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Geospatial Vector Geometry as a Native Spatial Modality for Vision-Language Models
Huang Fei, Boyi Chen, Hao Xue, Yang Yue, Yehong Xu, Xiaofang Zhou
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Abstract:Geospatial reasoning links VLMs to real-world action and decision making. Reliable reasoning requires accurate spatial information and effective spatial representations. However, current VLMs obtain this information mainly from language and vision. At larger geographic scales, limited visual observations make it difficult to establish accurate spatial references and recover precise spatial relations. This leads to a bottleneck for VLM spatial perception and reasoning. This paper proposes that geospatial vector geometry can become a native spatial modality within a VLM and introduces GeoVec-VLM. First, we develop a structured geometry representation that preserves the spatial structure and arrangement of vector objects, building an explicit spatial basis. Second, we introduce a geometry interaction strategy that brings this basis into multimodal computation, where it interacts with visual content and language references according to the queried spatial relations. Together, these designs allow perception and reasoning to operate on shared geometric references. Across five spatial reasoning tasks, GeoVec-VLM improves mean accuracy by about 11\% relative to the strongest baseline, maintains its gains under geographic transfer, and shows greater geometric consistency. Our results show that geospatial vector geometry offers a promising internal spatial basis for VLM spatial reasoning. this https URL
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- Source: https://arxiv.org/abs/2610.16769v1
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Preprint GEOSPATIAL VECTOR GEOMETRY AS A NATIVE SPA- TIAL MODALITY FOR VISION-LANGUAGE MODELS Huang Fei 1 , Boyi Chen 1 , Hao Xue 1 , Yang Yue 1∗ , Yehong Xu 2 , Xiaofang Zhou 2 1 The Hong Kong University of Science and Technology (Guangzhou), China 2 The Hong Kong University of Science and Technology, Hong Kong SAR, China ∗ Corresponding authors ABSTRACT Geospatial reasoning links VLMs to real-world action and decision making. Re- liable reasoning requires accurate spatial information and effective spatial rep- resentations. However, current VLMs obtain this information mainly from lan- guage and vision. At larger geographic scales, limited visual observations make it difficult to establish accurate spatial references and recover precise spatial re- lations. This leads to a bottleneck for VLM spatial perception and reasoning. This paper proposes that geospatial vector geometry can become a native spa- tial modality within a VLM and introduces GeoVec-VLM. First, we develop a structured geometry representation that preserves the spatial structure and ar- rangement of vector objects, building an explicit spatial basis. Second, we in- troduce a geometry interaction strategy that brings this basis into multimodal computation, where it interacts with visual content and language references ac- cording to the queried spatial relations. Together, these designs allow percep- tion and reasoning to operate on shared geometric references. Across five spa- tial reasoning tasks, GeoVec-VLM improves mean accuracy by about 11% rela- tive to the strongest baseline, maintains its gains under geographic transfer, and shows greater geometric consistency. Our results show that geospatial vector geometry offers a promising internal spatial basis for VLM spatial reasoning. https://github.com/TXFR/GeoVector-VLM 1INTRODUCTION Spatial intelligence is increasingly expected to understand and reason in geographic space, from navigation and autonomous driving to map-based spatial decision making (Anderson et al., 2018; Guo et al., 2025; Dihan et al., 2025). Recent Vision-Language Models (VLMs) have made rapid progress in spatial reasoning within visual and 3D environments (Yang et al., 2025; Wang et al., 2026), where camera-centered observations provide rich cues for recovering local geometry and re- lations among nearby objects, e.g., a chair is meters from a door. However, reasoning in geographic space is more difficult as it often spans vast extents, from hundreds of meters to tens of kilometers, while still requiring precise geometric relations (Stevens & Coupe, 1978; Dihan et al., 2025). Under a fixed visual input and encoding budget, these spatial structures remain difficult to recover accu- rately from visual observations alone (Liu et al., 2018; Rahmanzadehgervi et al., 2024; Chen et al., 2024). External tools can perform precise spatial computation (Zhang et al., 2024; 2025), but they do not directly change spatial representation inside the model. We ask: how should spatial structure enter a VLM to support reliable geographic-scale reasoning? We consider it from two perspectives: (i) Recent advances have begun to introduce visual primitives (Chen et al., 2023; Fan et al., 2025; Lu et al., 2026) such as points and bounding boxes that bring spatial references directly into the model’s computation, improving spatial grounding and perception (Xu et al., 2024; Cheng et al., 2026b). For geospatial reasoning, however, these location- and region-level primitives are insufficient, especially for representing object geometry and spatial layout. (i) Vector data naturally provide such spatial structure. Widely used in geographic information systems and spatial databases, they encode geom- etry and metric position in a shared coordinate system, supporting precise spatial measurements and relational computations (G ̈ uting, 1994; Jeung et al., 2010; Zheng et al., 2012; Saeedan et al., 2026). 1 arXiv:2610.16769v1 [cs.AI] 12 Oct 2026 Preprint A is east of B Distance: uncertain Largest parcel: A Image patches Text tokens Implicit / incomplete spatial references Recovering geometry from image patches + language Where are parcels A and B relative to point C? What is the distance between A and B? Which parcel has the largest area: A,B or C? Current VLMs: limited by implicit spatial cues ...... Structure-Preserving Geometry Representation Reduced Geometry Representation Point (x,y) Boundary segment Angle (휃) Global/local coordinates ... ... A parcel A parcel 휃 limiting access to fine-grained structure N 1. Geospatial vector data Our solution: geospatial vector geometry as a native spatial modality Images ... Vector geometry Question perception object formation Relation reasoning Align visual tokens, geometry tokens, and spatial query. Build object states from linked geometry and image regions Form role states and relation states for reasoning 2.Geospatial vector enhanced VLMs A is northeast of C Distance:420 m Largest parcel: B explicit spatial perception & stronger reasoning Spatial decision-making Spatial Q&A Site selection ... application Figure 1: Motivation and overview of GeoVec-VLM. Current VLMs infer spatial relations from raster images and language, where metric geometry and spatial relations are only implicitly repre- sented. GeoVec-VLM introduces geospatial vector data as a native spatial modality, preserves its geometric structure during representation, and integrates it with visual and language information for spatial perception and reasoning. Yet current interfaces often either serialize coordinates into language-like sequences (Ji et al., 2025) or compress spatial objects into fixed-size embeddings (Mai et al., 2023; Siampou et al., 2025; Chu & Shahabi, 2026), weakening the spatial organization available for multimodal reasoning (Knoblauch et al., 2026). Driven by this analysis, we introduce GeoVec-VLM, which incorporates Geospatial Vector data as a native spatial modality for VLMs. GeoVec-VLM addresses two challenges: preserving the spatial structure of vector data inside the model, and enabling this structure to interact with vision and language to provide a spatial bias for reasoning. First, GeoVec-VLM encodes vector objects as point and path tokens that preserve both global arrangement and local geometry, providing a geometric basis for spatial relations such as direction and topology. Second, inside the VLM, geometric biases and learnable spatial states bring this structure into multimodal computation, associating vector geometry with visual content and language references while forming query-specific spatial relations for reasoning and language generation. Structured spatial objectives supervise these states to be verifiable during training. We build a large-scale dataset of geospatial reasoning examples, and extensive experiments show consistent gains over images and serialized-geometry interfaces and strong generalization under zero-shot geographic transfer. Beyond accuracy, GeoVec-VLM exhibits stronger geometric consistency across related spatial judgments. Our contributions are as follows: • We introduce geospatial vector geometry as a native spatial modality for VLMs, allowing its spatial structure to form an internal basis for organizing multimodal spatial reasoning. • We propose GeoVec-VLM, which uses a structure-preserving vector representation and joint vector–vision–language association to connect vector structure with visual content, allowing geometric information to guide multimodal spatial reasoning and language gen- eration. • Our findings show that language-level accuracy can mask geometrically inconsistent spatial reasoning in VLMs. Native vector integration improves accuracy and better aligns model reasoning with the underlying spatial constraints. 2 Preprint 2RELATED WORK 2.1SPATIAL REASONING AND SPATIAL PRIMITIVES Spatial reasoning has been studied in both large language models (LLMs) and vision-language mod- els. LLM-based work has examined geographic knowledge and reasoning across global and urban settings (Manvi et al., 2024; Feng et al., 2025). More recent studies probe topological reasoning either from natural-language queries or by providing serialized vector geometries directly to LLMs (Xie et al., 2025; Ji et al., 2025). In parallel, VLM-based approaches improve metric and grounded spatial reasoning through spatial supervision, region-level representations, and depth cues (Chen et al., 2024; Cheng et al., 2024), while recent benchmarks continue to reveal limitations in fine- grained and compositional spatial reasoning (Jia et al., 2026). Recent studies further suggest that spatial reasoning cannot be addressed solely by stronger linguistic reasoning. For example, Yang et al. (2025) find that standard linguistic reasoning strategies provide limited gains on visual-spatial tasks, whereas explicitly constructed cognitive maps improve spatial distance reasoning. A related line of work makes spatial information explicit during multimodal reasoning. Visual CoT (Shao et al., 2024) grounds intermediate reasoning steps in image regions, GRIT interleaves language reasoning with bounding-box coordinates (Fan et al., 2025), and Thinking with Visual Primitives (Lu et al., 2026) uses points and boxes as reasoning primitives, including sequences of points for spatial paths. These approaches demonstrate the value of keeping spatial references accessible dur- ing reasoning. Their spatial interfaces, however, primarily operate on points, regions, or bounding boxes. Polygon geometries additionally carry metric and relational structure, including ordered co- ordinates, path progression, local direction, and object extent—from which spatial relations can be derived. Representing this structure while making it available to multimodal reasoning introduces a different representation problem. 