Spatial Reasoning

As vision-language models (VLMs) are increasingly deployed in geospatial question answering and visual scene understanding, improving their spatial cognition capability on street view imagery for complex logical reasoning has emerged as a key research priority. However, existing VLMs frequently suffer from "spatial semantic hallucinations" when perceiving object locations, distances, and directions in real-world street view scenes. Furthermore, such errors are often recalcitrant to tracing and calibration, posing a critical bottleneck for their practical deployment in geospatial tasks. To address this pressing challenge, this study proposes DM-KG (Direction-Metric Knowledge Graph), a structurally grounded spatial representation framework for street view imagery. By explicitly extracting directional and metric relationships between entities from a single 2D image, this framework enhances the spatial reasoning accuracy of VLMs through a structured knowledge graph. Specifically, we integrate panoptic segmentation with metric depth estimation to robustly compute entity-level 3D spatial coordinates. Subsequently, we encode the clock azimuths and Euclidean distances of entity pairs into a JSON-formatted knowledge graph, which is injected into the VLM as an explicit geometric prior to guide spatial reasoning. Experimental results on public spatial question-answering (QA) benchmarks demonstrate that DM-KG reduces the mean absolute error (MAE) in distance estimation by 31.1% and the mean angular error in direction judgment by 65.8%, while simultaneously maintaining a high QA success rate. By establishing a complete, augmented reasoning pipeline, this research significantly improves the spatial cognitive capabilities of VLMs in street view scenarios, thereby providing a flexible, generalized, and interpretable framework for geographic visual question answering (GeoVQA) in open environments.

Vision-language models (VLMs) are expected to reason about physical space -- which object is closer, what lies behind what, and how objects are arranged in 3D -- yet they still struggle with such spatial judgments. A natural remedy is to show the model a depth map, but we find that this can make performance worse. We show that depth is not absent: it reaches the language model, but becomes difficult to access for downstream reasoning, while rendered pseudo-depth maps act as noisy auxiliary images that frozen VLMs cannot easily regulate. We propose Depth-Ordinal Prompting (DOP), a training-free method that converts monocular depth into a single question-targeted ordinal text cue at the queried objects, without adding a depth image, training a module, injecting features, or using labels. Our key finding is form dependence: the same depth signal can hurt when shown as an image but help when told as text.Across benchmarks, models, and depth estimators, DOP improves spatial reasoning when pseudo-depth provides reliable object-level ordering and remains largely neutral in strong original-image regimes. It is also competitive with the strongest training-free depth-prompting alternative while being simpler and more targeted.

One of the expected abilities of vision-language models (VLMs) is spatial reasoning ability based on a given text and image. To evaluate the spatial reasoning abilities of VLMs, we focus on the use of spatial deictic expressions, which are defined as spatial expressions whose referent is determined by their situational context, such as this'' and that''. To handle spatial deictic expressions, VLMs must jointly reason over language and visual space, grounding context-dependent references in the image's spatial structure. In addition, selecting appropriate spatial deictic expressions across languages requires VLMs to understand the language-specific spatial distinctions encoded by these expressions. In this paper, we develop a benchmark to evaluate the multilingual ability of VLMs to use spatial deictic expressions in four languages. Our experiments using this benchmark reveal that the tested models use demonstratives in a manner different from that of humans, particularly in selecting the appropriate demonstratives based on the distance to the object.

Natural-language queries about 3D environments become actionable when responses are verifiable and metric. Verifiability requires explicit grounding to the referred 3D region, while metric answers report physical measurements in real-world units (e.g., size, thickness, clearance, and distance). Existing 3D large multimodal models (LMMs) approaches remain limited: conversational systems typically respond without explicit 3D grounding, while 3D grounding models are not designed for interactive, metric-aware dialogue. In this paper, we present Ground3D-LMM, a unified model that takes a point cloud and an optional RGB image as input and supports 3D spatial conversation with (i) point-grounded responses and (ii) metric numeric outputs at both object and part granularity, including multi-object queries. To evaluate this intersection of grounding and measurement, we define the 3D Grounded Measurement task, which requires predicting the referred 3D region and the corresponding metric quantities in real-world units. We introduce a large-scale dataset built on ScanNet and ScanNet++ datasets with dense object and part annotations and roughly 2.5M question-answer pairs spanning eight tasks, along with a manually verified test set. Extensive experiments on multiple datasets and tasks show that our proposed Ground3D-LMM model provides a strong baseline for grounded, metric-aware 3D conversational understanding. Our dataset and model are publicly available.

Learning motion latents for robotic manipulation heavily relies on extracting motion patterns from visual sequences, yet effective action abstractions require understanding three-dimensional geometric transformations. Here, we introduce GeoMoLa (Geometry-Aware Motion Latents), which learns discrete motion latent codes by predicting how point clouds evolve during manipulation rather than reconstructing visual observations. This four-dimensional objective -- spatial geometry changing through time -- forces latent representations to encode actual physical motion rather than appearance patterns. GeoMoLa achieves state-of-the-art performance using only single-view RGB-D input, while existing methods require multi-view reconstruction, succeeding across diverse manipulation benchmarks. Our ablations reveal that geometric prediction is the key to driving performance, quantitatively validating that manipulation depends on spatial understanding. Furthermore, the learned codes exhibit effective motion abstraction: applying them to novel scenes produces physically consistent transformations regardless of visual context. Our real-world experiments also confirm this robustness capability, achieving robust manipulation with minimal demonstrations in cluttered environments where geometric reasoning determines success. Thus, we demonstrate that effective motion latents for robot control can better emerge from understanding motion through its three-dimensional effects rather than pixel-level patterns.

Human spatial understanding arises from jointly perceiving geometry and semantics, enabling consistent object identification and localization across viewpoints and time. Current video segmentation models depend on explicit object appearance memory banks for instance tracking, yet they remain vulnerable to large viewpoint changes and long-term occlusions. Leveraging the spatial consistency afforded by modern feed-forward 3D reconstruction models, we propose the Geometry Grounded Tracking Anything Model (G$^2$TAM), a unified framework for promptable instance tracking in 3D using only unordered RGB images or videos. G$^2$TAM employs spatially aligned geometric representations as implicit memory, ensuring stable instance identity and localization across frames and views. At its core is a cross-modal spatial encoder that integrates visual and textual prompts into a shared geometric space, enabling end-to-end spatial reconstruction and instance-consistent mask prediction. To support training and evaluation, we construct InsTrack, a large-scale dataset with a dedicated validation split for benchmarking. Extensive experiments show that G$^2$TAM delivers strong cross-view consistency, promptable instance spatial tracking, video object segmentation and spatial reconstruction, establishing a foundation for interactive, geometry-grounded spatial reasoning.

Recent large language models (LLMs) have demonstrated remarkable progress in 3D spatial reasoning, spatial grounding, and fine-grained geometric understanding. However, their ability to reason about densely packed object placement under strict spatial and functional constraints remains largely unexplored, despite being a fundamental challenge in practical electronic design automation (EDA) workflows. To bridge this gap, we introduce OmniLayout, the first benchmark designed to evaluate LLMs on printed-circuit-board (PCB) layout placement reasoning under real-world geometric, routing, and connectivity constraints. OmniLayout contains 1,681 industrial-grade schematic-coupled PCB layouts and includes four tasks: (1) geometric reasoning for IC physical placement, with 77.24K placement instances constrained within PCB board boundaries; (2) routability-aware placement reasoning, generating physically valid component placements; (3) electrical functionality, preserving schematic-specified connectivity and electronic functional correctness; and (4) tool-augmented agentic reasoning for invoking external tools to accomplish tasks (1)-(3). Our results reveal substantial limitations of current LLMs in PCB layout placement, including weak geometric reasoning, poor routability optimization, and inconsistent preservation of electrical functionality.

Quantitative 3D spatial reasoning from egocentric RGB-D video is a critical capability for next-generation wearable assistants. Yet existing benchmarks do not reflect the challenges of handling (1) natural egocentric video, (2) posed RGB-D video inputs, and (3) challenging quantitative 3D spatial reasoning Q&A. To fill this gap, we introduce R3D-Bench (Reasoning in 3D), a benchmark of 3,033 quantitative spatial reasoning questions across 15 types -- spanning multiple-choice, distance-based, and volumetric reasoning questions -- built on top of 57 egocentric video sequences from Aria Digital Twin. To set a strong baseline on this dataset, we introduce R3D, a model-agnostic spatial tool-calling framework. In contrast to existing approaches that directly embed 3D information into the model's input representation, R3D constructs a 3D scene from video using segmentation and depth-lifted object representations. It provides this information to an LLM through eight composable spatial tools. On R3D-Bench, R3D with Qwen3-VL 235B achieves 73.5% mean relative accuracy, substantially outperforming the best depth-enabled baseline (CuTR+Tools, 61.9%) and the best RGB-only baseline (Gemini 3 Flash, 46.5%).

