilitates tasks such as trajectory classification and similarity search. State-of-the-art (SOTA) TRL methods transform raw GPS trajectories to grid or road trajectories to capture high-level travel semantics, i.e., regions and roads. However, they lose fine-grained spatial-temporal details as multiple GPS points are grouped into a single grid cell or road segment. To tackle this problem, we propose the BLUrred Encoding method, dubbed BLUE, which gradually reduces the precision of GPS coordinates to create hierarchical patches with multiple levels. The low-level patches are small and preserve fine-grained spatial-temporal details, while the high-level patches are large and capture overall travel patterns. To complement different patch levels with each other, our BLUE is an encoder-decoder model with a pyramid structure. At each patch level, a Transformer is used to learn the trajectory embedding at the current level, while pooling prepares inputs for the higher level in the encoder, and up-resolution provides guidance for the lower level in the decoder. BLUE is trained using the trajectory reconstruction task with the MSE loss. We compare BLUE with 8 SOTA TRL methods for 3 downstream tasks, the results show that BLUE consistently achieves higher accuracy than all baselines, outperforming the best-performing baselines by an average of 30.90%. Our code is available at https://github.com/slzhou-xy/BLUE.

Recent advances in machine learning have been supported by the emergence of domain-specific software libraries, enabling streamlined workflows and increased reproducibility. For geospatial machine learning (GeoML), the availability of Earth observation data has outpaced the development of domain libraries to handle its unique challenges, such as varying spatial resolutions, spectral properties, temporal cadence, data coverage, coordinate systems, and file formats. This chapter presents a comprehensive overview of GeoML libraries, analyzing their evolution, core functionalities, and the current ecosystem. It also introduces popular GeoML libraries such as TorchGeo, eo-learn, and Raster Vision, detailing their architecture, supported data types, and integration with ML frameworks. Additionally, it discusses common methodologies for data preprocessing, spatial--temporal joins, benchmarking, and the use of pretrained models. Through a case study in crop type mapping, it demonstrates practical applications of these tools. Best practices in software design, licensing, and testing are highlighted, along with open challenges and future directions, particularly the rise of foundation models and the need for governance in open-source geospatial software. Our aim is to guide practitioners, developers, and researchers in navigating and contributing to the rapidly evolving GeoML landscape.

Vision-centric hierarchical embodied models have demonstrated strong potential. However, existing methods lack spatial awareness capabilities, limiting their effectiveness in bridging visual plans to actionable control in complex environments. T o address this problem, we propose Spatial Policy (SP), a unified spatial-aware visuomotor robotic manipulation framework via explicit spatial modeling and reasoning. Specifically, we first design a spatial-conditioned embodied video generation module to model spatially guided predictions through the spatial plan table. Then, we propose a flow-based action prediction module to infer executable actions with coordination. Finally, we propose a spatial reasoning feedback policy to refine the spatial plan table via dual-stage replanning. Extensive experiments show that SP substantially outperforms state-of-the-art baselines, achieving over 33% improvement on Meta-W orld and over 25% improvement on iTHOR, demonstrating strong effectiveness across 23 embodied control tasks. W e additionally evaluate SP in real-world robotic experiments to verify its practical viability. SP enhances the practicality of embodied models for robotic control applications.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets, such as graphs and point clouds.

Deformable transformers deliver state-of-the-art detection but map poorly to hardware due to irregular memory access and low arithmetic intensity. We introduce QUILL, a schedule-aware accelerator that turns deformable attention into cache-friendly, single-pass work. At its core, Distance-based Out-of-Order Querying (DOOQ) orders queries by spatial proximity; the look-ahead drives a region prefetch into an alternate buffer--forming a schedule-aware prefetch loop that overlaps memory and compute. A fused MSDeformAttn engine executes interpolation, Softmax, aggregation, and the final projection (W''m) in one pass without spilling intermediates, while small tensors are kept on-chip and surrounding dense layers run on integrated GEMMs. Implemented as RTL and evaluated end-to-end, QUILL achieves up to 7.29x higher throughput and 47.3x better energy efficiency than an RTX 4090, and exceeds prior accelerators by 3.26-9.82x in throughput and 2.01-6.07x in energy efficiency. With mixed-precision quantization, accuracy tracks FP32 within <=0.9 AP across Deformable and Sparse DETR variants. By converting sparsity into locality--and locality into utilization--QUILL delivers consistent, end-to-end speedups.