Spatial Reasoning Benchmarks
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Advances in foundation models are driving efforts to introduce agents to assist people in the physical world. Such agents require agentic spatial intelligence: exploring unfamiliar environments, updating spatial understanding through interaction, and adapting actions based on feedback to sustain progress toward a sequence of goals. Existing benchmarks cover only a limited range of spatial layouts, scales, and traversal requirements. We introduce Mine Odyssey, a benchmark for evaluating agentic spatial intelligence using Minecraft reconstructions of real-world locations. It comprises 180 tasks covering 30 such locations across 20 countries and regions on five continents, including 20 outdoor and 10 indoor settings. These settings span diverse spatial scales, layouts, terrains, and connectivity patterns, from Midtown Manhattan and rural Entrup to Santa Lucía Hill and Buckingham Palace. We select meaningful waypoints, such as landmarks, buildings, and rooms, and manually verify their accessibility. Each task provides a natural-language instruction specifying which waypoints to visit and in what order. Completing these tasks requires agents to find accessible routes and entrances, open doors, and move between levels using stairs and ladders, while monitoring their progress and recovering from navigation errors. Across eight evaluated state-of-the-art models, GPT-6 Astra achieves the highest success rate of 85.6%. However, the second-best model, Claude Opus 5.5, completes 73.9% of tasks, while the strongest evaluated open-weight model, DeepSeek-V4.1-Flash, reaches 23.9%, highlighting substantial room for improvement in the agentic spatial intelligence of current models. Comprehensive analyses and ablation studies on Mine Odyssey reveal current models' limitations and provide insights for advancing agentic spatial intelligence.
GAGR-Lab: Evaluating Joint Spatial-Geometric and Analytic Function Reasoning
Joint spatial-geometric and analytic function reasoning requires translating a perceived spatial configuration into a symbolic function whose executed curve satisfies geometric constraints. We present GAGR-Lab, a framework for measuring this capability through Cartesian game scenes, explicit function semantics, and authoritative Rust trajectory execution. It distinguishes spatial perception, metric grounding, geometric relations, function interpretation, function construction, and constrained synthesis. We specify four configurable scene-difficulty presets and a prospective 24-cell diagnostic design, while reporting only the subset actually evaluated. A bounded pilot of one hosted model (Llama 3.2 11B Vision Instruct) using two API credentials as execution replicas yields 72 balanced games with 432 attempts, 429 valid provider responses, and no target hits; exploratory ordinary-function prompt variants also fail to hit, while the structured localization interface yields no scoreable outputs. A privileged analytic search control independently succeeds on 600 directional cases from 300 generated scenes, with exact repeatability and 1,200 successful vertical-reflection or translation checks. The framework separates serving reliability, symbolic compliance, and geometric success, and preserves exact model-visible inputs and realized paths. A staged protocol outlines diagnostic calibration, held-out replication, multi-model comparison, and paired robustness tests. The contribution is an operational research framework with an executed pilot and a clearly identified prospective study plan; the full difficulty matrix and comparative model results remain untested.
Relational Abstractions for Spatial Reasoning with Diffusion Models
Diffusion models excel at image synthesis, but they remain limited in their ability to reliably satisfy structured spatial reasoning constraints. In conditional data distribution modeling tasks with implicit logical structure, such as puzzles defined by visible clues paired with consistent solutions, state-of-the-art generative models tend to approximate pixel-space distributions without learning the underlying logical rules required for inference. To address this limitation, we present a novel framework for spatial reasoning with diffusion models that leverages unsupervised object discovery and abstractions of object relations. We show that the relational knowledge derived from object-centric representations enriches diffusion models with structural primitives, allowing them to effectively guide the generative representation space during both training and inference, and enabling conditional image generation that satisfies reasoning constraints. Additionally, we introduce a large-scale generative spatial reasoning benchmark with four datasets inspired by human-solvable puzzles. Our results show that relational abstractions significantly improve reasoning capabilities of diffusion models on a variety of complex reasoning tasks, while enabling robust generalization in out-of-distribution settings.