While Multimodal Large Language Models (MLLMs) have demonstrated exceptional capabilities in standard visual understanding, adapting them for active visual search in 360$^\circ$ panoramic environments exposes fundamental limitations. Specifically, standard MLLMs struggle to effectively model inherent panoramic properties, such as severe polar distortion and continuous cylindrical topologies, which significantly degrades target detection accuracy. Consequently, existing panoramic search methods attempt to compensate by relying heavily on fragmented local viewpoints. Burdened by rigid initialization and a lack of global panoramic priors, these approaches suffer from myopic, inefficient exploration and struggle with robust error recovery when targets are out of view. To overcome these challenges, we propose EAGLE-360, a novel Embodied Active Global-to-Local Exploration framework. Rather than performing exhaustive local searches, EAGLE-360 leverages global priors to establish an initial holistic perspective, iteratively reasoning and progressively narrowing the search space. Architecturally, we adapt RoPE Rolling, a coordinate-shifting positional encoding mechanism, to seamlessly model the continuous topologies of panoramas. To facilitate this paradigm, we construct the large-scale EAGLE-360 dataset, comprising 14,000+ 4K panoramas and 70,000+ rounds of high-quality VQA dialogues. By employing a training pipeline that integrates Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO), we effectively elicit complex spatial reasoning and tool-calling capabilities. Extensive experiments demonstrate that EAGLE-360 establishes a new state-of-the-art for 360$^\circ$ visual search, achieving nearly an 8-fold increase in accuracy over the base model while significantly enhancing exploration efficiency.

Visual-spatial understanding, defined as the ability to infer object relationships and scene layouts from visual inputs, is fundamental to downstream tasks such as robotic navigation and embodied interaction. However, pre-trained vision-language models (VLMs) remain constrained by spatial uncertainty stemming from inherently 2D observations and by the scarcity of data for 3D spatial understanding. To address these limitations, we proposed a novel framework, SpaceEra, in the NeurIPS 2025 Spotlight paper. Although it achieved significant performance gains, we further observed that its effectiveness is hindered by insufficient input from scanning videos and weak reasoning constraints. To tackle these newly emerged challenges, we extend the original framework into a comprehensive system, termed SpaceEra++, which spans data construction, model design, training optimization, and prompting inference. Specifically, to alleviate input insufficiency, we introduce ScenePick, a frame sampling strategy that balances spatial coverage with object semantics to produce compact yet comprehensive scene representations. In addition, to enhance spatial reasoning, we develop SpaceAlign, which enforces pairwise object constraints by jointly exploiting absolute coordinates and relative spatial relations, thereby aligning optimization with spatial accuracy. Extensive experiments across multiple benchmarks demonstrate consistent improvements over strong baselines, while ablation studies validate both the individual and joint contributions of each component, and further analyses provide guidance for future research.

We address robot localization in GPS-denied indoor environments by reframing it as a semantic reasoning task rather than a geometric estimation problem. Motivated by how humans localize using object-level cues and labeled maps, we ask whether a vision-language model, given a front camera image, a polar LiDAR scan, and a top-down semantic grid map, can infer the robot pose. We fine-tune Qwen2.5-VL-7B with LoRA and attach a lightweight regression head that predicts continuous pose coordinates (x, y, theta) directly from the final hidden state, bypassing text generation. Training uses a composite position-and-direction loss with curriculum learning on a custom Gazebo dataset of 120,112 samples and 527 scenes. On the in-distribution test set of 18,017 samples, the model achieves 98.23 percent position accuracy, 98.00 percent direction accuracy, 96.75 percent full pose accuracy, a mean position error of 0.11 m, and a mean orientation error of 5.7 degrees at 0.62 s per sample. Position accuracy drops by only 7.2 percentage points on seven unseen object categories, reaching 90.99 percent, supporting semantic spatial reasoning rather than appearance memorization. With incomplete maps, fine-tuning recovers performance to 93.72 percent position accuracy, showing adaptability to stale or partial map information. Two ablations highlight cross-modal complementarity. Without LiDAR, using only camera and map inputs, position accuracy remains 95.06 percent, only 3.2 percentage points below the full system. However, when the camera sees no visible objects in a wall-facing view, LiDAR sustains 92.33 percent position accuracy, compared with 70.74 percent when neither LiDAR nor visible objects are available. This shows that LiDAR becomes the primary localization signal when camera semantics are unavailable and provides a reliable fallback under occlusion or sparse layouts.

Spatial intelligence remains a persistent challenge for Multimodal Large Language Models (MLLMs), as it requires coherent spatial scene representations beyond basic object recognition. Existing methods typically build such representations through textual reasoning or 3D reconstruction. However, they often falter during multi-step reasoning, particularly when required to dynamically re-anchor evidence to the specific camera-, object-, or direction-centric reference frames demanded by complex queries. To address this, we propose OmniView-Space, a framework designed to maintain spatial consistency through multimodal egocentric evidence. Our approach consists of three core components: (1) Multi-Perspective Spatial Mapping (MPSM), which re-anchors reconstructed geometry into a query-aligned visual cognitive map and a textual spatial graph; (2) Tool-Guided Egocentric Reasoning, an interleaved policy trained to actively select the ego anchor required by the query and request the corresponding MPSM evidence; and (3) Cognitive-Map Distillation, which uses MPSM-generated trajectories and ego-frame rewards to train the model to reason with self-generated cognitive maps. Experiments on single- and multi-image spatial reasoning benchmarks show that OmniView-Space achieves state-of-the-art performance. Furthermore, the distilled model maintains this performance while reducing reliance on external geometry pipelines.

Benchmarks for vision-language models (VLMs) mostly test observational spatial reasoning: models describe relations already visible in the input. Existing what-if tasks typically vary the observer while keeping the scene fixed. Can VLMs instead predict the consequences of hypothetically moving or rotating an object? We introduce MindEdit-Bench, a benchmark of six spatial reasoning tasks built from three-photo smartphone triplets of newly captured indoor scenes via an automatic in-the-wild 3D scene-graph extraction pipeline. Four tasks probe perception and perspective transformation over observed structure; two new tasks, L4 (spatial editing) and L5 (cross-view visibility editing), probe object-level counterfactual reasoning, where correct answers are absent from all input images. Each question provides 8-24 structured answer choices, enabling answer-letter-level diagnosis of spatial and fallback errors. The benchmark covers 120 private indoor scenes not drawn from public datasets, reducing public-data pretraining-overlap risk. Across 15 VLMs on 1,003 human-verified questions, task-wise mean VLM accuracy is only 8%-31%, versus 81%-97% human majority-vote accuracy. The pooled human--best-VLM gap is 53 pp, with at least 39 pp on every task. The structured answer space further reveals non-uniform failures, including weaker camera-depth-axis inference and fallback behavior on difficult visibility-editing cases.

Vision-language models achieve strong general perception but often struggle with the spatial reasoning required for embodied tasks. We present RoboSpatialBrain, our submission to the RoboSpatial Challenge at the Embodied Reasoning in Action Workshop, CVPR 2026, built on RoboBrain2.5-8B-NV. RoboSpatialBrain combines two training-free, inference-time mechanisms: a forced <think> prefix activation strategy paired with a task-specific post-prompt that elicits deliberate reasoning on context and compatibility tasks, and an explicit reference-frame redirection pipeline that resolves camera-centric and object-centric ambiguity for context tasks. We additionally explore fine-tuning RoboBrain2.5 on compatibility data and present a detailed analysis of its interaction with prompting. RoboSpatialBrain achieved first place in the RoboSpatial Challenge, with an overall success rate of 80.9% on RoboSpatial-Home. Code is available at https://github.com/YuxiangXie2003/RoboSpatialBrain.

With the rapid advancement of aerospace embodied intelligence, enabling Unmanned Aerial Vehicles (UAVs) to autonomously understand and reason about complex environments has become increasingly important. However, existing UAV-based spatial reasoning approaches face critical limitations: single-view perception renders them vulnerable to occlusions and perspective distortions, while most VLMs lack explicit geometric modeling, relying on semantic cues and yielding inconsistent reasoning under viewpoint and scale variations. To address these challenges, we propose SatAgent, a UAV-Satellite collaborative spatial reasoning model inspired by the dual-pathway mechanism of the human visual system. By jointly leveraging satellite and UAV perspectives, SatAgent enables robust, accurate reasoning in complex urban environments. We first introduce a Geometric-Aware 3D Reconstruction Encoder that elevates 2D UAV features into explicit 3D spatial representations. Next, we design a multi-view topology-semantic alignment module integrating cross-view features within a unified BEV coordinate system. We further introduce a multi-view consistency loss encouraging viewpoint-invariant representations. Finally, we construct SatAgent-SR130K, the first large-scale UAV-Satellite collaborative multi-view spatial reasoning dataset. Experiments show SatAgent outperforms state-of-the-art general-purpose foundation models and specialized spatial reasoning models by 25.91% and 11.69%, respectively, across diverse tasks, achieving particularly high accuracy in complex geometric relationship reasoning.