2.2VECTOR GEOMETRY FOR MULTIMODAL SPATIAL REASONING Vector geometry provides spatial structure at multiple levels, from coordinates and local shape to paths, boundaries, and object extent. Existing spatial encoders capture this structure in increasingly expressive ways. Polygon encoders model vertex configurations and geometric properties (Mai et al., 2023), while Poly2Vec and Geo2Vec extend geometry-aware encoding to points, polylines, and polygons (Siampou et al., 2025; Chu & Shahabi, 2026). These methods preserve rich geometry during encoding, but typically expose each spatial object to downstream models through a fixed- size representation. Recent work has further connected geometric information with language and vision. LLMs can reason over serialized vector geometries (Ji et al., 2025), while SLM (Chu et al., 2026) projects Geo2Vec representations into the language-model embedding space. Rose (Bai et al., 2025a) and GeoLink (Bai et al., 2025b) combine imagery with vector map data, allowing image patches to interact with vector objects. Beyond geospatial vector data, recent spatial VLMs also integrate geometric features with visual and language representations through multimodal fusion (Zhang et al., 2026; Zhao et al., 2026). These studies show that geometric information can im- prove multimodal spatial reasoning, while also highlighting the interface between geometry, vision, and language as an important modeling choice. For complex vector objects, however, geometry is generally summarized at the object level before such multimodal interaction. Recent discussions of raster–vector learning similarly highlight the need to retain fine-grained vector structure across modalities (Knoblauch et al., 2026). GeoVec-VLM keeps the metric spatial reference and structure of vector objects accessible during vector-vision-language interaction. This provides a spatial basis through which visual content, language references, and vector geometry can be associated within the same spatial reasoning process. 3METHOD 3.1PROBLEM FORMULATION AND OVERVIEW GeoVec-VLM treats vector geometry as a native spatial modality alongside vision and language. Formally, given a raster image I , vector geometry X in the same spatial frame, and a language 3 Preprint 1. Structured Geometry Representation N vector geometryinput Object Encoder within-object structure Scene Context Encoder (cross-object context) Tokenized parcels Reference tokens: global cell anchor + local coordinate offsets tokenize � � Parcel 2 token1... token M Parcel N token1...token K Parcel 1 token1... token M Geometry Encoder Path tokens: arc/chord geometry, bearing, turn, sinuosity, ... Geometry Tokens 퐺 � � Geometry pretraining objectives 퐿 object · 퐿 context C A Geometry tokens, 퐺 Geometry Encoder Vector geometry spatial query token, 푄 C point (푥 푐 ,푦 푐 ) Visual tokens, 푉 Instruction tokens, 푇 Object state Role state Relation state 푂 퐴 푟 푍 푒 VLM Layer Qwen3-VL-8B Decoder Perception Layer Object Formation Layer Reasoning Layer � L8/16 � L24 � L28/32/35 bidirectional attention 푉 ... 퐺 ... C (푥 푐 ,푦 푐 ) 푄 causal attention 푇 ... Initialize spatial states Vector–Visual Perception Attention Block updated state 푂 퐴 � 푂 푁 � 푉 퐴 ̅ 퐺 퐴 � 푉 푁 ̅ 퐺 푁 ... ... Object Formation fuse VLM Layer � Output states � � LM Head 2. Structured Vector Geometry in VLM Spatial Reasoning 푇 O Object selection G Attention block scores 휋 푟 geometry memory 퐻 푟 Role formation Role state 퐴 푟 ... Attention block ... 퐻 푟 relation composition Relation state 푍 푒 Spatial relation reasoning [퐴 푟 , 푍 푒 ] Spatial memory 푞=퐻 푙 k, v =[퐴 푟 , 푍 푒 ], Cross Attention Language token 퐻 푙 [퐴 푟 , 푍 푒 ] ... Structured decoder Answer 푦 : parcel A is northeast of point C... direction topology proximity ... ... VLM Sequence [푇,푉,퐺,푄;퐴,푂,푍] 퐺 1 퐺 2 퐺 푁 O Figure 2: Architecture of GeoVec-VLM. The geometry encoder preserves within-object structure and scene-level metric structure in geometry tokens. Inside the VLM, geometry tokens interact with visual and spatial-query tokens, are organized into object states, and form query-conditioned role and relation states used by the language generation path. Structured decoders provide spatial supervision during training. instruction T specifying the spatial reasoning task, the model generates an answer y. We write it as: G =E vec (X), y =M VLM (I,T,G,Q |z model inputs ; O,A,Z |z spatial states ).(1) where G denotes the structure-preserving geometry tokens, and Q is included only for tasks with explicit numerical spatial inputs. Three types of learnable spatial states organize how geometry interacts with vision and language during multimodal reasoning. As shown in Fig. 2 and Eq. 1, GeoVec-VLM follows two main steps. First, a structured geometry encoder transforms vector geometry into geometry tokens while preserving both object geometry and scene-level spatial organization (Section 3.2). Second, GeoVec-VLM brings these geometry tokens directly into multimodal computation using spatial states inside the VLM. Section 3.3 asso- ciates vector geometry with visual contexts via object states O. Section 3.4 uses role states A and relation states Z to organize query-relevant geometry for spatial reasoning and language generation. 3.2STRUCTURE-PRESERVING VECTOR GEOMETRY ENCODING Spatial structure in vector data is determined by object geometry and georeferenced position. Geom- etry defines shape, boundary orientation, and local characteristics, while position dictates direction, distance, and overall spatial arrangement. Our vector encoder preserves both forms of structure when converting vector data into geometry tokens. Consider a scene with N polygonal geometries X =X i N i=1 , where X i denotes the i-th object. We represent each polygon boundary as a variable-length ordered sequence of reference points and path segments, X i = (x i,j ) M i j=1 , where M i is the number of geometric elements for geometry i. Each geometric element x i,j is associated with its source object μ i , normalized arc position σ i,j along the boundary, element type τ i,j , and metric coordinate c i,j ∈R 2 . Continuous features f i,j describe its local geometry: x i,j = f i,j ,μ i ,σ i,j ,τ i,j ,c i,j . This representation keeps object membership, boundary order, and metric position explicit. We encode the resulting geometry at two spatial scales. Within each polygon, let σ i = (σ i,j ) M i j=1 and τ i = (τ i,j ) M i j=1 denote the corresponding arc-position and element-type sequences. An object encoder models the ordered boundary using the relative arc position of its geometric elements: e U i = E obj (X i ;PE arc (σ i ),τ i ).(2) 4 Preprint We then jointly encode all polygons in the shared scene coordinate system. Using their metric co- ordinates C = c i,j and source-parcel identities, a scene encoder models the spatial configuration across parcels: U = E scene e U i N i=1 ; RoPE 2D (C) , U =U i N i=1 , U i = (u i,j ) M i j=1 .(3) The first stage models geometric structure within each object, while the second models metric re- lations across objects. Its output remains element-wise, with each input element x i,j represented by a scene-contextualized state u i,j rather than being pooled at the parcel level. Each u i,j is pro- jected into the VLM hidden space as a geometry token g i,j . The resulting geometry tokens are G =G i N i=1 and G i = (g i,j ) M i j=1 , which preserve the structured geometry of vector objects during multimodal computation. 3.3SPATIAL PERCEPTION AND OBJECT STATES Geometry tokens are encoded with spatial organization of the vector scene, while corresponding visual content is distributed across visual tokens V = (v p ) P v p=1 . We first enable cross-modal inter- action between these tokens inside the VLM and then organize the resulting representations around scene objects. LetP = [V ;G;Q] denote the visual, geometry, and optional numerical-query tokens. At selected VLM layers, tokens in P attend bidirectionally to one another, while language tokens retain the original causal attention pattern. This enables geometry, visual content, and numerical spatial queries to exchange information directly through the VLM backbone attention. We denote the resulting visual and geometry states by ̄ V = ( ̄v p ) P v p=1 and the geometry representation of parcel i by ̄ G i = ( ̄g i,j ) M i j=1 . We then use one learnable object state O i for each parcel i to aggregate this multimodal information. For each visual token ̄v p , let ρ(i,p) ∈ 0, 1 indicate whether its image footprint overlaps parcel i, and define ̄ V i = ̄v p | ρ(i,p) = 1. Each object state attends only to itself, the geometry states ̄ G i of its parcel, and the visual states ̄ V i overlapping that parcel. The exact update is given in Appendix A.3. To further encourage image–vector alignment, we introduce an auxiliary patch- association objective. The geometry states of parcel i are summarized as h G,assoc i = Pool( ̄ G i ), and their association score with visual token ̄v p is: s ip = W G LN(h G,assoc i ) ⊤ (W V LN( ̄v p )) √ d s , L assoc = BCE bal (s ip i,p ,ρ(i,p) i,p ). (4) where W G and W V project geometry and visual states into a shared d s -dimensional space and LN denotes layer normalization. The pooled representation is used only for this association objective, while the element-level geometry tokens remain intact and linked to their object states for subsequent reasoning in Section 3.4. 