Humanity's Sixth Sense: Benchmarking Intuitive Visual Reasoning in Multimodal Models
Humans perceive far more in a scene than what is explicitly depicted: a single glance captures past causes and future trajectories; a quick peek determines if a vehicle can fit between two parked cars; a few seconds of video reveals who holds authority in a room; and a fleeting clip highlights subtle abstract patterns like unwritten rules or hidden labels. This capacity reflects a form of humanity's sixth sense: an intuitive reasoning mechanism that recovers implicit information beyond raw sensory perception. Crucially, this rapid, zero-shot visual intuition underpins everyday navigation and social interaction, making it a vital capability for Multimodal Large Language Models (MLLMs) deployed alongside people. Existing visual benchmarks, however, target either deliberate expert-level analysis in academic and mathematical domains or low-level perception, leaving the intuitive reasoning that people perform largely untested. To bridge this gap, we introduce Humanity's Sixth Sense (HSS), a benchmark for intuitive visual reasoning. HSS spans diverse image and video inputs, organizes items under a structured taxonomy, and pairs each with human-written prompts probing the implicit temporal, spatial, social, and abstract structure that people infer at a glance. Frontier MLLMs fall short of human performance: participants reach 93.1% accuracy, while the strongest model, GPT-6-astra, reaches only 53.6% even at maximum reasoning effort. Despite excelling in many complex tasks that require advanced perception and knowledge, current models still struggle significantly on these visual tasks that are intuitive for humans. We further explore agentic setup that apply dynamic visual manipulation to HSS, which narrows but does not close the gap. HSS establishes intuitive visual reasoning as a measurable axis and directs attention to a capability that scaling on current benchmarks has so far left behind.
SpatialChain: A Benchmark for Auditing Spatial Reasoning Faithfulness in VLMs
Thinking-enabled vision-language models (VLMs) report ever-higher accuracy on spatial benchmarks, yet final-answer scores cannot reveal whether a correct prediction reflects faithful spatial reasoning or a linguistic shortcut. We introduce SpatialChain, a dataset of 28,350 training and 899 test examples pairing spatially-oriented GQA questions with scene-graph-grounded reasoning chains, retained only when the generated answer matches the symbolic ground truth, and a two-axis evaluation combining objective chain-overlap metrics with a scene-graph-aware LLM judge that scores faithfulness and completeness independently of the final answer. Applied to nine thinking-enabled VLMs, the protocol surfaces three findings invisible to standard accuracy: (i) four of nine models achieve 79% VQA accuracy while exhibiting shortcut rates above 39%, i.e., correct answers whose reasoning the judge marks as unfaithful; (ii) chain quality significantly predicts answer correctness for seven of nine models, but the two exceptions (Claude Sonnet 4.6, InternVL3.5-8B) reveal qualitatively distinct failure modes, terse output vs. verbose-decorative reasoning, that benchmark accuracy alone conflates; (iii) SFT on SpatialChain improves Qwen3-VL-8B by +6.2 pp in-domain and reduces its shortcut rate to 22%, while a stylistic specialization effect on external benchmarks motivates replay-augmented training as mitigation. The faithfulness judge is validated against 198 human-annotated items, where judge-human agreement matches human-human agreement, and against a second judge from a different provider, which preserves the model ranking ( = 0.88). Data, generation scripts, and evaluation code are released at https://github.com/spatialchain/SpatialChainBenchmark.
Agentic AI with Structured CoT for Enhancing AI's Spatial Intelligence: Visualization and Reasoning of Rotation
Recent studies show that artificial intelligence (AI) with language and vision capabilities still experiences limitations in spatial reasoning. In this paper, we have studied the spatial capabilities of advanced generative AI to understand the rotations of objects in 3D space, utilizing AI's image processing and language processing features. We trained and examined the spatial intelligence of a generative Agentic AI model (GPT-5.6) to understand the spatial rotation process with rotation diagrams based on the revised Purdue Spatial Visualization Test: Visualization of Rotations (Revised PSVT:R). We improvised the Revised PSVT:R by superimposing additional graphical and contextual features to evaluate how different Chain-of-Thought (CoT) reasoning strategies influence model performance. The results indicate that structured CoT reasoning improves the spatial reasoning performance of the base GPT-5.6 model in both datasets (PSVT:R and PSVT:R with coordinate system). We used three CoT approaches - (1) Structured CoT, (2) few-shot Structured CoT, and Structured CoT with Self-optimized Prompt. The three CoT approaches evaluated in this study showed no significant performance difference. Results showed that combining structured CoT reasoning with relevant contextual information leads to considerable improvements in VLM performance on 3D rotation tasks, demonstrating the potential of agentic AI for more effective spatial reasoning. However, when contextual information is removed, structured CoT reasoning alone provides limited improvement, and the models continue to exhibit notable difficulties in understanding spatial transformations. These findings suggest that effective spatial reasoning in VLMs relies on the integration of visual, textual, and reasoning-based information in future agentic AI systems for spatial intelligence.
From Reasoning Failures to Composable Video Spatial Intelligence
Spatial reasoning benchmarks evaluate vision-language models across diverse tasks, but task-level scores do not reveal which underlying capabilities account for success or failure. Each task requires recovering spatial evidence, representing geometry, and reasoning over it. We disentangle these capabilities by comparing predicted and ground-truth spatial context under a shared schema and coordinate contract. This comparison reveals four recurring sources of error: inaccurate perception, missing information in the spatial context, selection of the wrong measurement, and errors in reference frames or in tracking position and orientation. Guided by this diagnosis, we develop CROSS, a training-free library of typed geometric operators and spatial skills that function over available evidence to support reliable video spatial reasoning. The resulting library supplies verified context to non-coding VLMs or callable skills to a SpatialClaw agent. We evaluate \methodname{} on five benchmarks. \methodname{} raises the average score from 55.9% to 60.2% on ReVSI and improves the SpatialClaw result from 62.8% to 66.3% on DSI-Bench. These gains demonstrate that explicit handling of spatial conventions can repair systematic reasoning failures without additional training.
