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SpatialCORE: Confidence-Aware Grounded Spatial Reasoning in Large Vision--Language Models
Rafi Ibn Sultan, Xiangyu Zhou, Md. Sajid Alam Chowdhury, Chengyin Li, Prashant Khanduri, Marco Brocanelli, Dongxiao Zhu
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 92%
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Summary
The paper introduces SpatialCORE, a post-training framework for Large Vision-Language Models (LVLMs) that enhances spatial reasoning by incorporating the model's confidence in generated grounding (bounding boxes) as a learning signal. It utilizes a self-regulating spatial reward that weights bounding box matching quality by coordinate-token confidence, coupled with an answer gate to link grounding optimization to final answer correctness. SpatialCORE achieves state-of-the-art results on spatial reasoning benchmarks.
Entities (8)
Relation Signals (6)
SpatialCORE → improves → Spatial Reasoning
confidence 95% · SpatialCORE (Spatially COnfident REasoning), a post-training framework that turns the model's own confidence in generated grounding into a learning signal for spatial reasoning.
SpatialCORE → uses → GRPO
confidence 95% · Built on Group Relative Policy Optimization (GRPO) Shao et al. (2024), SpatialCORE optimizes sampled reasoning trajectories
SpatialCORE → utilizes → self-regulating spatial reward
confidence 95% · SpatialCORE realizes this through a self-regulating spatial reward that weights each predicted bounding box's matching quality by its coordinate-token confidence.
SpatialCORE → evaluatedon → OmniSpatial
confidence 90% · Table 1: OmniSpatial Jia et al. (2025) results across 10 spatial reasoning task categories. SpatialCORE is compared against...
SpatialCORE → isbuilton → Qwen3-VL
confidence 90% · We instantiate SpatialCORE with Qwen3-VL-Thinking Bai et al. (2025) backbones
Grounding DINO → usedfor → pseudo-GT BBoxes
confidence 85% · we use a Referring Expression Comprehension (REC) model (e.g. Grounding DINO Liu et al. (2024b)) to localize task-relevant objects.
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Abstract
Abstract:Large Vision-Language Models (LVLMs) have made remarkable progress across visual perception tasks, yet spatial reasoning remains a persistent weakness, especially for questions that require reasoning over visual space. Recent spatial-reasoning methods incorporate generated grounding, where models predict bounding boxes, masks, or other localization outputs for task-relevant objects as part of their reasoning trace. However, these approaches typically optimize final-answer correctness alone, allowing correct answers to be rewarded even when the model does not reason from confidently localized task-relevant objects. We introduce SpatialCORE (Spatially COnfident REasoning), a post-training framework that turns the model's own confidence in generated grounding into a learning signal for spatial reasoning. Its central idea is to reinforce grounding that is both accurate and confident, encouraging the model to reason from confidently localized task-relevant objects. SpatialCORE realizes this through a self-regulating spatial reward that weights each predicted bounding box's matching quality by its coordinate-token confidence. An answer gate further ties grounding optimization to final-answer correctness. SpatialCORE achieves state-of-the-art results among open-source and specialized spatial reasoning models across diverse benchmarks, and transfers effectively in zero-shot settings to unseen data distributions. The source code is available at this https URL.