3.4QUERY-CONDITIONED SPATIAL STATES AND LANGUAGE GENERATION The object states O = O i N i=1 organize the scene by object, while the language query determines which object geometry is relevant to the requested spatial relation. We use role states A to bind query roles to scene objects, and relation states Z to represent spatial relations over the corresponding geometries. For each query role r, the instruction representation ̄ t and a role embedding e r define a selection over the object states, π (r) i = softmax i (W q ( ̄ t + e r )) ⊤ W k O i / √ d . This language- conditioned binding is supervised byL select . The bound object determines its linked element-level geometry memory H r . F A aggregates this geometry into a role state A r =F A π (r) ,H r , allowing each query role to retain access to its associated element-level geometry. For a spatial instance e involving roles R e , the corresponding role states and geometry memories are further composed by F Z into a relation state, Z e = F Z (A r ,H r r∈R e ). Here, O organizes vector and visual content by object, A connects language-conditioned roles to the corresponding geometry, and Z represents relation-specific spatial evidence over the selected geometries. These states are updated at selected reasoning layers of the VLM. 5 Preprint The resulting role and relation states form the spatial memory M sp = [A;Z], which is read by the language states through gated cross-attention: e L = L + tanh(α) CrossAttn VLM (L, M sp , M sp ).(5) Structured decoders attached to the corresponding spatial states provide auxiliary supervision during training, while their predictions are not used by the language path. The overall objective is L =L LM + λ assoc L assoc + λ select L select + X k∈K λ k L k ,(6) where L k denotes a structured objective applied when the corresponding supervision is available. The stage-wise training procedure is described in Appendix A.3. 4EXPERIMENTAL SETUP Dataset. We construct a geospatial reasoning dataset from real street-block polygons, where each scene pairs a 512×512 raster image with spatially aligned vector geometry. The China dataset spans 221 city-level regions and contains 63,973 scenes, with 359,340 question–answer instances used for training. We split the data geographically into disjoint training, validation, and test regions, and restrict geometry-encoder pretraining to the training regions. For zero-shot geographic transfer, we further evaluate on six U.S. metropolitan regions (900 scenes) and Singapore (300 scenes), neither of which contributes to training or model selection. Full construction procedures and split statistics are provided in Appendix B.1. Tasks and Evaluation. We evaluate five spatial reasoning categories covering six task families, in- cluding eight-way direction, comparative proximity, parcel–parcel topology, point–parcel topology, area selection, and point to parcel boundary distance selection. Direction additionally includes con- tinuous horizontal and vertical displacement (∆x, ∆y). The China test set contains 1,800 questions per task, and the same protocol is applied to the U.S. and Singapore transfer sets, with 1,800 and 600 questions per task, respectively. To reduce shortcut solutions, we exclude ambiguous cases and include hard samples where centroid distance, bounding-box area, or nearest-vertex distance dis- agrees with the exact geometric relation. Reversible queries are evaluated in pairs for consistency. We report accuracy as the primary metric, together with reciprocal consistency and component-wise RMSE where applicable. Full construction and evaluation details are provided in Appendix B.2. Baselines and Input Interfaces. We evaluate GeoVec-VLM from two complementary perspec- tives. First, we compare against general-purpose and spatial VLMs using the geometry interfaces available to them. Qwen3-VL-8B serves as the primary same-backbone reference under image-only and image-plus-GeoJSON inputs. GeoJSON is a widely used format for encoding vector geographic data. Larger general-purpose VLMs are evaluated under the same supported interfaces as external capability references, while SpatialRGPT (Cheng et al., 2024) and SR-3D (Cheng et al., 2026a) are fine-tuned on our dataset with ground-truth region masks. Second, to isolate the effect of geom- etry representation, we conduct controlled comparisons under the same Qwen3-VL-8B backbone, training data, and task supervision using serialized coordinates, Geo2Vec (Chu & Shahabi, 2026), Poly2Vec (Siampou et al., 2025), a pooled GeoVec representation, and our element-level GeoVec interface. These controlled variants distinguish the benefit of providing vector information from the benefit of preserving its fine-grained geometric structure during multimodal reasoning. 5RESULTS AND ANALYSIS 5.1SPATIAL REASONING ACCURACY AND GEOMETRIC COHERENCE. Table 1 shows that general-purpose VLMs can recover some spatial relations from images, but adding vector geometry expressed as GeoJSON text does not consistently improve performance and can even reduce accuracy, as seen for Kimi K2.5 on Direction and Gemini 2.5 Flash on Area. GeoVec-VLM consistently improves the three supervised tasks, exceeding the strongest image/- GeoJSON baseline by 4.4–12.1 percentage points. These gains extend beyond directly supervised objectives: GeoVec-VLM remains competitive on Area and achieves the best Distance accuracy, 6 Preprint Table 1: Spatial reasoning on geographically disjoint test regions from China. † Area and Distance are evaluated through language generation without corresponding structured decoders or down- stream task supervision. SpatialRGPT ∗ (Cheng et al., 2024) and SR-3D ∗ (Cheng et al., 2026a) are fine-tuned from released checkpoints on our dataset. Masks denote ground-truth region masks. ModelInterfaceDirection↑ Proximity↑ Topology↑Area † ↑Distance † ↑ Qwen3-VL-8Bimage0.3120.5530.5390.5280.286 + GeoJSON0.3220.5660.5080.6020.336 DeepSeek-V4-Flash image0.6350.5620.5480.7390.417 + GeoJSON0.6090.5690.6310.7440.475 Kimi K2.5image0.6680.7140.6520.7560.591 + GeoJSON0.6550.7110.6930.7110.605 GPT-5.1image0.6140.7330.6510.6910.586 + GeoJSON0.5810.763 0.7110.7160.621 Gemini 2.5 Flashimage0.6400.6360.5840.7840.622 + GeoJSON0.6290.6330.6140.7660.626 Qwen 3.7 Plusimage0.6670.7060.6350.7480.643 + GeoJSON0.6830.7160.7070.7490.621 SpatialRGPT ∗ image + masks0.4360.6440.5970.5130.351 SR-3D ∗ image + masks0.3250.4970.5700.5930.298 GeoVec-VLM-8BNative vector0.8040.8070.8110.7780.659 even though these were excluded from structured decoders. In our adaptation setting, fine-tuned SpatialRGPT and SR-3D perform comparably to Qwen3-VL-8B, suggesting limited benefit from image- and region-mask-based spatial specialization for metric reasoning over explicit parcel geom- etry. GeoVec-VLM maintains performance under zero-shot geographic transfer, achieving 77.5% mean accuracy in the U.S. and 78.3% in Singapore, compared with 77.2% on the China test set (Appendix C.1). Task accuracy alone is insufficient to assess whether a model captures the underlying spatial rela- tions. As shown in Fig. 3(b), baseline outputs can change even when the geometry is unchanged. GPT-5.1, for example, achieves only 53% agreement between categorical direction and the direc- tion implied by its displacement estimate. Proximity decisions can also flip after candidate-order reversal, while topology outputs show a strong bias towards inside or outside. GeoVec-VLM is much less sensitive to these effects, reaching 81% agreement between direction and displacement and the highest reciprocal consistency of 0.88, while producing more stable and balanced results on proximity and topology. We attribute this stability to the explicit geometric structure preserved by vector data, which provides a direct basis for spatial reasoning. 5.2ABLATION AND MECHANISM ANALYSIS To understand where GeoVec-VLM’s gains come from, we analyze three parts of the model. Differ- ent geometry representations are first compared to validate whether preserving fine-grained structure is necessary. Cross-modal grounding and perturbation tests then assess whether vector objects can be reliably aligned with their corresponding visual regions. Finally, ablations on the spatial states and their supervision show how the encoded geometry is used in language generation. 7 Preprint GeoVec-VLM-8B Gemini 2.5 Flash Qwen 3.7 Plus GPT 5.1 Kimi K2.5 DeepSeek V4 Flash Qwen3-VL-8B Ground truthQwen3-VL-8BKimi K2.5DeepSeek V4 Flash GPT 5.1Gemini 2.5 FlashQwen 3.7 PlusGeoVec-VLM-8B GeoVec-VLM-8B Gemini 2.5 Flash Qwen 3.7 Plus GPT 5.1 Kimi K2.5 DeepSeek V4 Flash Qwen3-VL-8B Share of query pairs (%) Both correct Both wrong Order inconsistent Hard samples InsideOutside Recall (%) Share of answer (%) Contains Inside Outside (a) Reciprocal consistency and input list price Mean reciprocal consistency (b) Displacement predictions and categorical directions (c) Why proximity answers fail (d) point-parcel recall by true topology relation parcel-parcel topology relation answer concentration 0.850/0.863 0.729/0.908 GeoVec-VLM-8B Gemini 2.5 Flash Qwen 3.7 Plus GPT 5.1 Kimi K2.5 DeepSeek V4 Flash Qwen3-VL-8B Figure 3: Task accuracy can conceal geometrically inconsistent spatial behavior. (a) Mean reciprocal consistency over direction, comparative proximity, and topology. Because repeated errors can remain reciprocally consistent, panels (b–d) examine task-specific geometric constraints. (b) Categorical direction predictions are compared with the directions implied by predicted horizontal and vertical displacements. Polar histograms show the corresponding answer distributions. (c) Proximity is evaluated under candidate-order reversal, which preserves the physically closer parcel. Black ticks indicate hard-sample accuracy. (d) Point–parcel class-conditional recall and parcel– parcel prediction frequencies reveal query-dependent topology bias. Table 2: Retaining structured vector representations through multimodal interaction improves spatial reasoning. All variants use Qwen3-VL-8B with the same training split and task setting. Geo2Vec ∗ and Poly2Vec ∗ are our VLM adaptations of the open-source geometry encoders under this controlled setting. Pool GeoVec-VLM pools projected geometry tokens to a single embedding. Geometry RepresentationDirection↑Proximity↑Topology↑Area † ↑Distance † ↑ Geo2Vec ∗ (Chu & Shahabi, 2026)0.2030.5110.5260.5670.246 Poly2Vec ∗ (Siampou et al., 2025)0.2330.5030.5250.5660.248 Serialized GeoJSON0.2490.5170.5690.613 0.332 Pool GeoVec-VLM0.704 0.7560.7480.6030.568 GeoVec-VLM0.8040.8070.8110.7780.659 Structure-preserving representation matters The form in which vector geometry is exposed to the VLM substantially affects spatial reasoning. Table 2 compares several geometry interfaces under the same backbone and training setup. Geo2Vec and Poly2Vec, despite encoding geometric properties of complete spatial objects, perform close to or below serialized GeoJSON on several tasks, indicating that object-level geometry encoding alone may not retain enough structure for spatial reasoning. In contrast, Pool GeoVec-VLM already provides gains, and retaining the point- and path-level states throughout multimodal interaction improves all five tasks by a further 5.1–17.5 points. Since the pooled and full variants share the same geometry encoder and training setup, this difference isolates the benefit of preserving element-level geometric structure during reasoning. We further examine geometry-token components in Appendix C.2, and report input-token consumption together with task accuracy in Appendix D.1. 