Human reasoning is inherently multimodal: when problems become difficult, we rarely think in words alone. We often externalize our reasoning by sketching diagrams or drawing grids to understand the underlying conceptual structure and avoid mistakes. Building on this premise, our research investigates: (a) whether grounding multi-hop textual-spatial stories into geometry-aware modalities, such as layouts or grids, improves reasoning compared to natural language-based inference; and (b) whether a model can decide when to rely on natural language reasoning and when to switch to a structured modality. We address these questions by introducing a switching metric based on trustworthiness and complexity signals, which estimates when grounding a spatial story into structure is likely to improve performance. This takes a first step toward principled modality selection in Large Language Model (LLM) reasoning. Across our settings, switching from natural language-based reasoning to a grid-based representation improves LLM performance by up to 42%, highlighting the importance of modality choice in shaping reasoning outcomes.

The standard way to read latent knowledge out of a model, a linear probe confirmed by a steering recovery, can systematically overstate what a vision-language model (VLM) actually grounds in the image. We show this on spatial reasoning, where the error is invisible to both probing and steering yet exposed by a one-line causal control: replacing the image with a gray blank. Probes decode the within-axis answer at 73--97% across axes, and a training-free projection lifts a near-chance axis from 59% to 79%, exactly the signature of unlocking latent knowledge. The blank-image arbiter refutes it, revealing three grounding regimes that probing conflates: an axis can be grounded (vision-dependent, correct), a prior (vision-independent, with its decode and its apparent recovery a directional default rather than perception), or, surprisingly, inverted: decodable, causally controllable, but deployed with the wrong sign, so the model scores below chance and the error requires looking. The taxonomy holds across the studied VLMs: in fourteen models spanning six language-model families and 2B--27B, horizontal is grounded, vertical is a prior, and depth is inverted, with the inversion emerging at scale within families. The decode-versus-deploy inversion replicates on seven of eight models across five families, and the minimal edit that re-deploys it varies with geometry: a training-free rotation matches a trained edit on the cleanest model, while distributed inversions need a trained low-rank edit, tracing a per-model correction-complexity spectrum. The cheap, self-calibrating arbiter cleanly separates grounded perception, inverted perception, and prior substitution; we argue it should be a default control for latent-knowledge and steering claims in VLMs.

Multimodal Large Language Models (MLLMs) have demonstrated promising spatial reasoning capabilities, while these abilities remain underexplored in the emerging visual modality of panoramic imagery. The full 360°$\times$180° field of view of panoramas essentially supports complex global multi-step reasoning, which is also the fundamental advantage of panoramas in applications such as embodied intelligence. However, existing panoramic benchmarks largely focus on simplistic queries that rely on local cues or single-/few-step reasoning, thereby ignoring the fundamental advantage of panoramas and failing to fully exploit their potential. To address this gap, we introduce OmniCoT, a panoramic spatial reasoning suite designed to enable MLLMs to use global evidence and perform multi-step inference across viewpoints. It includes OmniCoT-B (6.7K data) for evaluation, which measures both answer accuracy and reasoning quality, OmniCoT-Real (1K data) as a manually annotated real-world subset to quantify the Sim-to-Real gap. For training, OmniCoT-T (14.3K data) is purpose-built with structured stepwise Chain-of-Thought annotations that explicitly link intermediate reasoning steps to panoramic evidence. Based on OmniCoT-T, we introduce OmniCoT-R1 and adopt a two-stage training strategy tailored to the geometrically complex panoramic space, where Supervised Fine-tuning (SFT) anchors reasoning to panoramic evidence (e.g., bearings, proximity) and GRPO penalizes geometrically incoherent paths to consolidate global 360° spatial consistency. Through OmniCoT, we aim to recalibrate the difficulty of panoramic spatial reasoning to better align with the intrinsic capabilities of panoramic imagery, thereby fostering meaningful progress in this research area.

Spatial reasoning remains a persistent challenge for many vision language models (VLMs), and improving it typically requires fine-tuning with substantial additional parameters. Our preliminary analysis reveals that rescaling activations in selected transformer layers-without modifying pretrained weights-can significantly influence downstream performance. Motivated by this observation, we propose ScAle, an ultra-lightweight adaptation method that learns a small set of scalar coefficients to modulate last-token attention and MLP activations in a fully frozen backbone. We evaluate our method on the synthetic spatial reasoning benchmark SpatialEval and on real-world VQA datasets (COCOQA and VGQA) across multiple model families. Our method, ScAle, achieves up to 134.1% relative accuracy gains using only 1K trainable parameters without requiring millions of trainable parameters as in standard PEFT methods such as LoRA. Despite its extreme compactness, our approach recovers a substantial fraction of standard PEFT performance while preserving strong non-spatial VQA accuracy. These results demonstrate that bounded activation reweighting provides a simple, architecture-agnostic, and highly parameter-efficient alternative for adapting pretrained VLMs.

Current VLM evaluations often conflate language priors with genuine spatial reasoning. To address this, we introduce CRISP, a novel structural-diagnostic evaluation paradigm that assesses visual spatial intelligence through consistency, the alignment between implicit perception and explicit reasoning. Unlike traditional black-box QA, CRISP utilizes metric 3D Scene Graphs and an oracle intervention protocol to decouple latent reasoning capabilities from perceptual bottlenecks. This granular diagnosis uncovers a systematic perception-reasoning disconnect. Crucially, we reveal that while proprietary models possess robust latent reasoning engines, they suffer from inaccurate metric estimation and a critical failure to leverage their implicit structural representations. Conversely, open-source models remain fundamentally bottlenecked by their lack of multi-hop compositional reasoning. By shifting the focus from merely guessing correctly'' via language priors to genuinely perceiving, verifying, and reasoning,'' CRISP offers a rigorous roadmap for multimodal alignment beyond end-to-end post-training. The code and dataset are available at https://github.com/iiyamayuki/CRISP-Bench.

This paper presents a modular training-free framework for zero-shot, language-guided robotic manipulation in semi-structured environments. The architecture bridges the gap between high-level reasoning and low-level kinematics by decomposing the vision-action pipeline into three stages: visual perception, semantic interpretation, and task execution. To overcome the spatial ambiguity and semantic hallucinations inherent in standard Vision-Language Models (VLMs), the perception module employs FastSAM and Set-of-Mark (SoM) prompting to dynamically generate grounded, alphanumeric visual anchors. The same foundation model then operates purely as a Large Language Model (LLM) to act as a semantic router, translating unconstrained human directives into verifiable, reconfigurable configurations. Finally, these configurations are dynamically parsed by a Task Orchestrator into MoveIt Task Constructor (MTC) to generate collision-free trajectories. The framework is evaluated across two zero-shot experimental setups: unconstrained open-world sequential manipulation and dense relational spatial reasoning, achieving a 62% end-to-end task success rate across both scenarios, demonstrating its capacity to reliably execute complex physical actions without domain-specific training or manual coordinate programming.

There have been many recent improvements in the ability of Large Language Models (LLMs) to perform complex tasks and answer domain-specific questions through techniques like Retrieval Augmented Generation (RAG). However, reasoning abilities of LLMs, including spatial reasoning abilities, are still lacking. Spatial reasoning is a key component required to answer questions in a variety of domains that are grounded in the physical world, including urban planning, civil engineering, travel, and many others. To advance the development of LLMs and facilitate an impact in these domains, new research techniques must be developed to enable LLMs to reason over spatial data, which is commonly stored in the form of a graph. In this paper we outline the challenges associated with spatial reasoning through LLMs and envision a future in which search engines integrate with LLMs to answer complex spatial questions through graph-enhanced reasoning.

Vision-Language Models (VLMs) remain unreliable when spatial reasoning requires composing relations whose meanings depend on frames of reference. Existing neuro-symbolic methods make reasoning more explicit, but often depend on brittle geometric procedures and hard decisions over noisy perception. We propose SATURN, a neuro-symbolic framework for perspective-aware compositional spatial reasoning. SATURN reconstructs an approximate 3D scene, derives soft perspective-aware spatial predicates, and composes them with a training-free Pythonic symbolic executor, separating perception from reasoning while preserving uncertainty through multi-hop inference. We also introduce 3D FORCE, a diagnostic benchmark that controls reasoning depth, view, and perspective composition across spatial arrangement grounding (SAG) and referring expression grounding (REF). On 3D FORCE, VLMs and spatially trained models degrade sharply as depth and perspective complexity increase, whereas SATURN remains stable and outperforms strong baselines. On the real-world MindCube benchmark, SATURN achieves 78.57% overall accuracy, outperforming the strongest baseline by 14 pp.