KilometerVision: A New Frontier for Large-Scale Spatial Intelligence in VLMs
We push the frontier of large-scale spatial intelligence in Vision-Language Models (VLMs) and introduce the first benchmark that probes geographical layout understanding from real-world videos, spanning up to 1km distances. Inspired by the cognitive science literature, we evaluate models against the hierarchical stages of human spatial awareness: anchoring via landmarks, connecting them through routes, and integrating these into global mental maps. Extensive experiments reveal a fundamental divergence in how current AI models process spatial information. Instead of utilising true path integration or forming geometric survey knowledge, we find that VLMs rely almost entirely on 2D visual recognition and text-matching to bypass complex spatial reasoning. The benchmark is publicly available at https://perception-test-challenge.github.io/kilometervision.html.
Network-based Spatial Context Retrieval for Open-weight LLMs: A Faithfulness Benchmark for Grounded Geographic Reasoning
Large language models (LLMs) encode substantial latent geographic knowledge, yet they reason poorly over space and are unreliable when queried from coordinates alone. Useful behaviour emerges only when structured spatial context is supplied in the prompt. This raises a question geographic evaluation has left unexamined: once the right context is supplied, does the model reason from it, or override it with its own parametric recall? We take up this question with an open pipeline for network-based spatial context retriev-al. In it, the surroundings of a selected point are defined by the pedestrian street network, the area actually reachable on foot. Using only open data and open-weight models, the pipeline retrieves features from OpenStreetMap and the GHS-POP population grid, computes indicators over the network catchment in code, and injects them as a compact spatial brief. On this basis we build a faithfulness benchmark. It labels every claim a model makes by its source (grounded in the brief, or drawn from training knowledge) and its correctness, and it probes each case with a planted false premise that the brief refutes. We evaluate sixteen open-weight model configurations across three families (Qwen, Gemma and Llama, with Gemma in two generations), four size classes and, where available, both thinking and non-thinking modes, on three con-trasting cities, resampling every case over ten seeds. The results show that resistance to the planted premise varies more strongly by model family and generation than by scale, while brief-reading competence forms a partly separate dimension. These behaviours are not captured by conventional world-correctness scores or single-shot evaluation. We release the implementation, spatial briefs, model outputs, and claim-level labels as a reproducible workflow at github.com/perezjoan/NSCR-LLM.
Uruqi: Learning Spatial Cognition from Visual Experience
Spatial intelligence requires maintaining a coherent understanding of the world as the embodied agent moves. Like humans, the agent must use its own motion to interpret changes across observations and update object locations and spatial relations accordingly. Despite spatial post-training having substantially broadened the spatial intelligence of vision-language models (VLMs), they still struggle with two atomic spatial capabilities: tracking self-motion and mapping the surrounding world during motion. To address this gap, we provide dense multi-turn supervision over interleaved atomic capabilities within each training episode, mimicking the visual experience of a continuously moving agent that reasons as it observes. To scale this up, we synthesize 11,738 motif-driven camera trajectories over a broad range of 3D scenes, supporting self-motion tracking, persistent object mapping, and rich spatial operations within each visual experience. By training models to reason over these atomic questions, our URUQI-8B improves accuracy from 15.84% to 47.73% on our Uruqi benchmark comprising 52k questions across 2.7k episodes. URUQI-SI-Mix-8B further reaches 50.41%, comparable to the 50.08% achieved by GPT-6 Astra. Trained solely on our synthesized data, URUQI-8B achieves an average relative accuracy improvement of 17.13% over its InternVL3-8B backbone across three external spatial benchmarks. These results highlight continuous visual experience as a scalable source of supervision for developing spatial cognition in VLMs.
VCN-Bench: A Video-Contextualized Navigation Benchmark for Spatial Reasoning over Prior Visual Experience
Spatial reasoning is fundamental to embodied agents, yet it remains unclear whether spatial understanding can be carried forward to guide sequential interactions. Existing spatial-reasoning benchmarks typically terminate at offline predictions, while navigation benchmarks evaluate spatial reasoning as part of instruction following and exploration. We introduce VCN-Bench, a \textbf{V}ideo-\textbf{C}ontextualized \textbf{N}avigation benchmark for probing closed-loop spatial reasoning over prior visual experience in MLLMs. Given a prior video covering both the initial location and destination, the agent is tasked with reasoning out the instruction-specified target and navigating toward it with the inferred spatial context. Built on Matterport3D, VCN-Bench contains five instruction types, 100k training episodes, and 1,250 evaluation episodes. Navigation serves as the primary evaluation, while diagnostic goal identification helps distinguish destination-resolution errors from subsequent navigation failures. We further propose MV-DualVLN, a planning-oriented baseline that jointly leverages prior video and in-episode observations. Experiments reveal limited navigation performance, a substantial destination-resolution-to-navigation gap, and frequent navigation failures even after correct destination identification.