8 Preprint Aligned visual + vector Interaction disabled Shuffled vector Input: Raster image + vector pred slot-3 (correct), F1=0.85 pred slot-4 (wrong), F1=0.68 pred slot-0 (wrong), F1=0.45 Object Top-1 Visual Support F1 Score 0.85 0.63 0.24 0.75 0.41 0.17 Aligned Interaction disabled Shuffled vector (b) Object and visual-support grounding Interaction disabled Aligned Shuffled Vector Score median 0.69 median 0.33 median 0.10 (c) Target-region patch F1 (a) Cross Modal Spatial Grounding (CSG) Kimi K2.5 GPT 5.1 Gemini 2.5 Flash Interaction disable GeoVec-VLM Score 0.679 0.442 0.664 0.283 0.879 (d) Grounding and decision-relevant visual attribution (Query point shown in red) Visual-token attribution 1.0 0.0 Grad × Activation 1.0 0.0 Probability Figure 4: Vector–visual alignment supports cross-modal grounding. (a) CSG requires mapping image-only query points to their corresponding vector parcels. (b–c) Grounding signals weaken when vector–visual interaction is disabled, and further deteriorate after shuffling vector geometry. (d) With aligned inputs, visual support and decision-relevant attribution focus on the corresponding parcel. The final panel shows positive Gradient×Activation for the gold grounding margin. Vector–visual alignment Given that the query point is visible only in the image, can the model identify its corresponding parcel from vector data? As shown in Fig. 4(a), GeoVec-VLM achieves 87.9% accuracy on this cross-modal grounding task, outperforming Kimi K2.5 by 20.0 percentage points. This capability depends strongly on vector–visual interaction, as disabling the interaction reduces accuracy to 28.3%. Fig. 4(b-c) further show that, with aligned inputs, the model more reliably selects the correct parcel and concentrates visual support within the corresponding region, reaching 0.85 Object Top-1 and 0.75 Visual Support F1. When the vector geometry is shuffled, these scores drop to 0.24 and 0.17, respectively, while the median target-region patch F1 decreases from 0.69 to 0.10. The example in Fig. 4(d) makes this effect spatially explicit, and Gradient×Activation attribution further localizes the grounding decision to visual tokens around the corresponding region. VariantDir. ↑Prox. ↑Topo. ↑Area↑Dist. ↑ Full0.8040.8070.8110.7780.659 w/o O/A/Z0.4530.5070.5730.3720.460 w/o Struct. Dec.0.7470.6320.7770.4990.406 w/o R–O Bind.0.7960.7720.8070.7460.622 Table 3: Ablation of spatial states and supervision. All values re- port final-answer accuracy. The w/o O/A/Z variant retains the geom- etry tokens G but removes the learned spatial states. The w/o Struct. Dec. variant removes the auxiliary structured decoders, whereas the w/o R–O Bind. removes language-conditioned role–object binding. Figure 5: Language and structured readouts without O/A/Z, attached directly to G. Spatial states in language generation Table 3 examines what is required for encoded geometry to support multimodal reasoning. Removing O/A/Z reduces answer accuracy by 19.9–40.6 percent- age points across the five tasks, while the structured readouts remain high at 70.3 to 80.2% in Fig. 5. This gap indicates that G retains substantial spatial information, whereas producing correct answers requires the O/A/Z states to organize geometry together with visual information and language- conditioned query roles. Structured supervision further improves answer accuracy by 3.4 to 27.9 points. Notably, Area and Distance improve by 27.9 and 25.3 points despite having no correspond- ing structured decoders, suggesting that spatial supervision transfers beyond the directly supervised relations. Role–object binding has smaller effects when candidate roles are explicit (0.4–3.7 points), 9 Preprint but yields about a 5-point gain when the referred object must be resolved from language, consistent with its role in selecting the relevant object geometry. Further analysis in Appendix C.3 traces how these spatial states affect the language path. 6CONCLUSION Spatial reasoning requires reasoning over the geometry that relates objects in a scene. In this work, we explore geospatial vector geometry as a native spatial modality for VLMs. We find that organiz- ing multimodal reasoning around this geometry provides an effective spatial substrate, improving both spatial reasoning accuracy and geometric consistency. We note that accurate answers do not necessarily imply geometrically consistent reasoning. A model may answer individual questions correctly while its predictions across related questions fail to agree with the same underlying geom- etry. We also find that geometric information can remain recoverable inside a VLM without being effectively used by its language predictions. We hypothesize that robust spatial reasoning emerges when different predictions are grounded in a shared internal representation of the underlying geom- etry. We hope this perspective will inspire further work on spatial structure as a native component of multimodal models. Limitations: we study settings where accurate vector geometry and raster imagery are both available. This lets us focus on how spatial structure can be represented and used inside a VLM, while leaving noisy, incomplete, outdated, or misaligned vector data for future work. Our experiments are limited to static 2D polygonal scenes. 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The encoder first models the geometry within each parcel polygon and then jointly models the relationships among all parcel elements in a scene. Geometry tokenization and element features. Our tokenization follows two structural principles from established geospatial representations that explicitly preserve spatial structure in geospatial to- kenization (Huang et al., 2025). Polygon geometry in GIS is represented by ordered rings with ex- plicit exterior and interior boundaries; accordingly, we preserve part and ring membership and ring orientation following GeoJSON conventions (Butler et al., 2016). OpenLR represents a path using an ordered sequence of reference points together with attributes that retain geometric information be- tween successive references (TomTom International B.V., 2012). We adapt this reference-point/path decomposition to polygon boundaries: retained boundary vertices form reference-point elements, while each interval along the original ring is represented by a path element carrying the geometry omitted by simplification. This representation reduces the explicit boundary sequence while pre- serving boundary order, connectivity, and local metric structure. All geometries are projected into a region-specific metric coordinate reference system before these features are computed. H3center 표 표푏푗 푥 푡푖푙푒 푦 푡푖푙푒 푦 표푏푗 푥 표푏푗 North Bearingin 휃 푖푛 Bearingout 휃 표푢푡 ∆휃 p0 휎 q = 푑 푅 (푝 0 ,푝 푞 ) 푙푒푛푔푡ℎ(푅푖푛푔) ∆푥 ∆푦 푥 표푏푗 , 푦 표푏푗 , 푥 푡푖푙푒 , 푦 푡푖푙푒 , 휎 푞 , sin 휃 푖푛 , cos 휃 푖푛 , sin 휃 표푢푡 , cos 휃 표푢푡 , sin∆휃, cos∆휃, 0, 0, 0, 0, 0, 0, 0 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ∆푥, ∆푦, log(1+푙 푎푟푐 ), log(1+푙 푐ℎ표푟푑 ), 푙 푎푟푐 푙 푐ℎ표푟푑 , atan2(∆푦,∆푥) , n p6 Simplifiedboundary Originalboundary Bounding box Reference point (RP) token (11D+7D padding) Path token (11D padding + 7D) 푑 푅 (푝 0 ,푝 푞 ) Cumulative boundary distance from 푝 0 to 푝 푞 Figure 6: Reference-point and path feature construction. Left: boundary simplification and the geometric features extracted for reference-point and path elements. Right: the features are packed into a shared 18-dimensional feature representation, where reference-point and path features occupy complementary channels and inactive channels are zero-padded. The complete feature definitions are summarized in Table 4. We apply Douglas–Peucker simplification independently to each ring according to the complexity, with a maximum tolerance of 2 meters. The retained vertices form reference points, and each pair of consecutive reference points defines the path element. For a ring R with simplified reference points p j m−1 j=0 , let γ j denote the path from p j to p (j+1) mod m . We serialize the ring as X R = h x rp 0 ,x path 0 ,x rp 1 ,x path 1 ,...,x rp m−1 ,x path m−1 i .(7) The ring sequences belonging to the same parcel are concatenated to form the object sequence X i . We record the part and ring indices to preserve the structural membership of each element. We extract complementary geometry- and topology-related features from reference-point and path elements using a shared 18-dimensional interface. As shown in Figure 6, reference-point elements occupy the first 11 channels and path elements use the remaining seven channels, with inactive channels zero-padded. We denote the element feature vector by f q . 14 Preprint Table 4: Geometric features of reference-point and path elements. RP featureGeometric interpretationPath featureGeometric interpretation (x obj ,y obj )Position normalized by the bounding box (∆x, ∆y)/1000Path endpoint displacement (x tile ,y tile )/1000Offset from the parcel’s H3-cell center log(1 + l arc )Lengthoftheoriginal boundary path σ q = d R (p 0 ,p q ) length(Ring) Normalized position along the ring log(1 + l chord )Chord length between path endpoints x (sinθ in , cosθ in ) Incoming direction l arc l chord How curvy compared to the straight chord (sinθ out , cosθ out )Outgoing directionatan2(∆y, ∆x)Chord bearing (sin ∆θ, cos ∆θ)Signed local turning angle nNumberofintermediate original vertices removed by simplification Table 4 summarizes the features and their geometric interpretation. These features are designed to preserve the spatial information most relevant to boundary reasoning: reference-point features encode location, boundary progression, and local turning geometry, while path features retain metric and shape information from the original boundary intervals that would otherwise be lost during simplification. Together, they reduce the number of explicit boundary elements while preserving both local shape and metric structure. A.2VECTOR GEOMETRY ENCODER PRETRAINING We pretrain the vector geometry encoder in two stages. Object-level pretraining learns the boundary structure within each polygon, and scene-level pretraining subsequently models spatial relations across neighboring polygons. Figure 7 summarizes the overall pipeline. Parcel polygon Dual-stream transformer block × 3 ⋯ RP0 RP stream RP Self-Attention + 1D RoPE Path stream Path Self-Attention 푅푃 푗 푃푎푡ℎ 푗−1 푃푎푡ℎ 푗+1 MLP 푃푎푡ℎ 푗 푅푃 푗 푅푃 푗+1 Shared FFN + Residual + Normalization Object-Level pre-training Cyclic Positive Shuffle Negative Hard-Negative Learned token embedding Parcel CLS embedding SpatialContextWindow Path0 RP1Path1 RP n Path n token 0 token 1 token 2 token 3 Token sequence of each parcel concatenate Anchor Context transformer block × 6 with2DRoPE ⋯ Scene-Level pre-training A: Point Relation Boundary Relation Context Characterization Learned token embedding Scene CLS embedding AddedCLStoken Each entry here is a 128D token feature CLS Figure 7:Vector encoder architecture and geometry pretraining. The object encoder pro- cesses alternating reference-point and path elements with separate attention streams and endpoint- conditioned cross-stream interaction. The resulting element sequences are then concatenated into a spatial context window and processed by the scene encoder with 2D positional encoding. Object-level pretraining. After feature standardization using means and standard deviations com- puted from the training split, each 18-D feature b f q is then linearly projected into the geometry hidden space. We additionally encode polygon membership and token type with learned embeddings to the same 128-dimension spaces and add them to the projected feature representation. 