Humans can effortlessly reason about scenes across different viewpoints, yet it remains unclear whether Vision-Language Models (VLMs) possess similar cross-view spatial abilities. Satellite-street scene pairs, with their complex contexts and extreme viewpoint variations, provide an ideal testbed. Motivated by this, we introduce CVSBench, a large-scale benchmark for evaluating cross-view spatial reasoning through satellite-street pairs. This benchmark supports multiple tasks, including cross-view VQA, cross-view grounding, and viewpoint identification. CVSBench comprises 3,297 cross-view image groups with 9,468 object-level annotations and 40,679 question-answer (QA) pairs, enabling systematic and controlled evaluation of cross-view spatial reasoning. Extensive evaluations reveal that advanced VLMs struggle to maintain object-level and layout consistency under drastic viewpoint changes. To bridge this gap towards human-like spatial cognition, we investigate two categories of approaches: spatially grounded reasoning and the incorporation of cognitive map inputs. Our findings demonstrate that language-only reasoning yields marginal improvements, while incorporating visual spatial imagination via a 3D scene imagination pipeline substantially improves cross-view reasoning. These results highlight the necessity of explicit visual-spatial representations for robust spatial cognition in VLMs. Our data and code are released at https://huggingface.co/datasets/zlyzlyzly/CVSBench.

Epidemic forecasting models typically rely on surveillance data reported over administrative regions, treating them as atomic units, thereby obscuring sub-regional spatial structure that shapes disease dynamics. We introduce a spatially structured multimodal epidemic forecasting setting that integrates region-level temporal surveillance data with spatially localized auxiliary signals that are misaligned in resolution and structure, reflecting realistic public health reporting constraints. Building on this formulation, we propose M-SPICE (Multimodal SPatIal Context for Epidemic Forecasting), a structure-aware spatiotemporal forecasting framework that performs joint reasoning over temporal disease dynamics and spatial context via attention-based multimodal fusion, allowing spatial signals to selectively condition temporal representations across forecast horizons. We evaluate our approach on real-world COVID-19, influenza, and influenza-like illness (ILI) forecasting tasks under realistic real-time evaluation protocols. Across all forecasting settings, our method consistently outperforms state-of-the-art multivariate time-series, multimodal, and epidemiological forecasting baselines while maintaining strong probabilistic forecasting performance. Finally, interpretability analyses reveal when, where, and how spatial signals are leveraged, highlighting settings in which purely temporal, region-aggregated models are most likely to fail.

Robots operating in open-world environments must seamlessly integrate localization, spatial reasoning, navigation, and long-horizon planning. While specialist models excel at individual tasks, deploying a multi-model stack is computationally expensive and prone to cascading errors. We present Vesta, a unified embodied generalist that consolidates these capabilities into a single foundation model. Our approach combines a diverse and massive curated corpus designed to induce spatial grounding and a simple multimodal memory harness that enables reasoning over extended time horizons. Across diverse benchmarks, Vesta on average beats individual SOTA baselines by >$20\%$ and beats an ensemble of per-category-best baselines by $>10\%$ -- thus demonstrating that a generalist model can match or exceed specialists. On real-world robotic tasks requiring memory and reasoning, Vesta improves task success by >35%. Our work thus demonstrates that a single generalist is a feasible, scalable, and arguably preferable alternative to combining specialists.

Real-world spatial intelligence requires reasoning over a continuous and evolving 3D world, yet existing VLMs and tool-augmented agents largely remain tied to static, stateless inference from isolated visual observations. We introduce \textbf{\textsc{S-Agent}}, a spatial tool-use agentic paradigm for understanding and reasoning over continuous multi-view images and videos. By formulating spatial reasoning as spatio-temporal evidence accumulation rather than isolated frame-level prediction, \textsc{S-Agent} reshapes spatial perception into scene-centric understanding beyond frame-centric recognition. Specifically, \textsc{S-Agent} casts the VLM as a semantic planner that decides what evidence is needed, while a hierarchy of spatial tools and experts grounds objects in 2D, lifts them into 3D geometric evidence, and aggregates this evidence into high-level spatial knowledge (\textit{e.g.}, counting, measurement, orientation, and relative position). Additionally, a temporal memory mechanism, including Scene Memory for maintaining the evolving scene state and Agent Memory for accumulating reasoning context, enables evidence integration across frames and reasoning steps. Comprehensive experiments on multi-view and video spatial reasoning benchmarks show that \textsc{S-Agent} consistently improves both open-source and closed-source VLMs in a training-free manner. Beyond inference-time augmentation, supervised fine-tuning (SFT) on \textsc{S-Agent}-generated spatial trajectories \textsc{S-300K} yields \textsc{S-Agent-8B}, a compact spatial agent that significantly surpasses similar-scale baselines (e.g., Qwen3-VL-8B) and performs comparably to advanced closed-source models (e.g., GPT-5.4 and Gemini 3).

Existing approaches to 3D scene understanding in Vision-Language Models (VLMs) either rely on complex, model-specific geometry encoders or large training budgets in pursuit of spatial reasoning. Instead, OneCanvas aggregates patch features from all views onto a single equirectangular panoramic canvas. Namely, each patch is unprojected to a 3D world coordinate using its depth and camera pose, then placed on the canvas at the continuous longitude and latitude of that point as seen from the canvas origin, with no rasterization or aggregation across overlapping views. A 3D position embedding of the patch's metric coordinates is added to its feature, restoring the depth lost when collapsing the world position to an angular canvas coordinate. Patches from all frames thus share one spatial coordinate system with no fusion or major architectural modifications of the backbone. The pretrained VLM consumes this representation as if it were an ordinary image. Because the canvas can be centered on any pose of interest, the same representation directly supports situated reasoning from a specific viewpoint, a common requirement in robotics and embodied AI. Thanks to this representation, we can also introduce a spatial pretraining curriculum: by procedurally placing patch features of objects, drawn from real images, at chosen 3D world positions on an otherwise empty canvas, we generate on-the-fly supervision spanning a broad range of spatial reasoning tasks, with answer distributions controlled to reduce spatial reasoning shortcuts. OneCanvas achieves state-of-the-art accuracy on SQA3D and VSI-Bench, and generalizes to out-of-distribution data on SPBench, using an order of magnitude less training compute than the strongest competing methods.

Spatial VLMs have made substantial progress in geometric perception, yet complex spatial reasoning requiring multi-step inference over depth, distance, and scene relations remains challenging. Moreover, different spatial queries call for fundamentally different strategies: some are best addressed through purely linguistic, step-by-step deduction, while others require explicit 3D grounding before quantitative inference. We present Dual-Path Spatial Reasoning via Reinforcement Learning for Spatial VLMs (SR-REAL), a unified framework that equips a spatial VLM with two complementary reasoning paths: Language-Only Reasoning (LOR), which performs step-by-step linguistic deduction, and Detect-Then-Reason (DTR), which detects 3D geometric cues (e.g., centers or bounding boxes) via region tokens before explicit geometric inference. SR-REAL begins with a cold-start supervised fine-tuning stage that constructs LOR and DTR chain-of-thought supervision and exposes a region-to-3D interface, followed by RL that optimizes the policy model with accuracy and format rewards; for DTR, a discrete center-based detection reward further refines geometric alignment. Across diverse spatial benchmarks, SR-REAL significantly outperforms spatial VLM baselines: (i) a single RL-trained model supports both reasoning paths, with DTR excelling in region-aware tasks through precise 3D localization and LOR enhancing general spatial reasoning; (ii) jointly training both paths fosters mutual reinforcement; (iii) high-quality, blended cold-start data is crucial for stable RL optimization; and (iv) the model generalizes across datasets and domains without per-task tuning, demonstrating positive transfer between LOR and DTR.

Remote-sensing vision-language models (RS-VLMs) have advanced Earth-observation analysis toward visual interpretation and instruction-following, yet fall short of operational geo-intelligence, which demands tool-grounded spatial reasoning and structured, evidence-backed decisions. We introduce GeoDisaster, an operational geospatial disaster reasoning benchmark with 2,921 verified instances across 43 question types and five task families: deforestation monitoring, multi-hazard analysis, building-damage assessment, flood-safe routing, and Sentinel-1 SAR flood monitoring. Instances integrate heterogeneous EO/GIS evidence-optical and SAR imagery, raster masks, vector geometries, road networks, and exposure layers-spanning hazard detection, damage assessment, exposure estimation, and diagnostic report generation. Ground-truth answers are grounded in executable geospatial workflows and deterministic consistency checks, removing the need for language-model annotation. We further propose an orchestrated multi-agent framework with 18 disaster-oriented tools, where role-specialized agents coordinate through explicit execution contracts, aligned via Role-Contract Expectation Alignment (RCEA): failure-aware supervised fine-tuning combined with contract-grounded reinforcement learning over dense step-level signals. Experiments show that GeoDisaster challenges existing RS-VLMs and agentic systems, while RCEA improves tool use, evidence grounding, state consistency, and decision generation.