Beyond Spatial Benchmarks: From Spatial Reasoning to Navigation
Does progress on spatial reasoning benchmarks translate into better navigation? Existing benchmarks test isolated inferences from images or videos, with little connection to downstream navigation. Our analysis reveals a gap between benchmark-oriented spatial specialization and navigation performance, and shows how aligning spatial supervision with navigation goals, phases, and decision learning improves navigation. Guided by these findings, we build \textsc{Spatial-Nav-100K} and fine-tune in two stages, \textit{i.e.} first learning a shared spatial-navigation foundation, and then specializing each phase with the abilities it relies on. We further introduce Spatial-NPD, where a teacher conditioned on spatial priors produces grounded action preferences and distills them into a student policy, so no explicit spatial reasoning is needed at inference. With 45 A100 GPU-hours of policy training, our 8B model reaches SR/SPL of 77.4/35.4 on HM3D-v0.2, 60.2/30.5 on HM3D-v0.1, and 47.9/20.6 on train-unseen MP3D. It outperforms several systems that rely on closed-source models or thousands of GPU-hours of training, at 148 ms per action step. All code and datasets will be publicly available at https://github.com/ylwhxht/Spatial-Nav.
ReSTI: A Source-Grounded Audit and Repair of STI-Bench
Spatial--temporal benchmarks are valid only when their questions, source annotations, and answer options identify the same physical quantity. We audit STI-Bench against the official ScanNet, Waymo, and Omni6DPose sources and find systematic coordinate-system and timestamp errors, under-specified targets and times, and disagreements between keyed options and answer details. We introduce ReSTI, a source-backed revision that reconstructs every recoverable answer under an explicit target, time, coordinate system, physical quantity, and unit. Source reconstruction reveals task-level geometric failures: ScanNet Grounding omits the required alignment between annotation and raw camera coordinate systems, while Orientation measures camera rotation on the wrong plane. ReSTI replaces these labels with explicit, source-consistent geometric definitions and corrects other source-verifiable defects, including Waymo poses evaluated at the wrong timestamp. Across 2,064 legacy questions, ReSTI retains 1,782 questions and records 282 evidence-backed exclusions. ReSTI therefore provides a conservative and source-traceable basis for evaluating precise video spatial--temporal reasoning. Project page: https://github.com/pengzhansun/ReSTI.
Do LiDAR Language Models Really Understand Spatio-temporal Relationships?
Recent 4D LiDAR language models aim to reason about objects and their evolving spatial relationships. Yet, in our evaluation, always selecting the same option nearly matches the multiple-choice accuracy of two B4DL-derived configurations. We introduce LiDAR-Hallu, a geometry-referenced benchmark and diagnostic protocol with 10,000 questions across 150 nuScenes scenes. It covers object existence, ego-relative position, distance ordering, relative motion, and temporal localization, with explicit rules for selecting objects, comparing times, and determining reference answers. Our protocol combines fixed-answer and candidate-content controls, cross-scene pairs with identical prompts but opposite reference answers, and relation-specific recall. Analysis of 100,000 recorded responses reveals failures hidden by aggregate accuracy. Candidate duration alone makes temporal answers predictable without observing LiDAR. On paired questions, the models frequently give the same answer to scenes requiring opposite answers. Relation-specific analysis further shows that both configurations miss every positive lateral-motion case across all tested conditions. Temporal-shuffle contrastive decoding provides little net improvement, as repairs are largely offset by new errors and the main failures persist. These results show that evaluating spatio-temporal reasoning requires testing whether models distinguish the queried physical relationships, rather than relying on individual-answer accuracy alone. The source code, checkpoints, and data are released at https://github.com/Awesome4D/4DMLLM_Hallucination_Bench.