15 Preprint As illustrated on the left of Figure 7, the object encoder consists of three dual-stream Transformer blocks with four attention heads. Reference-point and path elements are processed by separate attention streams. Reference-point attention applies one-dimensional RoPE using the normalized arc position σ q , while cross-stream MLPs exchange information between incident reference points and paths. The encoder produces contextualized element states e U i = ( ̃u i,j ) M i j=1 , and a learned CLS query performs attention pooling over these states to obtain the parcel representation. Object-level pretraining targets three complementary properties of polygon boundaries: invariance to the arbitrary starting point, sensitivity to boundary order, and discrimination between embedding- similar parcels. To learn cyclic invariance, we use a symmetric NT-Xent loss L cyclic that treats a one-pair cyclic shift as the positive view and other parcels in the batch as negatives (τ cyclic = 0.1). Both views are perturbed with Gaussian feature noise (σ = 0.01) and token feature-vector dropout (p = 0.05). To preserve boundary order, a cosine margin-ranking loss L order requires the cyclic view to be more similar to the original than a randomly permuted view (m = 0.1). Finally, a hard- negative InfoNCE loss L hard improves discrimination using K = 5 embedding-similar parcels (τ hard = 0.05), mined offline after an initial round of pretraining. Let h i , h + i , and h − i denote the L2-normalized parcel representations of the original, cyclic, and shuffled views, respectively, and let h h i,k denote the k-th hard negative of parcel i. Using cosine similarity sim(·,·), we define s + ij = sim(h i ,h + j ), s − i = sim(h i ,h − i ), s h ik = sim(h i ,h h i,k ).(8) L cyclic =− 1 2B B X i=1 " log exp s + i /τ cyclic P B j=1 exp s + ij /τ cyclic + log exp s + i /τ cyclic P B j=1 exp s + ji /τ cyclic # .(9) L order = 1 B B X i=1 max 0, m− s + i + s − i .(10) L hard =− 1 B B X i=1 log exp s + i /τ hard exp s + i /τ hard + K X k=1 exp s h ik /τ hard .(11) Here, τ cyclic = 0.1, τ hard = 0.05, m = 0.1, and K = 5. The complete object-level objective is L obj =L cyclic + 5L order +L hard .(12) Scene-level pretraining. To model cross-parcel spatial relations, we assemble object-encoder el- ement states into an anchor-centered local scene. For each parcel, a 4-D scene-relative feature r i = [∆I i , ∆J i ,δx cell i ,δy cell i ], combining H3-cell displacement and within-cell centroid offset, is projected and added to its element states together with a learned parcel-slot embedding. Anchor- relative element coordinates are supplied to 2D RoPE for fine-grained spatial encoding. Reference points use their own coordinates and paths use endpoint midpoints. The concatenated sequence is then processed by the scene encoder, yielding contextualized element states U = U i N i=1 and a scene-level CLS representation. As illustrated on the right of Figure 7, we pretrain the scene encoder with three spatial objectives. The point-relation task predicts the containing parcel (or outside) and the distance to the nearest parcel boundary. The boundary-relation task predicts a four-bin gap category and the exact distance between a queried pair of boundary segments. For context characterization, a regression head op- erating on the scene CLS representation predicts six scene-level statistics: log bounding-box area, parcel density, the mean and standard deviation of log parcel area, coverage ratio, and fragmentation. The corresponding objectives are: L point = CE(ˆy p ,y p ) + 0.25 SmoothL1( ˆ d p , ̃ d p ),(13) L boundary = WeightedCE(ˆy b ,y b ) + 0.25 SmoothL1( ˆ d b , ̃ d b ),(14) L context = 0.5 MSE( ˆ y c , ̃ y c ),(15) 16 Preprint Here distance targets are standardized after the log(1 + d) transform; boundary classification uses inverse-frequency class weights. During scene-level pretraining, we optimize the six-layer scene encoder and the task-specific prediction heads. All object-encoder parameters are frozen except the final dual-stream block, which is fine-tuned at 1× 10 −5 . After the two-stage geometry pretraining, the complete vector geometry encoder is frozen for subsequent GeoVec-VLM training. The detailed architecture and optimization settings are reported in Table 5. Table 5: Configuration of vector geometry encoder pretraining. SettingObject levelScene level Architecture Input18-D element features128-D object element states ProjectionLinear 18→ 128Spatial 4→ 128→ 128 Encoderd = 128; 4 heads; FFN 128→ 512→ 128 d = 128; 4 heads; FFN 128→ 512→ 128 Cross-stream MLP Path: 512→ 128→ 128 RP: 384→ 128→ 128– Context limit256 tokens / parcel384 tokens / parcel; 16 parcels; 1024 tokens / scene Output128-D element states; 128-D parcel representation 128-D element states; 128-D scene representation Optimization OptimizerAdamWAdamW Learning rate3× 10 −4 3× 10 −4 Regularizationweight decay 0.01; dropout 0.1; clip 1.0weight decay 0.01; dropout 0.1; clip 1.0 Epochs86 Batch size / GPU51232 A.3SPATIAL STATES, STRUCTURED SUPERVISION, AND GEOVEC-VLM TRAINING Object and role states. For each parcel i, GeoVec-VLM maintains an object state O i that attends only to itself, the geometry representations ̄ G i associated with the parcel, and the visual representa- tions ̄ V i overlapping its footprint. This restricted interaction associates vector geometry and visual content around the same spatial object while keeping the element-level geometry accessible. Given the object-selection distribution π (r) defined in Section 3.4, each query role r reads the geometry of its selected parcel and updates its role state. The same selection is reused across reasoning layers, while the geometry representations continue to evolve with the backbone: O i = LN O 0 i + MHA O 0 i , [O 0 i ; ̄ G i ; ̄ V i ], [O 0 i ; ̄ G i ; ̄ V i ] , a (ℓ) rij = softmax j W gq LN(O (ℓ) i ) ⊤ W gk LN(g (ℓ) i,j ) p d g , h (ℓ) r = X i π (r) i M i X j=1 a (ℓ) rij W gv LN(g (ℓ) i,j ), A (ℓ) r = LN e A (ℓ) r + tanh(α A )W A h (ℓ) r . (16) The last equation gives the implementation of F A in Section 3.4. It allows each role state to remain tied to the queried object while repeatedly accessing its element-level geometry. Relation states. Relation states combine the participating role states with geometry organized ac- cording to the queried relation. For ordered relations, including direction and parcel topology, we preserve argument order through the projected role-conditioned geometry and their signed differ- ence: φ (ℓ) r = W P LN(h (ℓ) r ), m (ℓ) e = LN h φ (ℓ) r 1 ;φ (ℓ) r 2 ;φ (ℓ) r 2 − φ (ℓ) r 1 ; φ (ℓ) r 2 − φ (ℓ) r 1 ⊙ φ (ℓ) r 2 + φ (ℓ) r 1 i . (17) 17 Preprint For comparative proximity, geometry is compared before object-level aggregation. For two bound- ary elements, let ̃g a and ̃g b denote their projected element-level geometry representations. Boundary- element pairs are represented using ̃g a + ̃g b ,| ̃g a − ̃g b |, and ̃g a ⊙ ̃g b . A learned scalar function scores these pairs, and a differentiable soft minimum summarizes the closest boundary interactions be- tween the anchor and each candidate. The resulting relation representation is combined with the participating role states and written into the relation-state block Z e : B (ℓ) e = h A (ℓ) r 1 + p 1 ;... ;A (ℓ) r k + p k ;W m m (ℓ) e + e τ e i , ∆Z (ℓ) e = MHA LN( e Z (ℓ) e ), LN(B (ℓ) e ), LN(B (ℓ) e ) , b Z (ℓ) e = LN e Z (ℓ) e + tanh(α Z )∆Z (ℓ) e , Z (ℓ) e = LN b Z (ℓ) e + FFN LN( b Z (ℓ) e ) . (18) This corresponds to F Z in Section 3.4. The same role- and relation-state modules are used at layers 28, 32, and 35. Structured supervision. For relation instance e, let A e = [A r ] r∈R e collect its participating role states. Each supervised relation instance is summarized from its role and relation states by a learned relation-type query, q e = LN (q τ e + MHA (q τ e , [A e ;Z e ], [A e ;Z e ])). For topology, the two or- dered role states separately read Z e , v j = LN A r j + MHA(A r j ,Z e ,Z e ) , and form the logits ℓ top = [s in (1, 2),s out ,s in (2, 1)], where s in is order-sensitive for inside/contains, while s out is sym- metric for outside. For comparative proximity, the anchor C and each candidate X ∈A,B form a relation-specific readout q CX = LN (q dist + MHA (q dist , [A C ;A X ;Z CX ], [A C ;A X ;Z CX ])), and d CX = f dist (q CX ). For continuous displacement, a shared two-dimensional reader takes the relation-query state, vector-query state, and eight-way direction probabilities. For the two object orders, its outputs are antisymmetrized as ˆ δ AB = 1 2 (f AB − f BA ). The target is the centroid dis- placement from B to A, normalized by the rendered window side length s,δ ∗ AB = ∆ m AB /s. Predic- tions are rescaled by s for RMSE evaluation in meters. Direction, continuous displacement, parcel topology, and comparative proximity are supervised from these states: L direction = CE (W dir q e + b dir ,y dir ), L topology = CE (ℓ top ,y top ), L proximity = CE ([−d CA ,−d CB ],y prox ), L disp = SmoothL1 ˆ δ AB ,δ ∗ AB . (19) Language-conditioned object selection is supervised by L select = − 1 |R| P r∈R logπ (r) y r while image–vector association follows Eq. (4). Area selection and point-to-boundary distance have no corresponding structured decoder. Table 6: Training configuration for GeoVec-VLM. SettingValue Stage-1 warmup12,000 instances; 4×Ada6000 GPUs; global batchsize 100; 240 updates Stage-2 training8×Ada6000 GPUs; global batchsize 1,024; 680 updates Vector–visual interaction layers8, 16 Object formation layer24 Spatial reasoning layers28, 32, 35 Language–spatial fusion layers28, 32, 35 LoRA rank / α / dropout16 / 32 / 0.05 LoRA targetself-attention q/k/v/o LoRA learning