Spatial reasoning, the ability to determine where objects are, how they relate, and how they move in 3D, remains a fundamental challenge for vision-language models (VLMs). Tool-augmented agents attempt to address this by augmenting VLMs with specialist perception modules, yet their effectiveness is bounded by the action interface through which those tools are invoked. In this work, we study how the design of this interface shapes the agent's capacity for open-ended spatial reasoning. Existing spatial agents either employ single-pass code execution, which commits to a full analysis strategy before any intermediate result is observed, or rely on a structured tool-call interface that often offers less flexibility for freely composing operations or tailoring the analysis to each task. Both designs offer limited flexibility for open-ended, complex 3D/4D spatial reasoning. We therefore propose SpatialClaw, a training-free framework for spatial reasoning that adopts code as the action interface. SpatialClaw maintains a stateful Python kernel pre-loaded with input frames and a suite of perception and geometry primitives, letting a VLM-backed agent write one executable cell per step conditioned on all prior outputs, enabling the agent to flexibly compose and manipulate perception results and adapt its analysis to both intermediate text and visual observations and the demands of each problem. Evaluated across 20 spatial reasoning benchmarks spanning a broad range of static and dynamic 3D/4D spatial reasoning tasks, SpatialClaw achieves 59.9% average accuracy, outperforming the recent spatial agent by +11.2 points, with consistent gains across six VLM backbones from two model families without any benchmark- or model-specific adaptation.

While recent vision-language models (VLMs) demonstrate strong multimodal understanding, they remain limited in spatial reasoning tasks that require active evidence acquisition and multi-step visual interaction. This limitation suggests that relying solely on implicit visual representations from vision encoders is insufficient for recovering fine-grained spatial evidence. We introduce PERception-Interaction-reason Agent (PERIA), a tool-augmented visual agent for spatial reasoning tasks across map reasoning, visual probing, and vision reconstruction. PERIA uses two lightweight tool families: vision perception tools for exposing textual, symbolic, and spatial evidence, and vision interaction tools for manipulating visual context, tracing paths, and verifying spatial relations. To train PERIA, we develop a unified recipe that combines supervised tool-use trajectory synthesis, composite rewards, and Observation-Relaxed Group-in-Group Policy Optimization (OR-GIGPO) for effective multi-tool behavior. Experiments on 13 benchmarks from 8 datasets show that PERIA-8B improves over the Qwen3-8B backbone by 10.0% on in-distribution benchmarks and 4.4% on out-of-distribution benchmarks, while outperforming previous state-of-the-art baselines of similar size by 7.0%-14.8%. It also achieves performance comparable to much larger models such as Qwen3-VL-235B-A22B-Thinking and GPT-5, demonstrating the effectiveness of PERIA in enhancing spatial reasoning capabilities.

Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers -- reward functions that check for geometric and semantic consistency under transformations -- we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.

Spatial reasoning remains a challenge for Multimodal Large Language Models (MLLMs), as it requires reliable multi-hop inference over both intermediate states and state transitions. Current studies often leave intermediate states unverified and treat state transitions as implicit processes, which limits reliability in multi-hop spatial reasoning. To address this, we propose State-aware Visualization-of-Thought (SVoT), a reinforcement learning framework that generates interleaved, verifiable intermediate states and visualizations. SVoT integrates transition reasoning chains into the generation processes, enabling the model to verify action preconditions and effects through interleaved textual and visual reasoning. We train SVoT via Group Relative Policy Optimization (GRPO), instantiating verification through reward design and evaluating the efficacy of different fine-grained rewards. As existing benchmarks reduce state transitions to single-variable updates, substantially simplifying the problems, we establish five domains by extending classical environments and introducing two novel domains, Pacman and Gather, that require multi-object interactions and numerical reasoning. These domains support systematic evaluation of multi-hop spatial reasoning with quantitative verification of generated intermediate states and transition reasoning. SVoT with transition-aware supervision achieves state-of-the-art performance across the introduced domains, yielding up to a 65% absolute accuracy gain on out-of-distribution test sets.

Spatial reasoning remains a persistent challenge for multimodal large language models (MLLMs). Existing approaches largely rely on large-scale, statically curated datasets, where all training samples are treated uniformly regardless of the model's evolving capabilities. This static paradigm is inherently data-inefficient: training capacity is often spent on samples that are either trivial or overly difficult for the model at its current stage. To address this limitation, we propose Ouroboros-Spatial, a self-evolving training framework in which the model plays dual roles as a proposer and a solver. In each iteration, a frozen proposer generates spatial question-answer (QA) pairs from 3D scene metadata and raw video frames, together with executable code for deriving reliable ground truth. A learnable solver is then fine-tuned on the accepted samples, and its per-sample prediction confidence is used as a difficulty signal. This signal is fed back to the proposer in the next iteration, guiding it to generate questions better matched to the solver's current capabilities. Through this closed-loop design, the training distribution co-evolves with model ability, reducing redundant trivial examples while filtering out ambiguous or uninformative samples with limited learning value. Across six spatial reasoning benchmarks, Ouroboros-Spatial substantially improves Qwen3-VL-4B and Qwen3-VL-8B while using an order of magnitude fewer training examples than recent large-scale curated datasets. On VSI-Bench, it yields absolute gains of 9.9 and 6.8 points for the 4B and 8B models, respectively, enabling both to outperform a wide range of strong open-source and proprietary baselines.

Spatial reasoning from egocentric videos is inherently challenging because the observable evidence is constrained by the camera trajectory. Existing methods rely on single-turn inference, forcing models to resolve geometric ambiguity through semantic priors rather than verifiable evidence. We argue that spatial reasoning should be revisitable: conclusions formed under limited evidence should remain open to revision when complementary viewpoints become available. Building on this insight, we propose Reason, then Re-reason (ReRe), a training-free, inference-time framework with two phases: in the Reason Phase, an MLLM forms a spatial hypothesis from the original video; in the Re-reason Phase, it verifies or revises the hypothesis by observing a synthesized novel-view video. To enable effective cross-view revisiting, we design a Geometry-to-Video pipeline that renders strategically complementary novel views from predicted 3D geometry. These views feature an elevated, oblique perspective with scene-spanning coverage, while preserving the MLLM's native video interface without architectural modifications. Extensive evaluations on VSI-Bench and STI-Bench demonstrate that ReRe substantially boosts open-source MLLMs to rival proprietary state-of-the-art performance. Project page: https://zhenjiemao.github.io/ReRe/

Spatial reasoning is a foundational capability for multimodal large language models (MLLMs) to perceive and operate within the physical world. However, existing benchmarks predominantly rely on passive evaluation (e.g., static VQA) or simulator-specific pipelines, failing to assess general interactive spatial understanding. We introduce SpatialWorld, a unified benchmark designed specifically for evaluating the interactive spatial understanding of multimodal agents in complex real-world tasks. Integrating eight heterogeneous simulation backends under a shared, simulator-agnostic protocol, SpatialWorld features 760 human-annotated tasks across diverse domains (e.g., household routines, travel, social collaboration). Agents must solve tasks under vision-only partial observability, actively gathering egocentric visual evidence and expressing decisions via a unified, text-based action interface native to MLLMs. For reliable evaluation, each task includes a human-validated initial state, a reference trajectory, and a terminal-state verifier. Evaluating 15 advanced agents reveals that robust spatial task solving remains challenging: the strongest model, GPT-5, achieves an average task success rate (TSR) of only 17.4%, while the leading open-source model, Qwen-3.5, reaches 14.1%. Further analysis exposes a clear mismatch between task success and execution efficiency, alongside substantial domain-specific performance variations. These bottlenecks in active exploration and long-horizon planning position SpatialWorld as a rigorous testbed for future spatial agents.

Vision-and-Language Navigation in continuous environments requires agents to understand the spatial structure of previously unseen environments in order to follow language instructions. Although foundation models have opened a promising path toward zero-shot navigation without task-specific policy training, many navigators still rely on local visual cues and linear history-based reasoning, overlooking the spatial nature of navigation across explored regions, traversed paths, landmarks, and their spatial relations. In this paper, we propose SpaceVLN, a navigation agent built around Spatial Cognitive Memory and Task-Guided Spatial Reasoning. Specifically, SpaceVLN introduces an efficient stagewise closed-loop framework where planning and execution are organized around verifiable space--landmark stages. During navigation, the agent progressively abstracts explored regions into Spatial Waypoints and dynamically maintains subtask-grounded landmark evidence, forming a hierarchical Spatial Cognitive Memory for progress localization and spatial-relation understanding. Built on this memory, Spatial-CoT integrates task-progress reasoning with spatial perception, analysis, and prediction, enabling Task-Guided Spatial Reasoning for embodied navigation. The unified stage interface enables SpaceVLN to address both Vision-and-Language Navigation and Object-Goal Navigation under a unified zero-shot setting, without task-specific policy training. Across R2R-CE, RxR-CE, GN-Bench, and HM3D-OVON, SpaceVLN achieves state-of-the-art zero-shot performance, and real-robot deployment further validates its applicability. These results highlight Spatial Cognitive Memory and Task-Guided Spatial Reasoning as a practical foundation for stronger embodied navigation agents.