OmniEcho: Audio-Visual Spatial Understanding for Omni-Modal Embodied Agents
Humans can effortlessly localize the direction of a sound source and integrate it with visual cues for reasoning, yet this remains challenging for embodied agents. In particular, it is still unclear how to effectively evaluate and model spatial audio understanding in embodied settings. To address this gap, we introduce \textbf{OmniEchoBench}, a unified benchmark for spatial audio-visual perception and audio-vision-language navigation. OmniEchoBench comprises six tasks over 197 real-world spatial audio-visual scenes, 2,972 question-answer pairs, and 900 navigation samples with first-order ambisonics (FOA) audio collected from 30 real-world environments. To enable scalable training supervision, we develop a controllable rendering pipeline for spatial audio. It preserves geometric consistency among sound sources, visual observations, and agent trajectories. Building on this, we propose \textbf{OmniEcho}, a spatially aware omni-modal model. It introduces an FOA spatial encoder alongside a pretrained semantic audio pathway. Extensive experiments show that OmniEcho achieves state-of-the-art performance on spatial audio-visual perception. For our sound-guided navigation, OmniEcho reaches a performance level close to that of traditional vision-language navigation. These results demonstrate that spatial audio can serve as a valuable signal for embodied scene reasoning and navigation, while also highlighting fine-grained spatial localization and distance estimation as important open challenges. Our code and data will be available in https://github.com/PKU-VaLuE-Lab/OmniEcho/tree/main
VABench: Measuring Embodied Spatial Intelligence through Visual Demonstrations, Active Perception, and Metric Control
Spatial intelligence requires more than describing object locations. Under incomplete observation, models must identify and acquire missing evidence, interpret it in a common spatial frame, and act on it. We introduce VA-Bench to evaluate the complete observe-reason-act-revise loop. General-purpose MLLMs learn procedural context from RGB-only demonstrations, actively select camera viewpoints, issue metric Cartesian commands, and revise them from execution feedback. Models receive no privileged object poses, oracle trajectories, or learned action heads. A fixed model-agnostic controller executes only model-specified targets. VA-Bench contains 14 base task families (11 single-arm and three dual-arm), seven held-out geometry/layout variants, and a long-horizon five-object composition track. We evaluate 12 primary model conditions in three independent runs over the same 20 physically verified seeds per base task, reporting terminal success, nine trajectory-level behavioral diagnostics, and subtask progress. First, the best-performing model scores 100.0% on target localization and 78.9% on spatial relations in the annotated run. Its three-run macro-average task success is only 53.93+/-3.17%. Second, active camera control significantly improves task success over passive multi-view observation. In one matched comparison, success rises from 27.86% to 57.50%. Third, held-out geometric transfer can reduce task success by over 30 percentage points. No model completes a strict long-horizon episode, despite substantial partial progress. VA-Bench thus tests whether general-purpose MLLMs can turn visual demonstrations and actively acquired evidence into successful embodied action.
EgoPathBench: Evaluating Zero-Shot Egocentric Waypoint Decision-Making in Vision-Language Models
Zero-shot waypoint navigation requires vision-language models to select, from the current first-person observation, a sequence of spatial actions that is feasible for the agent and reaches the goal, placing joint demands on the integrated spatial intelligence of today's foundation VLMs. Existing spatial-intelligence benchmarks primarily evaluate isolated judgments of relations, directions, or targets and therefore do not directly measure the integrated navigation ability required to combine target recognition, action-consequence assessment, distance estimation, and path planning. To fill this evaluation gap, we introduce EgoPathBench, a dataset and five-task benchmark for first-person waypoint decision-making. Each question presents an egocentric RGB image, a natural-language goal, and numbered visible waypoints; a model returns traversable candidates or an ordered route. Predictions are evaluated for candidate feasibility, adjacent-edge legality, and goal arrival under point-agent or embodied geometry. EgoPathBench contains 31,852 training, 1,345 validation, and 1,111 benchmark questions and retains at least one geometrically verified reference route for every route question. Across nine VLMs, the highest EgoPath Score is only 28.3. The top-ranked model reaches 35.9% success on Point Path, but only 2.9% and 4.0% on Embodied Path and Intent Path, respectively, showing that current models remain limited in forming complete, goal-consistent routes under embodiment constraints. Beyond the evaluation data, we release the corresponding training resource. Fine-tuning Qwen 3.5 4B on the released training split raises its EgoPath Score from 3.9 to 38.9 and improves all four reported evaluations across three external spatial benchmarks, with gains of 1.4--9.6 points.
SceneBench: A Hierarchical Benchmark for Vision-Language Understanding of 3D Scenes
Vision-language models excel at 2D image understanding but remain limited in 3D spatial reasoning. Progress is hindered by limitations in current benchmarks. First, 3D datasets often rely on point clouds that capture geometry but discard rich visual features like texture, text, and materials. Second, annotations treat objects in isolation while ignoring real-world hierarchical organization (scenes, rooms, functional areas, object groups). Third, evaluation tasks focus narrowly on basic recognition rather than multi-step spatial reasoning. In this context, we introduce SceneBench, a benchmark of 966 photorealistic 3D scenes reconstructed with Gaussian Splatting and densely annotated with hierarchical semantics spanning scenes, rooms, functional areas, object groups, and individual objects. These annotations are produced through a human-in-the-loop pipeline combining vision-language models with roughly 1,500 human-hours of iterative refinement and verification, producing over 183K annotated nodes with textual descriptions and 3D bounding boxes. Building on this representation, we define three evaluation tasks: Existence-Based Questions probing object attributes, Spatial Intelligence Questions covering counting, size comparison, distance, and directional relations, and Grounded Question-Reasoning-Answer (QRA) triplets requiring multi-step reasoning across semantic levels. Experiments with state-of-the-art vision-language models show that while models perform well on basic recognition tasks (e.g., up to 85% accuracy for detection), performance drops substantially on hierarchical and compositional reasoning (e.g., down to 60% for counting), revealing limitations not captured by existing benchmarks. SceneBench provides a realistic testbed for developing and evaluating models capable of fine-grained spatial reasoning in photorealistic 3D environments.