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- Source: https://arxiv.org/abs/2609.38716v1
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Preprint SPATIALCORE: CONFIDENCE-AWARE GROUNDED SPATIAL REASONING IN LARGE VISION–LANGUAGE MODELS Rafi Ibn Sultan 1 Xiangyu Zhou 1 Md. Sajid Alam Chowdhury 1 Chengyin Li 2 Prashant Khanduri 1 Marco Brocanelli 3 Dongxiao Zhu 1,4 1 Department of Computer Science, Wayne State University 2 Department of Radiation Oncology, Henry Ford Health 3 Department of Electrical and Computer Engineering, The Ohio State University 4 Institute for AI and Data Science, Wayne State University ABSTRACT Large Vision-Language Models (LVLMs) have made remarkable progress across visual perception tasks, yet spatial reasoning remains a persistent weakness, es- pecially for questions that require reasoning over visual space. Recent spatial- reasoning methods incorporate generated grounding, where models predict bound- ing boxes, masks, or other localization outputs for task-relevant objects as part of their reasoning trace. However, these approaches typically optimize final- answer correctness alone, allowing correct answers to be rewarded even when the model does not reason from confidently localized task-relevant objects. We introduce SpatialCORE (Spatially COnfident REasoning), a post-training frame- work that turns the model’s own confidence in generated grounding into a learn- ing signal for spatial reasoning. Its central idea is to reinforce grounding that is both accurate and confident, encouraging the model to reason from confi- dently localized task-relevant objects. SpatialCORE realizes this through a self- regulating spatial reward that weights each predicted grounding, i.e., bound- ing box’s matching quality by its coordinate-token confidence. An answer gate further ties grounding optimization to final-answer correctness. Spatial- CORE achieves state-of-the-art results among open-source and specialized spa- tial reasoning models across diverse benchmarks, and transfers effectively in zero-shot settings to unseen data distributions. The source code is available at https://github.com/rafiibnsultan/SpatialCORE. 1INTRODUCTION Large Vision–Language Models (LVLMs) Alayrac et al. (2022); Li et al. (2023); Liu et al. (2023a); Dai et al. (2023); Bai et al. (2023) have achieved strong performance on multimodal perception tasks, yet they remain unreliable when reasoning about spatial structure Qi et al. (2025a); Ranasinghe et al. (2024); Zhou et al. (2025); Xu et al. (2026b); Yang et al. (2025a); Song et al. (2025). Even with accurate object identification, they often struggle to understand spatial arrangements and relationships Liu et al. (2026); Zhang et al. (2025); Yu et al. (2025); Sun et al. (2025); Liu et al. (2025a). Spatial reasoning requires the model to move beyond recognizing scene elements and construct a coherent understanding of the environment through fine-grained relationships among objects Yang et al. (2025b); Gholami et al. (2025); Batra et al. (2025); Lee et al. (2025). This gap between object recognition and spatial understanding limits the use of LVLMs in real-world settings such as robotics G ́ oral et al. (2024), autonomous driving Wu et al. (2024), and pedestrian assistance Sultan et al. (2026), where correct decisions depend on reasoning about spatial relationships rather than recognizing objects alone. Efforts to address this weakness have taken different forms. Some methods rely on external guidance, such as user-provided points, regions, or spatial anchors, to indicate where task-relevant objects are located or how they should be compared spatially Pothiraj et al. (2025); Cheng et al. (2024); Cai et al. (2025b); Gholami et al. (2025); Shen et al. (2025). While effective, these methods depend 1 arXiv:2609.38716v1 [cs.CV] 30 Sep 2026 Preprint on such guidance and do not directly train the model to reason spatially on its own. A second line post-trains LVLMs on spatial reasoning tasks by supervising grounding predictions, such as segmentation masks or BBoxes, as model outputs Ning et al. (2025); Chen et al. (2024a); Yang et al. (2025b); Ranasinghe et al. (2024). While this improves localization as a standalone training objective, the grounding remains separate from the reasoning trace. Most recently, inspired by “Thinking with Images” OpenAI (2025b), models have been encouraged to incorporate generated grounding during reasoning Wu et al. (2025b); Zheng et al. (2025); Ma et al. (2026); Batra et al. (2025); Chen et al. (2025c); Li et al. (2025). In these methods, generated grounding indicates the task-relevant objects the model uses while reasoning, typically through bounding boxes (BBoxes), masks, or similar localization cues. However, neither answer correctness nor localization quality alone explicitly captures the model’s confidence in generated grounding. (BBox Entropy) (BBox Entropy) Correct answer, uncertain grounding (a) Baseline LVLM(b) SpatialCORE Reasoning Question: From the perspective of the girl, where is the lamp placed? Options: (a) back, (b) back-right, (c) right (d) front Baseline LVLM: <think> "lamp": [0,125,130,250] "girl": [165,335,305,450] ..spatial reasoning.. </think> Answer: (b) back-right Correct