ratestage 1: 2× 10 −5 ; stage 2: 6× 10 −5 Spatial-module learning ratestage 1: 1× 10 −4 ; stage 2: 4× 10 −4 OptimizerAdamW Weight decay0.01 Gradient clipping1.0 Precisionbf16 Learning-rate schedulelinear warm-up followed by cosine decay 18 Preprint GeoVec-VLM Training. GeoVec-VLM undergoes a two-stage training process. In stage 1, the structured spatial pathway is warmed up, using 12,000 QA instances, with 4,000 instances each for direction, topology, and proximity. During this stage, vector–visual interaction operates at layers 8 and 16, object formation at layer 24, and the role and relation states at layers 28, 32, and 35. The geometry projector, spatial-state parameters, and structured prediction heads are optimized us- ing the structured spatial objectives. In stage 2, the same spatial pathway remains active, while language–spatial fusion is enabled at layers 28, 32, and 35, allowing language states to read the role and relation states. The autoregressive language objective is then optimized alongside the struc- tured objectives over the full training split. Area and Distance QA instances are excluded from the language-generation objective throughout training. Language states access role and relation states via these fusion layers before proceeding through the language pathway for answer generation. L S1 = λ assoc L assoc + λ select L select + X k∈K λ k L k , L S2 =L LM + λ assoc L assoc + λ select L select + X k∈K λ k L k . (20) whereK = direction, displacement, topology, proximity, λ assoc = λ select = 0.5, and λ k = 1. Each structured objective is evaluated only on instances carrying its corresponding supervision, with unrelated objectives masked out. During training, the geometry and vision encoders, along with the original Qwen3-VL backbone weights, are frozen. The backbone is adapted solely through LoRA on the q, k, v, and o self- attention projections. The geometry projector, spatial-state modules, structured prediction heads, and language–spatial fusion modules are trained from scratch. Both stages utilize identical LoRA and optimizer configurations. The remaining optimization settings are reported in Table 6. BDATASET AND EVALUATION B.1DATASET CONSTRUCTION AND GEOGRAPHIC SPLITS (b) U.S. metropolitan transfer pool (c) China geographic split Hawaii 76 metropolitan regions 87,906 pool scenes Seattle Sacramento Phoenix Austin Detroit Bubble area ∝ pool scenes (log scale) 50 5005,000Zero-shot test (6 metros) 221 regions region-disjoint train/validation/test split Training (188 regions) Validation (17 regions) Test (16 regions) 66,159 scenes total includes 2,186 robustness-only scenes 500 m Test scene in Suzhou,China United States China Singapore (a) Geographic coverage Figure 8: Geographic coverage and region-disjoint evaluation design. (a) Geographic coverage of the China, U.S., and Singapore datasets. (b) U.S. metropolitan regions and the six regions used for zero-shot transfer evaluation. (c) Region-disjoint training, validation, and test split in China. 19 Preprint Our data are constructed from Multi-level Street-block Cities Worldwide dataset (MSDCW) (Tang et al., 2025), which provides street-block polygons at five spatial levels based on road hierarchy. We use “parcel” throughout the paper as a shorthand for these polygonal street-block units. Each VLM scene pairs a 512× 512 image with spatially aligned vector geometry in the same coordinate frame and can support multiple question–answer instances. Polygon preprocessing and Local context construction. For the China data, we use the L3 and L4 levels from 221 city-level regions. All geometries are projected from geographic coordinates to a region-specific metric coordinate system before metric quantities are computed, and invalid source geometries are repaired before further processing. We then apply the polygon preprocessing and structure-preserving boundary representation described in Appendix A.1. To avoid retaining geometries whose shape must be excessively simplified solely to satisfy the representation budget, we exclude polygons for which the simplification tolerance must be increased to meet the prescribed boundary-token cap. This filtering removes 28,715 of the 372,698 source polygons, leaving 343,983 retained polygons. Local spatial contexts are constructed from the retained L4 polygons separately within each region. For each anchor parcel, neighboring parcels are selected according to boundary proximity. We retain contexts with 3–16 neighboring parcels, a maximum inter-parcel gap of 120 m, and at least 0.30 facing-boundary coverage within a 60 m boundary buffer. This procedure produces 230,566 candidate local contexts before VLM-scene selection. Image–vector scene construction. Each accepted context is materialized as a spatially aligned image–vector scene. A square metric window is constructed around the retained parcels and ren- dered as a deterministic north-up 512× 512 image, while the corresponding vector geometries and world-to-image transform are retained. Its resolution is fixed across scenes, whereas the geographic extent varies with the local context; the resulting meters-per-pixel scale is therefore recorded for each scene. Exact projected geometry is retained offline for label construction and validation. Af- ter scene-level quality checks and materialization, the China dataset contains 66,159 scenes. Of these, 47,980, 7,998, and 7,995 scenes form the standard training, validation, and test sets, respec- tively, while 2,186 additional scenes are reserved for robustness evaluation. The downstream VLM splits are geographically disjoint, comprising 188 training, 17 validation, and 16 test regions. No held-out-region polygons contribute gradients during geometry-encoder training. Table 7: Dataset statistics for geometry pretraining, VLM training, and evaluation. (a) Geometry encoder data from China GeographyRegionsL3 polygonsL4 polygonsContext samples Training18865,767211,139185,296 Validation / Test3315,33051,74745,270 (b) VLM scene data from China SplitRegionsScenesQA instances Training18847,980359,340 Validation177,99859,997 Test167,99559,830 (c) Zero-shot geographic transfer GeographyRegionsScenesEval. regionsEval. scenesQA instances / task United States7687,90669001,800 Singapore16601300600 20 Preprint (a)(b) (c) Cumulative fraction 푙 10 projected area (푚 2 ) Reference-point countGeometry-token count China train U.S. transfer Singapore transfer Figure 9: Geometry distribution shifts between training and transfer geographies. Empirical cu- mulative distributions of (a) projected polygon area, (b) retained reference-point count, and (c) geometry-token sequence length for L4 polygons in the China training regions and the U.S. and Singapore transfer geographies. Transfer distributions are computed over the polygons in the re- ported evaluation regions. Geographic transfer. We further evaluate zero-shot geographic transfer to the United States and Singapore using the same preprocessing and scene-construction pipeline. The U.S. dataset spans 76 metropolitan regions, of which six are used for the reported evaluation, while Singapore is evaluated as a single-region transfer set. Neither geography contributes to model training or model selection. Figure 8 summarizes the geographic coverage and region-disjoint evaluation design, and Table 7 reports the resulting data sizes. Figure 9 compares the scale and geometric complexity of the L4 polygons used for China training with those from the U.S. and Singapore transfer geographies. The U.S. polygons are moderately larger in area while remaining similar in boundary complexity to the China training distribution. Singapore exhibits a stronger shift in boundary complexity, with more retained reference points and longer geometry-token sequences, despite a comparable polygon-area range. Transfer evaluation distributions show geographic and geometric complexity variations. B.2TASK CONSTRUCTION AND METRICS Task selection. We select tasks to cover three fundamental forms of spatial reasoning used in GIS and spatial databases: directional, topological, and metric reasoning (G ̈ uting, 1994; Carniel, 2024). Direction evaluates relative orientation, while parcel–parcel and point–parcel topology test containment relations across different spatial object types. Proximity, area, and boundary distance evaluate metric reasoning over inter-object distance, object extent, and point-to-boundary distance, respectively. We evaluate six spatial task families. Direction additionally uses a continuous two- dimensional displacement target on the same ordered object pairs. Table 8 summarizes the evaluated relations and sample sizes. Table 8: Spatial tasks used in evaluation. TaskQueryPredictionQuestions DirectionParcel pair8-way direction / continuous (∆x, ∆y)1,800 ProximityAnchor + candidatesCandidate with smaller boundary distance1,800 Parcel topologyParcel pairinside / contains / outside1,800 Point topologyquery point + parcelinside / outside1,800 AreaParcel setparcel with largest / smallest area1,800 Distancequery point + parcel setparcel with nearest / farthest boundary distance to query point 1,800 Question counts are reported for the China test set. Displacement uses the same 1,800 ordered pairs as direction and therefore does not add separate question–answer instances. 