Multimodal Foundation Models (MFMs) have made substantial progress, yet remain fragile in spatial reasoning over the physical world. A key bottleneck lies in their inability to transform local egocentric observations into a global allocentric spatial representation. To address this, we propose AlloSpatial, an agentic framework for allocentric spatial cognition in foundation models. AlloSpatial introduces World2Mind, a plug-and-play cognitive mapping sandbox that converts egocentric observations into structured allocentric priors, including Allocentric-Spatial Trees and route maps that support querying object topology, geometric relations, passability, and trajectories. To utilize these priors reliably under noisy reconstruction and ambiguous visual evidence, AlloSpatial introduces a Spatial Reasoning Harness for tool-use judgment, modality-decoupled cue collection, and geometry-semantic arbitration. We further internalize this process in Qwen3-VL through cold-start reinforcement learning with a harness-gated trajectory-level reward. Experiments on VSI-Bench and MindCube show that AlloSpatial improves proprietary models by 5%-18% in a training-free setting, while ASTs alone support strong spatial reasoning even when visual inputs are removed. The trained AlloSpatial agents further outperform larger general-purpose models and competitive spatial baselines, suggesting that structured allocentric representations, active tool use, and verifiable reasoning offer a promising route toward spatially capable foundation models.

Despite advances in 3D scene understanding, existing 3D Large Multimodal Models operate in offline settings, requiring complete scene observations or predefined video clips. In this paper, we present an online 3D vision-language model that enables real-time spatial understanding from streaming video. Our approach adopts an autoregressive streaming control modeling based on the LLM's next-token prediction objective to learn when to respond, and employs a lightweight Visual-Spatial Feature Integration (VSFI) module to incrementally inject temporally aligned geometry priors into the visual stream. To alleviate long-context decoding overhead, we propose a plug-and-play Geometry-Adaptive Voxel Compression (GAVC) module for efficient visual token compression. To address the scarcity of streaming 3D-language data, we further develop a scalable data generation pipeline that curates over 1M online spatio-temporal 3D QA pairs and establishes a comprehensive benchmark spanning 29 tasks. Extensive experiments show that our approach significantly outperforms both proprietary and open-source models across online and offline 3D spatial understanding, reasoning, and grounding tasks. The project page is available at https://stream3d-vlm.github.io/

While Vision-Language Models (VLMs) have shown strong visual reasoning capabilities, their spatial reasoning abilities remain largely constrained to the observed images and text-oriented chain-of-thought. They often struggle to infer unobserved layouts, maintain cross-view consistency, and reason from alternative viewpoints when only limited egocentric observations are available. In this work, we study this problem as thinking with imagination, where a VLM actively acquires imagined visual evidence by interacting with a world simulator during reasoning. We propose Astra, an agentic spatial reasoning framework that empowers VLMs with action-conditioned visual imagination. Specifically, Astra couples Astra-VL, an RL-trained VLM policy, with Astra-WM, a Bagel-based world simulator that generates novel-view observations from context images and natural-language camera motions. To provide reliable imagined evidence, Astra-WM is trained with view consistency tuning to improve pose and content consistency across views. In the RL stage, we propose a world-simulator-in-the-loop two-phase RL curriculum to stabilize tool-use exploration and advance the model's ability to invoke the simulator only when imagined observations improve over direct answering. Experiments demonstrate that both the world simulator and the agentic policy are necessary: Astra-WM improves simulator-augmented Gemini-3-Flash on MMSI-Bench from 45.1 to 49.5, while Astra-VL improves the Qwen3-VL backbone from 29.8 to 38.8 on MMSI-Bench and from 36.8 to 42.7 on MindCube. These results show that imagined observations can provide useful spatial evidence, but effective world-model-augmented reasoning requires learning when, where, and how to imagine.

Dense 3D reconstruction has demonstrated immense potential for spatial understanding, yet its viability as a real-time, onboard representation for autonomous driving remains an open challenge. Existing large-scale visual geometry models typically require substantial computational resources and lack the long-range geometric fidelity, surround-view consistency, and real-time efficiency demanded by dynamic driving environments. To bridge this gap, we present \textbf{LiAuto-GeoX}, an efficient grounded driving transformer designed for deployable, ego-centric 3D scene understanding. Our approach begins by learning a high-capacity driving geometry model from large-scale surround-view data, utilizing sparse LiDAR priors to provide robust geometric grounding in distant, ambiguous, or structure-sparse regions. We then instantiate this capability into a highly compact 155M-parameter onboard model through a novel geometry-preserving distillation framework. This framework employs mask-guided depth-aware distillation to retain fine-grained metric structures by emphasizing geometrically informative regions, and relative-pose relational distillation to enforce cross-view spatial consistency through pose-induced geometric relations. Extensive evaluations reveal that \textbf{LiAuto-GeoX} runs at 220 FPS on KITTI while maintaining high-fidelity dense reconstruction, enabling real-time deployment. The learned geometry transfers seamlessly to downstream autonomy tasks, achieving 90.6 PDMS in trajectory prediction, 24.63 mIoU in occupancy prediction, and 47.67 IoU in future-frame prediction. These all demonstrate that efficient dense 3D reconstruction can transcend its traditional role as a perception target to serve as a scalable, foundational geometric representation for next-generation autonomous driving.

Spatial planning maps are central to territorial governance, translating planning objectives, regulations, and spatial strategies into visual forms for decision-making, public communication, and institutional coordination. Their interpretation, however, requires fine-grained visual perception, spatial reasoning, and policy-informed professional judgment, creating major challenges for both human learners and AI systems. With the rapid progress of Vision-Language Models (VLMs), their use in urban planning analysis is gaining attention, yet existing multimodal benchmarks mainly target general visual understanding and overlook the domain-specific cognitive processes of planning practice. To address this gap, we introduce PlanBench-V, the first comprehensive benchmark for evaluating VLMs in spatial planning map interpretation. We first build the Spatial Planning Map Database (SPMD), an expert-annotated dataset of 223 planning maps and 1629 question-answer pairs curated by professional planners, covering diverse geographic regions and cartographic styles. We then propose a theory-informed evaluation framework assessing four progressive capabilities: Perception, Reasoning, Association, and Implementation, corresponding to the cognitive pipeline of planning map interpretation. Extensive experiments across two generations of VLMs show clear progress but persistent limitations. The best 2026 agentic reasoning model, Qwen3.6-Plus, substantially outperforms the best 2025 model, GPT-4o, by 27%. Nevertheless, all models still struggle with implementation-oriented tasks requiring evaluative judgment, policy sensitivity, and constraint-aware decision-making. These findings reveal fundamental limitations of current VLMs in professional planning contexts and highlight the need for domain-adaptive multimodal reasoning frameworks. Code and data are available at https://plangpt.github.io.

Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators. To address this limitation, we introduce the \emph{Spatial Language Model (SLM)}, the first multimodal LLM that treats location information as a first-class modality and enables geometric spatial reasoning within the model's inference process. SLM directly operates on learned spatial representations rather than textual descriptions of spatial relations. To support effective training, we construct a \emph{Spatial Instruction Dataset} that aligns spatial representations, atomic geometric operations, and natural language instructions. We further propose a new benchmark named \emph{SpatialEval}, which is designed to evaluate spatial reasoning across attributes, distance, topology, and relative-position tasks. Extensive experiments show that SLM significantly outperforms existing LLM-based approaches that rely on symbolic reasoning via prompt engineering or textual abstraction, demonstrating the benefits of integrating geometric spatial representations for robust spatial reasoning. Our instruction dataset, evaluation benchmark, model training codes, and models' checkpoints can be found at: \hyperlink{https://github.com/chuchen2017/SLM}{https://github.com/chuchen2017/SLM}.

Vision language models (VLMs) excel at many tasks but still struggle with spatial reasoning when critical information is not directly observable. Many such problems require imaginative perception: inferring what would be seen from an unseen viewpoint, tracing paths through occluded spaces, or integrating partial observations into a coherent spatial representation. We introduce Imaginative Perception Tokens (IPT), intermediate perceptual representations that externalize what a VLM would perceive under alternative spatial configurations while remaining consistent with the observed input. To study this capability, we formulate three tasks, Perspective Taking (PET), Path Tracing (PT), and Multiview Counting (MVC), and construct datasets of approximately 20K examples with ground truth imaginations, answers, and evaluation benchmarks. Using the unified VLM BAGEL as the backbone, IPT supervision consistently improves spatial reasoning and often outperforms textual chain of thought training, even without generating images at inference time. On MVC, IPT improves accuracy by 3.4% and achieves competitive performance with strong closed-source models on PT. We further find that combining IPT and label-only supervision yields additional gains, whereas textual chain of thought can substantially degrade performance, suggesting a modality mismatch when spatial computation is forced through language. Overall, IPT provides a principled supervision signal for reasoning about unobserved spatial structure, improving generalization while producing interpretable intermediate representations.