answer, confident grounding "girl""lamp" "lamp" "girl" Question: From the perspective of the girl, where is the lamp placed? Options: (a) back, (b) back-right, (c) right (d) front SpatialCORE: <think> "lamp": [112,220,205,334] "girl": [372,170,530,336] ..confidence-aware spatial reasoning.. </think> Answer: (b) back-right Figure 1: Correct final answers do not necessarily imply con- fident grounding. Although both models answer correctly, (a) the baseline LVLM produces high-entropy predicted BBoxes, with dashed candidate BBoxes spread across off-target loca- tions. (b) Our SpatialCORE produces lower-entropy pre- dicted BBoxes, with dashed candidate BBoxes concentrated around the selected BBoxes, and more confidently localizing the task-relevant objects. Solid BBoxes denote the predicted BBoxes in the reasoning trace; dashed BBoxes denote candi- date BBoxes reflected by spatial uncertainty. This is especially problematic for spa- tial reasoning, where generated grounding should localize the task-relevant objects needed to compare positions, distances, and relationships. Most training objectives primarily reward correct final answers Li et al. (2025); Ma et al. (2026); Batra et al. (2025), even when reasoning includes pre- dicted BBoxes for these objects. Some of these methods add spatial or trajectory- level rewards, but still do not account for how confidently the model generates its grounding. A predicted BBox’s coordinate- token uncertainty provides a way to esti- mate this confidence during reasoning. Fig- ure 1a illustrates this distinction: the base- line correctly answers “back-right” when asked where the lamp is relative to the girl, yet generates high-uncertainty BBoxes that poorly localize both objects. Because the answer is correct, a final-answer reward re- inforces the entire trajectory, including its uncertain grounding. This motivates our central question: Can spatial reasoning in LVLMs be improved by learning from the confidence of their own generated grounding? To address this, we propose Spatially COnfident REasoning (SpatialCORE), a post-training frame- work that enhances spatial reasoning in LVLMs by learning to ground with confidence. As illustrated in Figure 1b, SpatialCORE encourages correct answers to be supported by low-uncertainty BBoxes for task-relevant objects. Its self-regulating spatial reward uses the model’s own confidence, esti- mated from BBox coordinate uncertainty, to weight geometric overlap with reference BBoxes. This makes grounding confidence a learning signal even among trajectories reaching the same correct answer. An answer gate further couples spatial and answer rewards by scaling the spatial reward according to final-answer correctness. Our contributions are summarized as follows: • We introduce SpatialCORE, a novel post-training framework that makes the model’s own confidence in generated grounding an explicit learning signal for spatial reasoning in LVLMs. •We propose a self-regulating spatial reward that evaluates generated grounding through both localization quality and coordinate-token confidence, with an answer gate connecting grounding optimization to final-answer correctness. • We demonstrate state-of-the-art results among open-source and specialized spatial reasoning models, with effective zero-shot generalization. Controlled ablations establish the value of confidence weighting, while grounding analyses reveal improved alignment between confidence and localization quality. 2 Preprint 2RELATED WORKS Externally Guided Spatial Grounding. A common strategy for improving spatial reasoning in LVLMs is to provide explicit spatial anchors as input. Points, regions, masks, or referenced objects are supplied with the query to direct the model toward task-relevant objects Bigverdi et al. (2025); Yang et al. (2025b); Cheng et al. (2024); Shen et al. (2025); Ma et al. (2025); Cai et al. (2025b). These approaches are effective when reliable anchors are available, but their dependence on inference-time guidance limits open-ended use: when anchors are absent or ambiguous, the model must still identify relevant objects on its own. Thus, spatial reasoning may not transfer to settings without external anchors. Geometry-Enhanced Visual Understanding. Another line improves spatial reasoning by adding ge- ometric cues to the visual representation. These methods use depth maps, point clouds, segmentation masks, or multi-view geometry to encode scene layout and spatial relationships Liu et al. (2025b); Chen et al. (2024b); Hu et al. (2025); Wang et al. (2025b); Wan et al. (2025); Cai et al. (2025a); Chen et al. (2025a); Sultan et al. (2026); Ning et al. (2025); Daxberger et al. (2025); Hong et al. (2023); Wu et al. (2025a); Xu et al. (2026a); Zhao et al. (2025b); Chen et al. (2026b); Zhou et al. (2026). Such representations can improve spatial perception, but they mainly change what the model observes, not how it learns to generate and use grounding during reasoning. These representations do not by themselves specify how grounding confidence should affect the post-training reward. Inference-Time Reasoning Scaffolds. Spatial reasoning can also be improved at inference time by structuring the model’s response without post-training. These