21 Preprint Direction Proximity Topology Topology Area Selection Distance Selection Prompt: What is the direction of parcel A relative to parcel B? Answer with one of: North, Northeast, East, Southeast, South, Southwest, West, or Northwest. Prompt: Which parcel is closer to parcel C, A or B? Prompt: Parcels A and B are enclosed by the blue and orange boundaries, respectively. What is the topological relation of parcel A to parcel B? Answer with: Inside, Contains, or Outside. Prompt: Is the query point inside or outside parcel A? Answer with: Inside or Outside. Prompt : Which parcel has the [smallest/largest] area, A, B, C, or D? Prompt : Which parcel has the [closest/farthest] distance from the query point to its boundary, A, B, C, or D? Gold: North; ∆=(+0.18, +1.56) km Gold: B Gold: ContainsGold: Outside Gold: Largest: D; Smallest: B Gold: Farthest: B; Closest: D Figure 10: Representative examples from the benchmark. Each panel shows the visual input, one prompt realization, and the target answer. Geometric target and paired query construction. All task labels are generated deterministically offline from the exact projected geometries, without manual or model-generated annotation. Di- rection is defined from the ordered displacement between parcel centroids and quantized into eight compass sectors, with the same ordered pairs additionally assigned continuous displacement targets (∆x, ∆y). Comparative proximity is determined by the minimum polygon distance between the anchor parcel and each candidate. Parcel–parcel and point–parcel topology are computed from ex- act geometric relations, while area and boundary-distance selection use projected polygon area and point-to-boundary distance, respectively. To evaluate geometric reasoning beyond coarse spatial cues, we exclude ambiguous samples and construct hard cases where commonly used geometric proxies disagree with the exact target rela- tion. Specifically, proximity hard cases are selected when centroid distance conflicts with minimum boundary distance; area hard cases when bounding-box area differs from polygon area; and distance hard cases when nearest-vertex distance differs from exact boundary distance. These cases reduce the possibility of solving tasks through simple geometric approximations. Queries involving reversible or opposite relations are evaluated in matched pairs to measure geomet- ric consistency. Direction reverses the ordered parcel pair, proximity swaps candidate objects while preserving the anchor parcel, and topology evaluates reciprocal relations such as inside/contains. Similar paired constructions are used for opposite extrema queries where applicable. These paired evaluations support the consistency analyses in Section 5.1. Figure 10 presents representative baseline examples from the six evaluated task families, including the visual input, one prompt realization, and the corresponding target answer. The examples illus- trate how spatial objects, query points, and candidate sets are presented to the model. Area and Distance include both extrema queries to evaluate metric reasoning beyond the structured objectives used during training. 22 Preprint Common instruction for GeoVec-VLM System. You are performing a geospatial reasoning task over a spatial scene. Object references. References such as parcelA, parcelB, and parcelC denote the polygonal spatial objects assigned to the corresponding query slots. For GeoVec-VLM, these symbols identify objects through the vector query slots and are not rendered as text labels in the image. When a query point is present, its location is defined by the center of the crosshair marker in the image. Answer using only the requested answer format. Representative task prompts Direction. Query: What is the direction of parcelA relative to parcelB? Output: Answer with one of: North, Northeast, East, Southeast, South, Southwest, West, or Northwest. Comparative proximity. Query: Which parcel is closer to parcel C, parcelA or parcelB? Output: Answer with A or B. Parcel–parcel topology. Query: What is the topological relation of parcelA to parcelB? Output: Answer with one of: Inside, Contains, or Outside. Point–parcel topology. Query: Is the center of the query crosshair inside or outside parcelA? Output: Answer with Inside or Outside. Area and boundary-distance selection. The retained candidates are identified by letters A, B, C, and D. The query asks for the candi- date with the largest/smallest area or nearest/farthest boundary distance, and the output is the corresponding candidate letter. Prompt construction and object references. Each question combines a common geospatial rea- soning instruction with a task-specific query. Queried spatial objects are internally represented by vector-object IDs and mapped to temporary symbolic slots such as parcelA, parcelB, and parcelC during language interaction. These slots refer to underlying vector objects and are not visual annotations rendered in the image. For point-based tasks, the query point corresponds to the center of the crosshair marker. GeoVec-VLM receives images without alphabetical parcel labels, while image-only baselines use rendered labels to identify referenced parcels. Thus, object correspondence is provided through vector structure only for GeoVec-VLM and through visual annotations for image-only baselines. Training prompts are generated from compositional templates rather than a single fixed form. Each prompt is generated by combining role descriptions, question formulations, and output constraints. Four role descriptions, four question formulations, and two output constraints are combined for each task family, resulting in 4× 4× 2 = 32 surface forms. Evaluation uses independently constructed prompt forms that do not overlap with training templates. Cross-modal spatial grounding metrics. For CSG, Object Top-1 is correct when the highest- scoring parcel candidate (including outside) matches the ground-truth object. For visual support, each valid parcel slot predicts a binary mask over visual patches using ˆm ip = 1[σ(s ip ) > 0.5]. Visual-support F1 is computed from TP, FP, and FN pooled over all valid parcel-slot–patch pairs within a sample: F 1 = 2TP 2TP + FP + FN . 23 Preprint Target-region patch F1 uses the same measure but restricts the comparison to the ground-truth target parcel and its annotated visual-patch mask. Figure 4(c) reports the per-sample target-region patch F1 distribution. B.3QUALITATIVE SPATIAL REASONING CASES After collecting the constrained task answers used for quantitative evaluation, we issue a separate post-hoc explanation query for qualitative analysis. These explanations do not affect the reported task predictions or accuracy. Figure 11 presents two representative cases in which fluent visual reasoning does not necessarily correspond to the underlying geometry. In comparative proximity, several general-purpose VLMs produce plausible visual explanations based on apparent gaps, adja- cency, or intervening parcels, yet arrive at the wrong candidate. These explanations illustrate how a model can construct a coherent spatial narrative from the image while failing to recover the geomet- ric relation that determines the answer. GeoVec-VLM selects the correct parcel and attributes the decision to spatial evidence from the aligned vector geometry and image boundaries. The parcel– parcel topology example exposes a related failure more directly. Here, one parcel is contained by the other while part of their boundaries coincide. This configuration is difficult to resolve reliably from image appearance alone: several baselines classify the parcels as Outside, while another reverses the ordered relation and predicts Inside. GeoVec-VLM instead has direct access to the underlying vector geometry in the shared spatial frame, allowing the ordered containment relation to be resolved from the geometric structure itself. GeoVec-VLM—`B` (correct): B is closer to C than A is, based on direct spatial evidence within vector geometry and the raster-defined boundaries. Kimi K2.5 —`B` (correct): Parcel B shares a direct boundary with D, which in turn shares a boundary with C, making B's minimum distance to C shorter than A's isolated position. GPT-5.1 —`B` (correct): Parcel B touches parcel D, which in turn shares a boundary with anchor C, creating a shorter polygon-to-polygon boundary path than any gap-separated route from parcel A to C. DeepSeek-V4-Flash —`A` (incorrect): A sits as a separate polygon with a clear gap from C, while B shares a long direct boundary with C, so A has the smaller minimum boundary distance. Gemini 2.5 Flash —`A` (incorrect): The distance between polygon A and polygon C is visually shorter than the distance between polygon B and polygon C. Qwen3.7-Plus—`A` (incorrect): Parcel A is spatially isolated but positioned closer to the outer edge of parcel C than parcel B, which is separated from C by the intervening parcel D. Question: Which parcel is closer to C, A or B? Gold answer: B GeoVec-VLM—` contains ` (correct): Contains indicates Parcel B is entirely within Parcel A, confirmed by direct measurement and spatial comparison using raster and vector data. Kimi K2.5 —` inside` (incorrect): Parcel A is a smaller region completely surrounded by and nested within the larger parcel B, with A's boundary fully contained inside B's boundary. GPT-5.1 —` outside` (incorrect): The area marked A is visually located in a distinct, separate polygonal region that does not overlap with or lie within the larger polygonal region labeled B. DeepSeek-V4-Flash —` outside` (incorrect): Parcel A and Parcel B are separated by a distinct boundary line, indicating they are disjoint polygons with no shared interior. Gemini 2.5 Flash —` outside` (incorrect): Parcel A and parcel B are distinct, non-overlapping regions, with a clear white boundary line separating them. Qwen3.7-Plus—` outside` (incorrect): Label A sits on a boundary line above B's region, indicating A is outside B's parcel. Question: What is the topology relation of parcel A to parcel B? Gold answer: Contains Figure 11: Post-hoc explanations for representative comparative proximity and parcel–parcel topol- ogy predictions. Explanations are elicited only after the constrained task answers have been col- lected and are used for qualitative analysis. B.4BASELINE IMPLEMENTATION Spatial VLM baselines. SpatialRGPT and SR-3D are initialized from their released checkpoints and adapted to our task using a balanced subset of 3,840 China-training instances (640 per task family). We additionally tested adaptation with 12,000 training instances, which did not improve 24 Preprint validation performance; we therefore report the 3,840-instance configuration. Both models receive the same image scenes and ground-truth parcel masks through their native region-prompt interfaces. SpatialRGPT is evaluated without depth input, while SR-3D uses its official single-view pathway with frozen Depth Anything V2 features. Adaptation is performed with rank-8 LoRA modules on the language-model attention and MLP projections with α = 16 and zero dropout. We train for one pass over the adaptation set using answer-token cross-entropy and AdamW with a learning rate of 2× 10 −5 , batch size 10, 20 warm-up steps followed by cosine decay, and bf16 computation. For API-based general-purpose VLMs, referenced parcels are marked directly in the image with alphabetical labels corresponding to the query roles. As shown in Figure 10, these labels provide the visual reference needed to identify parcels A, B, and C; no vector geometry is supplied unless the evaluated interface explicitly includes GeoJSON. Serialized GeoJSON, Geo2Vec and Poly2Vec. For the controlled representation comparison in Table 2, Serialized GeoJSON, Geo2Vec, and Poly2Vec use the same scene objects, query-role as- signments, Qwen3-VL-8B backbone, and downstream training split. Geo2Vec and Poly2Vec follow their respective released geometry encoding procedures and expose each object through a fixed-size embedding projected into the VLM hidden space. Serialized GeoJSON provides vector objects as textual coordinate sequences.Polygon and MultiPolygon geometries are transformed into a scene-local coordinate system normalized to [0, 1] 2 and simplified at