With the increasing development of Vision-Language Models, it becomes imperative that their predictions are readily explainable to relevant stakeholders. However, the field of explainability has not kept pace with the multimodal surge. While recent Multimodal Explainable AI (MxAI) methods generate explanations to attribute the interaction between different modalities, current evaluation protocols lack the ground truth required to distinguish between true cross-modal reasoning (e.g., spatial composition) and shallow cross-modal shortcuts (e.g., Bag-of-Words attribute matching). It remains unknown whether MxAI methods faithfully capture synergistic interactions or merely hallucinate reasoning on models acting as simple feature detectors. In this paper, we introduce GridVQA-X, the first diagnostic framework specifically designed to evaluate cross-modal explainability. Unlike natural datasets, GridVQA-X leverages a closed-world synthesis logic to generate unique, mathematically guaranteed explanations. We utilize this controlled environment to train paired ground-truth models on identical architectures: $M_{\text{pure}}$, which learns robust spatial-relational reasoning and $M_{\text{spur}}$, which is structurally forced to rely on cross-modal shortcuts. This behavioral divergence creates a rigorous testbed: a faithful explainer must report distinct reasoning pathways for each model. Our findings reveal that widely used methods fail to distinguish between models relying on genuine spatial-relational reasoning and those exploiting cross-modal shortcuts, highlighting a critical gap in capturing true cross-modal synergy and misrepresenting how multimodal models actually make decisions.

Embodied navigation connects intelligent agents with the physical world and is fundamental for general robotic intelligence. Limited availability and quality of navigation data have constrained Vision-and-Language Navigation (VLN) systems' generalization and long-horizon capabilities. To address this, we curate diverse 3D scenes and develop an automated pipeline for large-scale navigation data, resulting in the GN-Matrix dataset. Building on a 3D Gaussian Splatting (3DGS) engine, we introduce a high-fidelity simulation platform supporting interactive roaming and collision-aware navigation. We further propose GN-Bench, the first BEV-based benchmark incorporating dynamic 3DGS avatars for human-robot interaction evaluation. To leverage the simulator, we develop an RL-driven navigation foundation model, Break and Establish (BAE). After supervised learning, DAgger exposes the model to rollout-induced states, breaking narrow expert-centric distributions and enabling downstream RL exploration. This unified VLN paradigm integrates map-based and map-free tasks, including instruction following, human following, and goal navigation. GN-BAE formalizes high-fidelity 3DGS-rendered Bird's Eye View representations as compact memory, unlocking latent spatial reasoning in VLMs. Extensive evaluations on GN-Bench and VLN-CE show that GN0 outperforms state-of-the-art VLN methods. Overall, GN-Matrix offers a unified framework spanning data, simulation, and learning, advancing embodied navigation in research and industrial applications.

Vision-language models (VLMs) have been explored for visual programming, where they generate code to solve visual tasks. However, most prior work focuses on visual programming for productivity; it remains unclear how well current VLMs perform on education-oriented visual programming and what factors limit their performance. To bridge this gap, we introduce TurtleAI, a benchmark containing 823 tasks curated based on real-world visual programming tasks in the Turtle Graphics domain. Solving these tasks requires models to perceive geometric patterns, reason about spatial relationships, and synthesize Python code that faithfully reproduces geometric patterns. We evaluate 20+ VLMs, including GPT-5, GPT-4o, and Qwen2-VL-72B, and find that they struggle significantly, with most achieving success rates below 30%. To address these limitations, we propose a data generation technique that requires only a small set of seed samples. Fine-tuning Qwen2-VL-72B on the resulting synthetic data yields an improvement of about 20% on real-world tasks. Our failure analysis reveals that GPT-4o struggles with spatial reasoning and precise visual replication, whereas fine-tuning primarily improves the alignment between visual reasoning and code implementation.

Wide-baseline matching (WBM) requires integrating geometric understanding, viewpoint changes, fine-grained perception, and occlusion reasoning, making it a challenging testbed for spatial reasoning in multimodal large language models (MLLMs) deployed in physical environments. However, current MLLMs lack systematic evaluation and training frameworks for these capabilities. We introduce ReasonMatch-Bench, a benchmark stratified by viewpoint displacement and matching granularity across indoor, outdoor, and object-centric scenarios, and show that current MLLMs still struggle with fine-grained wide-baseline correspondence: on a difficult 90-sample subset, human annotators achieve 84.0 F1, while the best existing baseline reaches 37.2. To bridge this gap, we build a scalable data-generation pipeline that automatically extracts wide-baseline view pairs from large-scale video-3D corpora, including RGB-D videos and SfM reconstructions, yielding diverse and verifiable supervision. We further propose Dynamic Correspondence Reinforcement Learning (DCRL), which combines Image-Level Viewpoint Progression and Point-Level Correspondence Curriculum to improve WBM training through verifiable rewards without explicit CoT supervision. Extensive experiments show that DCRL substantially improves ReasonMatch-Bench and transfers to related spatial benchmarks, while maintaining general visual understanding performance with modest gains on several benchmarks.

Recent World Action Models (WAMs) have demonstrated impressive capabilities in embodied decision-making. However, whether their effectiveness stems from explicit future imagination during inference or representation learning induced by predictive training remains an open question. Emerging evidence suggests the primary advantage lies in learning robust latent representations rather than generating future observations at test time. Nevertheless, existing WAMs mainly rely on RGB-based future prediction, which provides limited structural and spatial understanding of complex environments. To address this, we propose a structured world modeling framework that enhances latent representations through geometric and semantic supervision. Alongside future RGB prediction, our model introduces two auxiliary prediction branches for future geometry and semantic representations, enabling it to jointly capture scene dynamics, spatial geometry, and semantic context within a unified latent space. Crucially, our approach preserves efficient inference by avoiding explicit future rollout or video generation at test time. Extensive experiments show that incorporating structured world supervision consistently improves action prediction accuracy, scene understanding, and robustness under challenging embodied scenarios, highlighting its potential for advancing scalable and efficient WAMs.

Recently, zero-shot 3D scene understanding via 2D Vision-Language Models (VLMs) has gained increasing research interest due to their promising spatial reasoning capabilities. Typically, multiple 2D views are sampled from a 3D point cloud and fed into pre-trained VLMs to answer a given question. This paradigm highlights the critical role of input context quality and raises the challenge of retaining as many task-relevant 3D details as possible under a limited input budget. We propose \texttt{KeyVT}, a hierarchical approach for input context collection at both the view and token levels. Specifically, we combine pixel features with camera parameters and assess view importance based on both semantic content and geometric position, resulting in spatially consistent and task-relevant views. Furthermore, we address redundancy among patches across selected views by identifying representative tokens under the optimal transport (OT) framework, where view tokens and key tokens are formulated as two discrete distributions in the embedding space. These key tokens are expected to cover all view features by minimizing the OT distance. We evaluate our framework on three widely used benchmarks, demonstrating significant improvements over existing tuning-free methods and performance comparable to training-based approaches.

Multimodal spatial reasoning often relies on long chains of intermediate textual and visual thoughts, where accumulating visual tokens and dense cross-modal attention incur substantial computation and memory overhead. To address this challenge, we propose Spectral-Progressive Thought Flow (SpecFlow), a novel lightweight multimodal spatial reasoning framework that represents intermediate visual thoughts in a fixed-size discrete cosine space. By exploiting strong energy compaction, SpecFlow preserves global layout and relational structure while introducing high-frequency details only when increased spatial precision is required. To align visual state evolution with linguistic intent, classifier-free guidance enables autoregressive textual thoughts to steer flow-based updates of the visual workspace/state without expanding the context. As a result, SpecFlow maintains a bounded visual workspace whose updates depend only on the current visual state and accumulated textual trace, enabling long-horizon inference with stable latency and memory usage independent of reasoning depth. Empirical results show that SpecFlow achieves competitive or superior reasoning performance while reducing computation and KV cache costs by up to 2.1 times.

Spatial reasoning is fundamental to robotics, autonomy, and embodied AI, yet modern vision-language models (VLMs) remain unreliable on metric distance queries. A common assumption is that consistent predictions across viewpoints reflect geometric grounding. We test this assumption and find the opposite: leading VLMs often produce view-invariant and consistent answers even when those answers are incorrect, indicating weak coupling between predictions and viewpoint-specific visual evidence. We introduce \textbf{ViewDiag}, a controlled multi-view evaluation protocol built from Hypersim, ScanNet, and KITTI360, comprising 176 object-pair tracks across 80 scenes with 2--10 views per track. The protocol evaluates models along three axes: metric accuracy, distributional concentration, and internal collapse, the last of which is assessed using a latent feature probe. Across diverse models, we observe a consistent pattern of high prediction stability paired with substantial error, clustering in a regime characterized by strong consistency but low accuracy. \noindent These results challenge the common use of cross-view consistency as a proxy for geometric understanding. Instead, we show that stable predictions may reflect prior-driven collapse rather than evidence-sensitive reasoning. ViewDiag provides a controlled benchmark and diagnostic framework for evaluating whether spatial VLMs are not only accurate, but also meaningfully coupled to visual evidence.