MindTopo: Can Foundation Models Reason in Topological Space?
Spatial reasoning depends not only on metric properties such as distance, angle, and shape, but also on topological relations that remain invariant under continuous deformation. Cognitive science identifies these relations as foundational to spatial understanding, yet foundation-model evaluations largely focus on metric or viewpoint-dependent relations. We introduce MindTopo, a benchmark of topological intuition across five properties grounded in cognitive science and formal topology: continuity, separation, order, enclosure, and knots. MindTopo evaluates each property at two cognitive levels. Reasoning asks a model to identify topological relations or infer how they change. Planning instantiates a foundation model as a closed-loop agent whose policy selects environment actions. MindTopo contains 11,030 instances across 13 procedurally generated task types with controllable difficulty. We benchmark 14 MLLMs and study agent configurations augmented with image and video generation, including 3 video generative models in planning settings. Every MLLM performs better on reasoning than on planning, and the best-performing model remains far below observed human performance. On Qwen3-VL-2B-Instruct, supervised fine-tuning and reinforcement learning improve reasoning more than planning. Generated observations retain local cues and reach plausible endpoints, but audited rollouts do not reliably follow environment dynamics or preserve topology across transitions. Our website is at https://mind-topo.github.io/
MV-STRIDE: Enabling MLLMs to Master Multi-View Spatial Reasoning via Hierarchical Capability Modeling
Despite the rapid progress of Multimodal Large Language Models (MLLMs) in 2D vision-language tasks, robust multi-view spatial reasoning remains a fundamental bottleneck due to the lack of structured 3D cognitive pathways in existing datasets. To address this, we introduce MV-STRIDE, a Multi-View hierarchical SpaTial Reasoning dataset with Interdependent and DEcomposed capabilitiEs. Moving beyond flat data structures, MV-STRIDE explicitly models the dependency relationships between foundational perception, scene understanding, and complex contextual reasoning, providing a coherent learning pathway aligned with human spatial cognition. We develop a systematic QA generation pipeline leveraging diverse 3D scene sources that enforces cross-view dependency constraints to prevent single-view solvability, generating multi-level spatial reasoning tasks supported by cognitively grounded chain-of-thought supervision for complex inference. Extensive evaluations demonstrate that our multi-stage training framework based on our hierarchical dataset achieves state-of-the-art performance across multiple spatial reasoning benchmarks, notably the multi-view oriented MMSI-Bench. Our approach enables MLLMs to maintain robust, 3D-consistent spatial reasoning across diverse viewpoints. The code and dataset are available at https://co1dspring.github.io/MV-STRIDE/.
Autoregressive Mosaics: Probing 2D Spatial Reasoning in Text-Only Language Models
Large language models (LLMs) trained only on text and code can sometimes generate programs that draw recognizable images. However, it is unclear whether this reflects an internal representation of 2D spatial layout or simply the ability to translate spatial descriptions into code. We introduce Autoregressive Mosaics (AM-Bench), a benchmark that separates these factors: First, a translation task gives a model a fully specified geometry of a picture in words as a prompt and asks for the code that produces it. Second, a layout task requires the model to compose an image from an underspecified prompt. Across eight open-weight text-and-code-only models, all models reliably translate specified geometry into code, but their open-ended layout performance differs substantially, indicating that these differences are not explained by code-generation ability alone. An output-medium ablation further shows that the interface or medium of expression that the model uses matters: replacing procedural code with raw SVG improves layout scores across all models. Finally, probing model activations shows that a coarse layout plan is present before generation, but reflects only the layout implied by the prompt. During generation, models track the evolving geometric state instead of executing an initially fixed plan. Overall, these results show that 2D spatial performance in text-only LLMs depends on both the model and the output medium, and is not explained by code-generation ability alone.