approximately the image resolution. The coordinate convention is ex- plicitly specified in the prompt, with southwest as (0, 0) and northeast as (1, 1).Each ob- ject is represented with an opaque scene-local identifier (e.g., object 03), while query roles are separately specified through bindings such as A=object03.An object is serialized as"geometry":"coordinates":[[[0.12,0.34],...]],"type":"Polygon", "properties":"feature id":"object00","type":"Feature". Geo2Vec and Poly2Vec replace coordinate serialization with fixed-size object-level geometry em- beddings. Geo2Vec representations are learned without task labels using its location and shape branches, whose 128-dimensional outputs are concatenated into a 256-dimensional embedding. Poly2Vec applies its Fourier-based encoder to scene-normalized coordinates mapped from [0, 1] 2 to [−1, 1] 2 , producing a 420-dimensional embedding. These geometry embeddings are projected into the Qwen hidden space through a two-layer MLP h i = W 2 GELU(W 1 f i + b 1 ) + b 2 , and the projected vectors replace the corresponding placeholder embeddings before the VLM forward pass. The geometry embeddings remain frozen during downstream training, while the projector and rank-16 language LoRA are optimized under the same configuration. CSPATIAL MECHANISM AND GENERALIZATION C.1GEOGRAPHIC TRANSFER EVALUATION Table 9: Spatial reasoning performance under geography transfer. Baselines use image + GeoJSON; GeoVec-VLM uses native vectors. † Area and Distance receive no corresponding downstream task supervision. RegionModelDirection↑Proximity↑Topology↑Area † ↑Distance † ↑ U.S. DeepSeek-V4-Flash0.6520.5910.5480.7580.408 Kimi K2.50.6950.7510.5990.7810.590 Gemini 2.5 Flash0.6720.7080.5780.7730.569 Qwen 3.7 Plus0.7440.7380.6180.7790.692 GPT-5.10.6540.7470.6640.7380.579 GeoVec-VLM-8B0.8010.7990.8240.7940.657 Singapore DeepSeek-V4-Flash0.6350.5970.5820.8350.403 Kimi K2.50.6670.7430.6340.8510.598 Gemini 2.5 Flash0.6280.7130.6280.8650.588 Qwen 3.7 Plus0.6920.7130.6280.8320.658 GPT-5.10.6150.7720.6750.7880.535 GeoVec-VLM-8B0.7750.7820.8480.8500.658 25 Preprint Table 9 shows that the gains in Table 1 are not concentrated in a single test region. GeoVec-VLM ranks first on all three supervised tasks in both the U.S. and Singapore, with particularly stable gains on Topology (+16.0 and +17.3 points over the strongest image+GeoJSON baseline). Its performance on these tasks also varies by only 1.7–2.6 percentage points between the U.S. and Singapore trans- fer sets. Area and Distance, which receive no corresponding structured supervision, show smaller margins but remain competitive in both regions. The regional split therefore supports both the geo- graphic robustness of GeoVec-VLM and the transferability of its learned spatial representations. C.2TARGETED GEOMETRY-TOKEN INTERVENTIONS We further examine which components of the structured geometry representation support spatial reasoning. Starting from the trained GeoVec-VLM, we apply three targeted interventions at in- ference time while keeping the model parameters, visual and language inputs, and non-targeted geometry cues unchanged. As shown in Table 10, the three interventions remove the shared scene reference (-SCENEREF), suppress reference-point geometry (-RPGEOM), or remove explicit hierar- chical identifiers (-HIERID). Table 11 reports the resulting change in final-answer accuracy relative to the intact model. Table 10: Definition of the targeted geometry interventions. Each intervention disrupts one source of geometric information while preserving the remaining representation. InterventionDisrupted informationPreserved information -SCENEREFObject-level H3/centroid placement and RP tile/context coordinates in the shared scene frame. Within-object relative contour, path attributes, hierarchical identifiers, and object identity. -RPGEOMObject-local RP coordinates, bearing/turn features, and pointwise tile/local/context co- ordinates, which are collapsed to the object center. Object centers and cross-object placement, arc phase, path attributes, and hierarchical identifiers. -HIERIDExplicit part, ring, ring-role, local-structure, and phase identifiers. Token type, sequence order, RP/path alterna- tion, attention masks, and boundary-neighbor connectivity. Table 11: Effects of targeted geometry-token interventions across evaluation regions. Values are percentage-point changes in final-answer accuracy relative to the intact GeoVec-VLM. Larger negative changes indicate greater reliance on the disrupted spatial information GeographyInterventionDir. ∆Prox. ∆Parcel Topo. ∆Point Topo. ∆Area ∆Dist. ∆ China −SceneRef-63.94-30.06-20.06-0.67-0.61-23.61 −RPGeom+1.39-4.61-17.50-0.56-4.28+0.06 −HierID-13.06-8.72-8.72-7.17-3.83-1.94 U.S.−SceneRef-61.39-28.11-33.72-1.11-4.00-26.72 −RPGeom-2.72-4.11-17.17-0.33-7.17+0.39 −HierID-10.78-22.59-10.78-12.94-8.39-6.17 Singapore −SceneRef-60.83-26.50-37.83-2.50-4.50-28.00 −RPGeom-0.17-4.83-9.67-2.67-7.50-3.17 −HierID-27.17-14.33-18.00-6.76-11.50-12.00 The three interventions reveal distinct roles of the geometric information preserved by GeoVec. Re- moving global placement produces the largest degradation on Direction and Proximity, and also substantially affects Parcel Topology and Distance. These tasks depend on relative object positions or cross-object metric relations in a shared coordinate frame. In contrast, removing local shape has little effect on Direction but consistently degrades Parcel Topology and Area, showing that within- object contour information contributes more directly to shape- and boundary-sensitive reasoning. Removing explicit structure IDs causes broader but generally smaller degradation, indicating that 26 Preprint hierarchical identifiers help organize element-level geometry beyond the information already avail- able from token order, RP/path alternation, and boundary connectivity. These intervention effects vary across geographies. For example, the Parcel Topology drop caused by removing global placement increases from 20.1 points in China to 33.7 in the U.S. and 37.8 in Singapore, while removing structure IDs has larger effects on several tasks in the transfer sets. These changes are consistent with the geometry-distribution differences reported in Fig. 9, including shifts in polygon scale and boundary complexity. The intervention results therefore suggest that the same structured representation can support a task through different mixtures of geometric cues as the underlying parcel distribution changes. Figure 12: Spatial information enters and structures the language path. (a) Vocabulary-head readout of the answer-prefix state around language–spatial fusion. With multimodal inputs, top-1 accuracy rises sharply after the language states read the spatial memory; removing this fusion sup- presses the transition. (b) Pairwise distances between direction-conditioned language states increase with physical angular separation. (c) Proximity-state variation tracks the physical distance advan- tage between candidates. C.3HOW VECTOR GEOMETRY INFLUENCES ANSWER GENERATION Figure 12(a) examines how instance-specific spatial information enters the language path. Without image and vector inputs, correct-answer probability may increase across language layers without improving top-1 accuracy. With complete inputs, accuracy rises sharply after language–spatial fu- sion; removing the fusion eliminates this transition. This identifies the spatial states as the pathway through which instance-specific spatial information reaches answer generation. The language states after fusion also preserve continuous geometric structure shown in Fig. 12(b–c): representational distance tracks angular separation for direction (ρ = 0.895) and the physical distance advantage for proximity (ρ = 0.418). The fused language representation therefore retains geometric structure beyond the discrete task labels. DEFFICIENCY AND CAPABILITY PRESERVATION D.1INPUT TOKEN CONSUMPTION. Fig. 13 compares the total input consumed over each evaluation set with the corresponding mean task accuracy. On the controlled China benchmark, Geo2Vec and Poly2Vec use 4.90M input tokens but expose each vector object through fixed-size embeddings; increasing the input to 7.01M with 27 Preprint element-level GeoVec tokens raises mean accuracy from 41.1–41.5% to 77.2%. Serialized Geo- JSON exhibits the opposite regime, consuming 37.27M tokens while reaching only 45.6% mean accuracy. The same pattern becomes more pronounced for API models on the transfer sets, where GeoJSON-based inputs consume 143–325M tokens in the U.S. and 58–132M in Singapore, sub- stantially exceeding GeoVec while remaining less accurate. These results suggest that the useful bandwidth of a geometry interface depends on both how much geometric information remains ac- cessible and how that information is structurally organized for multimodal computation. Figure 13: Total input-token consumption and spatial reasoning accuracy across evaluation sets. Token counts include the complete model input, including visual inputs, language instructions, and geometry when present. For API models, counts are those reported by the corresponding model interface. China and U.S. each contain 10,800 evaluated questions, while Singapore contains 3,600. Geo2Vec and Poly2Vec are evaluated only in the controlled China setting, consistent with Table 2. D.2GENERAL CAPABILITY PRESERVATION Table 12: General capability after GeoVec adaptation. GeoVec retains the trained language pa- rameters while disabling the GeoVec-specific spatial pathway. BenchmarkScopeNQwenGeoVec∆ (p) IFEvalOverall54184.47%85.03%+0.55 MMLUOverall114077.54%77.28%-0.26 STEM36073.06%72.78%-0.28 Humanities26080.77%80.38%-0.38 Other28076.79%76.79%+0.00 Social sciences24081.67%81.25%-0.42 GeoVec-VLM adapts the frozen Qwen3-VL-8B-Instruct backbone with LoRA during spatial train- ing. We examine whether this adaptation alters capabilities of the original backbone that are unre- lated to the spatial tasks used for training. We retain the trained language parameters while disabling the GeoVec-specific spatial modules and evaluate instruction following on IFEval (Zhou et al., 2023) and multidisciplinary knowledge on MMLU (Hendrycks et al., 2021). Table 12 shows little change relative to the original Qwen3-VL-8B-Instruct. Strict prompt accu- racy on IFEval changes from 84.47% to 85.03%, while MMLU accuracy changes from 77.54% to 77.28%. The MMLU differences remain small across STEM, humanities, social sciences, and other subjects. The paired 95% confidence intervals for IFEval ([−1.29, +2.40] percentage points) and MMLU ([−0.61, +0.09]) both include zero. These diagnostics provide no evidence of a measurable loss in instruction following or multidisciplinary knowledge after GeoVec training. 28