Enabling Vision-Language Models (VLMs) to perform spatial reasoning remains challenging. Existing approaches treat VLMs as passive observers, which is difficult for real-world applications. Moreover, reinforcement learning methods rely on sparse rewards, limiting their effectiveness for complex reasoning tasks. Inspired by pigeons' building and exploiting cognitive maps for navigation, we propose a novel agentic pipeline for spatial reasoning. First, we introduce a new \emph{dynamic cognitive map} parameterizing scene layout as object positions and orientations, serving as persistent memory for new observations. Second, we propose a novel \emph{Spatial Assertion Codes (SAC)}, Python expressions programmatically describing spatial relationships. By collaborating with the dynamic cognitive map, SAC enables verification of intermediate reasoning steps, providing dense reward signals. We optimize the model via supervised and reinforcement finetuning. Experiments on the MindCube benchmark demonstrate state-of-the-art performance with \emph{80.5%} overall accuracy, outperforming the best current method by \emph{29.5} accuracy points (a relative improvement of \emph{53.2%}) on the challenging \textsc{Rotation} subset. Our code and data are open-sourced at https://github.com/dw-dengwei/active-spatial-reasoning.git.

Existing LLM graph benchmarks typically ask models to answer graph-theoretic questions or compute symbolic solutions rather than construct spatial layouts. Within-task difficulty is also primarily stratified by vertex count. However, existing research also suggests that task difficulty is more closely related to the number of constraints imposed by the edges than to the number of vertices being arranged. We introduce PlanarBench, a benchmark that asks models to produce crossing-free ASCII drawings of planar graphs given only an edge list. Across 91 model configurations and 199 non-isomorphic connected planar graphs with 2-7 vertices, edge count is more strongly associated with mean task score than vertex count ($r=-0.85$) versus ($r=-0.47$) and remains strongly associated after controlling for vertex count ($r_p=-0.80$). PlanarBench provides a controlled setting for separating these two difficulty axes. In addition, neither drawing area nor total response length demonstrated a meaningful correlation with score, which is evidence against a simple output-size explanation. Performance varies widely: the best model scores 159.5 out of 199, most models below 30B parameters score under 25, and substantial failures remain among frontier systems.

Multimodal large language models (MLLMs) remain unreliable on spatial multiple-choice questions, and their failures are often attributed to poorly attended visual information. We identify a complementary failure mode, spatial lexical bias: a spatial relation word added to the answer options can act as a lexical-semantic distractor that draws the model's decision toward that option. Using nine open-weight MLLMs, we show that this phenomenon is widespread. We then isolate diagnostic cases in which a model answers a binary spatial question correctly yet consistently chooses a newly added third spatial option, which we call binary-stable but ternary-fragile cases. Leveraging mechanistic interpretability tools on these cases, we find that the failure arises on the language side rather than the visual side: visual attention analyses and residual-stream probes show the correct spatial relation remains internally available, while irrelevant-option controls, activation patching, and sparse component interventions trace the bias to specific LLM-side channels and neurons. Accordingly, we show that a lightweight LLM-only DPO update on tiny single-object-pair synthetic data mitigates the bias, lifting four-way robust accuracy by up to 100 points on synthetic data, and by 68.0, 32.6, and 20.1 points on broader evaluation datasets WhatsUp, SpatialMQA-Direct, and VSR.

We study multiple-choice video question answering on the ImplicitQA benchmark, where the correct answer is never explicitly shown but must be inferred from off-screen events, line-of-sight cues, causal structure, and cross-shot spatial layout. On this benchmark a single frontier video LLM already operates near its accuracy ceiling, and we observe that conventional self-consistency strategies -- majority voting across repeated samples of the same model -- can hurt rather than help, because the model's errors on hard questions are correlated. We propose disagreement-based cross-model routing, a pure inference-time procedure that requires no labels and no training. We triple-sample a native-video model (Gemini 3.1 Pro Preview) at temperature zero, exploit the genuine sample-to-sample variance of its video-processing pipeline to identify the roughly 20% subset of questions where the three samples disagree, and route only that subset to a second model from a different family (Claude Opus 4.8) that consumes uniformly sampled frames with adaptive thinking. On the 1001-question validation set with public ground truth -- our main evaluation -- the method improves AvgAcc by +1.43 over the best single sample of the primary model, with per-category gains concentrated on Motion & Trajectory (+5.49), Inferred Counting (+3.45), and Vertical Spatial Reasoning (+1.82) -- the categories most dependent on cross-shot reference resolution. The same pipeline applied to the held-out 172-question CVPR 2026 ImplicitQA challenge test set achieves 82.03 AvgAcc / 79.71 MacroAvgAcc (+1.81 over the best single sample of the primary model), confirming the validation result on an independent split.

Vision-Language Models (VLMs) exhibit emerging spatial reasoning capabilities, yet they remain unreliable on tasks requiring precise spatial understanding, such as viewpoint reasoning, directional comparison, and distance estimation. In multi-view images and monocular videos, relevant spatial cues are often sparse and distributed across redundant observations, making them difficult to organize and exploit. Reconstruction-based Vision Foundation Models (VFMs) offer a natural way to aggregate such observations into explicit spatial memory, such as point clouds. However, simply exposing reconstruction models as free-form tools is brittle, VLMs may invoke tools incorrectly, skip required spatial transformations, or misuse intermediate results. We propose \textbf{Reasmory}, a framework that formulates spatial reasoning as structured program execution over reconstructed spatial memory. Reasmory constructs explicit 3D memory, augments it with semantically grounded 3D object instances, and introduces a lightweight Domain-Specific Language (DSL) that constrains how VLMs query objects and cameras, transform viewpoints, and render observations during reasoning. Generated programs are parsed and validated before execution, enabling more reliable interaction with spatial memory than unconstrained tool use. Experiments on multi-view image and video spatial reasoning benchmarks show consistent gains of 6--18% over strong baselines, including GPT-5-mini and Gemini-3-flash, indicating that explicit 3D memory is most useful when accessed through constrained, validated operations rather than free-form tool calls.

Reasoning is essential for autonomous driving (AD) in long-tail scenarios, where vehicles must apply commonsense knowledge, understand spatial relations, infer agent interactions, and make safe decisions. However, existing AD datasets and benchmarks mainly target perception, prediction, or planning, and provide limited supervision for reasoning over realistic long-tail driving scenes. We introduce nuReasoning, a large-scale real-world dataset and benchmark for reasoning-centric AD. Following the lineage of nuScenes and nuPlan, nuReasoning advances real-world AD datasets and benchmarks toward reasoning in long-tail driving scenarios. The dataset contains 20,000 clips, each 20 seconds long, collected across multiple cities, with synchronized multi-camera images, LiDAR data, HD maps, object annotations, and human-verified reasoning annotations spanning Spatial Reasoning, Decision Reasoning, and Counterfactual Reasoning. Unlike prior datasets that focus primarily on visual question answering, nuReasoning supports both reasoning evaluation and planning evaluation, enabling a direct study of how reasoning supervision affects driving performance. Experiments show that fine-tuning VLMs on nuReasoning substantially improves driving-specific question answering, while incorporating reasoning supervision into VLA training improves planning performance even when textual reasoning outputs are disabled at inference time. These results establish nuReasoning as a foundation for evaluating and improving robust, interpretable, reasoning-driven AD systems in realistic long-tail settings.

Large Language Model (LLM)-based navigation systems commonly construct explicit spatial representations (e.g., topological graphs, semantic raster maps) and translate them into textual descriptions as LLMs' inputs. However, the linguistic structures of such text-based spatial representations and the choices of contextual features (e.g., topology, geometry) they contain are often treated as neutral engineering decisions rather than key factors that shape LLMs' behavior. To fill the gap, we propose a dual-interventional framework that disentangles linguistic structures from different contextual cues to evaluate the linguistic inductive bias of LLMs for navigation planning. In the framework, representation intervention varies the linguistic format and the degree of linguistic compression, clarifying when linguistic representations support or inhibit navigation planning. Context intervention, combined with contextual feature combination and conflict probing, explicitly clarifies the preferences and weaknesses of LLMs when processing different contextual cues. Experiments across diverse spatial reasoning tasks and multiple model scales reveal a consistent pattern: topological information is a sturdy shield and the backbone of robust planning; linguistic format is a double-edged sword whose effect depends on model size, task demands, and the compression level; and semantic information is a fatal Achilles' heel -- incorrect semantic cues can systematically derail the planning process. Overall, our study shows that effective text-based spatial representations in LLM-based navigation should preserve topological integrity, calibrate representational compression to model capacity, and ensure semantic correctness, rather than simply adopting a single representation. Our code is publicly available at https://github.com/jonesdong150/LLM-Navigation-Inductive-Bias.