Reactivating Test-Time Scaling for Plane Geometry Problem Solving
Plane geometry problem (PGP) solving has become a critical benchmark for multimodal reasoning because it requires accurate visual perception and precise multi-step symbolic deduction. Although test-time scaling (TTS) has demonstrated remarkable success in general mathematical reasoning, it fails to scale effectively under the symbolic-program paradigm for plane geometry. We identify two key obstacles: limited reasoning diversity induced by rigid symbolic programs and insufficient explicit visual grounding before symbolic deduction. To address these issues, we propose Multi-Trace Synthesis (MTS), which converts each symbolic program into heterogeneous reasoning traces, including executable Python scripts and CoT-augmented variants. We further propose Perception-Augmented (PA) training, which parses diagrams into structured semantic clauses before deduction, and Consensus-Guided Multi-Trace Ensemble (CG-MTE) for efficient self-adaptive inference. Experiments on three geometry benchmarks show that our method consistently improves PGP-solving across model scales and achieves strong performance against both general-purpose MLLMs and specialized geometry solvers. Under test-time scaling, CG-MTE achieves comparable accuracy to high-budget self-consistency while reducing sampling cost by up to 8x. Code and data are publicly available at https://github.com/Jason8Kang/ReTTS-PGPS.
UrbanGround: From Local Perception to Spatial Agency in a Real-Scale City
Multimodal large language models (MLLMs) can interpret a street view, but reliable urban action depends on whether such local evidence remains useful after the agent starts to move. In this paper, we investigate how far current MLLM agents can turn local urban perception into reliable action in a real-scale city. We propose UrbanGround, an urban sandbox built from Hong Kong's territory-wide 3D geospatial data. It combines the city's geographic structure with continuous, collision-constrained control through a shared evaluation interface. Agents use first-person observations and an interactive map to select actions across tasks ranging from local question answering to long-horizon navigation. Our analysis follows the growth of the spatial problem through three research questions. We first test whether an agent can gather and interpret local visual evidence to answer spatial questions. Then we ask whether these abilities support navigation as destinations become farther away and less explicit. Finally, we examine whether the resulting behavior survives changes in route availability and pedestrian motion. MLLM agents usually show useful atomic abilities in visual recognition and short-range spatial reasoning, while orientation and pedestrian-aware movement remain unreliable. Their central failure emerges over extended exploration, where local abilities do not compose into sustained goal-directed behavior and errors accumulate without effective correction. We hope UrbanGround will support broader study of how far MLLM agents can explore reliably in open-ended urban environments.
GeoRefer-Bench: A Benchmark from Referring Pixels to Verifiable Geospatial Reasoning
Referring segmentation in overhead imagery is inherently relational: a query may ask for the buildings north of the road or the pond closest to a residential area, so the correct referent can contain one object, several objects, or none. Existing benchmarks mainly score mask overlap, which cannot verify whether a model actually resolved the stated spatial relation. We introduce GeoRefer-Bench, a benchmark for verifiable geospatial referring segmentation. Each query is represented by an executable logical form over a metric scene graph, and predictions are evaluated with Exact Query Success (EQS), which is satisfied only when the returned instance set exactly matches the set denoted by the query. GeoRefer-Bench contains 700 whole 2048x2048 UAV scenes (2.94 Gpx) at 12.5 and 25 cm ground sampling distance, 26,217 instances, 142,796 spatial relations, and 20,916 executable queries spanning five reasoning levels. It further includes three paraphrases per query, 24.0% unanswerable queries, 2,477 counterfactual pairs, and five leakage-controlled evaluation splits. An independent audit re-derives object geometry, mask ownership, relation values, query execution, and split provenance, finding zero issues across all 700 scenes. Relation-blind strategies can retain non-trivial mIoU while achieving at most 22.7 EQS overall, showing that overlap alone does not certify relational grounding. Across fifteen current models, the strongest reaches 74.1 EQS but drops from 98.9 at level 1 to 60.5 at level 5, while ten models score below 5 EQS on two-hop queries. GeoRefer-Bench turns geospatial referring segmentation from mask matching into verifiable reference resolution.
CausalSplat: Towards Comprehensive Hierarchical Reasoning in 3D Gaussian Splatting
While 3D Gaussian Splatting (3DGS) has advanced open vocabulary scene understanding, existing methods remain confined to explicit queries. They struggle to interpret implicit intents, complex spatial constraints, and commonsense reasoning required for practical embodied interactions. To address this gap, we introduce the task of reasoning 3D Gaussian segmentation and construct two benchmarks, Causal-LERF and Causal-ScanNet. These benchmarks systematically evaluate commonsense, spatial, affordance, and counterfactual reasoning. Evaluations reveal that current state of the art methods perform poorly on these reasoning challenges. Therefore, we propose CausalSplat, a framework that integrates vision-language models with 3D scene graphs to disentangle explicit structural perception from implicit logical inference. Extensive experiments demonstrate that CausalSplat achieves state of the art performance on our reasoning benchmarks while showing strong generalizability on standard referring and open vocabulary 3D segmentation tasks. Project Page: https://jiayuding031020.github.io/CausalSplat
360CityArena: A Realistic Virtual Urban Navigation Benchmark for Embodied Agents
We present 360CityArena, a benchmark for evaluating the urban exploration capabilities of embodied agents within a photorealistic environment constructed from 360-degree videos. Existing outdoor benchmarks either lack sufficient photorealism or complexity, resulting in a considerable gap from real-world urban environments. 360CityArena is built on a realistic reconstruction of the Akihabara district in Tokyo, Japan, using 602 360-degree video segments covering 85 streets, and consists of 175 meticulously human-crafted tasks. It encompasses three task categories: Environment Understanding, Path Reasoning, and Spatial Reasoning, covering fundamental abilities required for urban exploration, such as localization, landmark search, path planning, and relational spatial reasoning, thereby enabling comprehensive evaluation in realistic urban scenes. Our evaluation using state-of-the-art LMM-based agents shows that even the strongest model, Gemini 2.5 Flash, performs far below human level (human: 77.3% vs. Gemini 2.5 Flash: 17.1%), revealing substantial challenges that remain in city-scale embodied navigation and reasoning. 360CityArena provides a necessary and challenging testbed for photorealistic urban-district navigation and spatial reasoning.
GeoBenchLLM: A Comprehensive Benchmark for Evaluating LLMs on Geo-Related Tasks
In the context of geodata, existing Large Language Models have often been studied in a homogeneous setting, which has considerably limited insights into their generalization capabilities. In this paper, we present \benchName, a comprehensive benchmark for probing LLMs on geo-related tasks. We leverage a careful selection of twelve publicly available datasets from diverse geo-related tasks and domains, and evaluate a set of LLMs on geo-spatial and temporal understanding using our benchmark. Our results show that reasoning and size have a strong impact on overall performance. GeoBenchLLM is publicly available at https://github.com/Rfr2003/GeoBenchLLM.
Geo-Spatial Concept Probing of Large Language Models: Abstraction, Compositionality, and Grounding
Understanding concepts is fundamental to generalization. Despite their impressive performance on a wide range of tasks, Large Language Models (LLMs) still struggle with genuine concept understanding. Prior work has evaluated conceptual understanding in LLMs using natural-language benchmarks or narrowly scoped synthetic tasks, but these settings often conflate multiple skills or lack precise control over the underlying concepts and their properties. To support controlled probing of concepts in LLMs, we design tests on their core properties: abstraction, compositionality, and groundness. We set up a concept-centric benchmark, targeting spatial concepts such as direction, distance, topology, and their compositions, and use question answering tasks serving as a proxy. We conduct extensive experiments across multiple LLM architectures and training regimes to analyze how model scale and design impact conceptual understanding. The results reveal clear limitations in current LLMs and provide insights into the factors shaping their ability to acquire and compose structured concepts. Our findings shed light on how concept-based LLMs can be redesigned for improved information access and knowledge management. The code will be available at https://github.com/rd20karim/concept-probing.
GST-Bench: Can VLMs Develop Global Spatial Awareness from Video?
Spatial intelligence is fundamental to embodied agents, yet existing benchmarks focus on local spatial perception from single or few viewpoints, overlooking global spatial awareness over continuous, long-horizon visual streams. To address this limitation, we introduce the Global-Spatial-Temporal Benchmark (GST-Bench), a VQA benchmark for global spatial intelligence in video understanding, comprising human-verified questions derived from 6,790 minutes of synthetically generated video. It requires models to perform accurate spatial inference from novel viewpoints unseen in the input video and to map egocentric observations onto global top-down images. A comprehensive evaluation of 22 state-of-the-art VLMs exposes a striking gap between models and humans: the strongest zero-shot model attains only 42.68, far below the human score of 79.08. To probe the cause of this gap, we construct GST-Bench-Local and find that models, despite strong local spatial understanding under the same task formulation, still fail to consolidate long-horizon observations into a globally consistent scene representation. We further provide GST-Train, a dataset for global spatial reasoning, as a complementary resource to facilitate future research on this challenge.
MultiGlobeQA: A Multilingual and Globally Diverse Benchmark for Geospatial Reasoning
Geospatial reasoning, i.e., computing distances, containment, and other spatial relations over real-world entities, is central to navigation and logistics, yet large language models (LLMs) struggle with the required geometric and topological computation despite storing considerable geographic knowledge. Existing benchmarks localize these failures only partially: they are synthetic or smallscale, largely monolingual, and offer limited control over geographic coverage. We introduce MultiGlobeQA, a multilingual benchmark of 46,060 question-answer pairs spanning 14 spatial-function families and 15 answer formats, with execution-based ground truth over three knowledge graphs. It covers 201 countries and territories via income- and density-stratified sampling, with parallel questions in English and 16 additional high- and low-resource languages. Across parametric, reasoning, and agentic settings, LLMs collapse on tasks requiring grid indexing and shape computation, while topological relations and directions fare best. Retrieval and tool use yield considerable gains, yet performance plateaus below two thirds even when gold facts are supplied, indicating that computation, not access to knowledge, is the bottleneck. Models also underperform on low-income regions, a gap that gold facts widen rather than close.