methods guide reasoning through cognitive maps, scene graphs, perspective-aware representations, compositional prompting, or related scaffolds Liao et al. (2024); Gholami et al. (2025); Lee et al. (2025); Ma et al. (2024); Mitra et al. (2024); Yang et al. (2025a), and may also intervene at decoding time Chen et al. (2025b); Huang et al. (2025); Yan et al. (2026). While training-free, their gains are often tied to specific task formats, prompts, scaffolds, or decoding procedures, leaving the model’s spatial reasoning behavior unoptimized. Training-Based Spatial Reasoning. A more direct strategy is to optimize spatial reasoning during training Kancheti et al. (2026); Chen et al. (2026a); Li et al. (2026). One line enriches the reasoning trace with spatial content, such as generated grounding or other task-relevant spatial outputs Ma et al. (2026); Chen et al. (2025c); Batra et al. (2025); Wang & Ling (2025). Inspired by “Thinking with Images” OpenAI (2025b), a related line further supervises generated grounding in the reasoning trace with RL-based objectives that reward correct localization of task-relevant objects Wu et al. (2025b); Zheng et al. (2025); Xu et al. (2025); Sarch et al. (2025); Zhao et al. (2025a); Li et al. (2025). These approaches emphasize what grounding is produced and whether it is correct. SpatialCORE introduces the model’s confidence in producing that grounding as an additional learning signal, training spatial reasoning through both grounding quality and certainty. 3METHOD We develop SpatialCORE (Figure 2a), a post-training framework that improves spatial reasoning in LVLMs through confidence-aware grounding. Built on Group Relative Policy Optimization (GRPO) Shao et al. (2024), SpatialCORE optimizes sampled reasoning trajectories using a self- regulating spatial reward that weights generated grounding by model confidence, encouraging reasoning from confidently localized task-relevant objects. The reward measures uncertainty in predicted bounding-box coordinates (Figure 2b) and is combined with format and answer rewards through an answer gate. The resulting trajectory-level rewards are normalized within each rollout group for the GRPO policy update (Figure 2c). 3.1PROBLEM FORMULATION Given an imageIand a spatial reasoning queryq, a LVLM policyπ θ generates a trajectoryo = (x 1 ,...,x T ) consisting of a reasoning trace with generated grounding tokens that specify predicted bounding boxes (BBoxes), followed by a final answer. Based on the next-token distributionπ θ (·| 3 Preprint Policy LVLM "bbox_2d": [300, 240, 390, 345], "label": "black sedan ahead" "bbox_2d": [500, 95, 590, 220], "label": "traffic sign" We have the positions of the relevant objects. Let's think. ... compare grounded objects with the answer choices ... </think> Final answer: (b) black sedan. Spatial Reward Format Reward Answer Reward Policy Update (a) SpatialCORE: Confidence-Aware Grounded Spatial Reasoning Question: Which object would a driver encounter first when moving forward? Options: (a) traffic light, (b) black sedan (c) both at equal distance, (d) cannot determine (Expanded) Trajectory Trajectory Trajectory Reward Reward Reward "bbox_2d":[...], "black sedan ahead" "bbox_2d":[...], "traffic sign" "bbox_2d":[...], "black sedan", validity: 0.8 "bbox_2d":[...], "traffic light", validity: 0.6 Predicted BBoxPseudo-GT BBox Valid Reasoning Segment Single Answer Token Valid Grounding Format Spatial Reward (b) Self-Regulating Spatial Reward Spatial Reward Predicted BBox Uncertainty Label Sim.higher "black sedan ahead" ↔ "black sedan" Label sim.lower "traffic sign" ↔ "traffic light" Format RewardAnswer Reward (c) Adaptive Reward Composition Self-Regulating Gate Group Relative Advantages Figure 2: Overview of SpatialCORE. (a) The LVLM policy samples trajectories comprising a reasoning trace with generated grounding expressed as bounding boxes (BBoxes), followed by a final answer. (b) The self-regulating spatial reward uses predicted BBox coordinate-token uncertainty to estimate the grounding confidence, which then weights each BBox’s matching quality. Predicted BBoxes are matched to pseudo-GT BBoxes using geometric overlap, label similarity, and pseudo-GT validity. For example, black sedan ahead and black sedan have high label similarity, while higher pseudo-GT validity, such as black sedan, validity: 0.8, gives the match more weight. (c) Spatial, format, and answer rewards are composed through an answer gate to produce trajectory-level rewards, which are used to compute group-relative advantages for policy update. x <t ,I,q), the trajectory likelihood π θ (o| I,q) is defined as π θ (o| I,q) = T Y t=1 π θ (x t | x <t ,I,q).(1) For each input(I,q), the policy performs a GRPO rollout by sampling a group ofGtrajectories o i G i=1 , as illustrated in Figure 2a. The rollout assigns each trajectory a rewardr i and computes the corresponding group-relative advantage A i , which then enters the GRPO policy objective: r i = R(o i ), A i = r i − 1 G P G j=1 r j σ G + ε ,(2) whereσ G is the standard deviation of the group rewards andεis a small constant for numerical stability. 3.2SELF-REGULATING SPATIAL REWARD The self-regulating spatial reward operates on predicted BBoxes within each reasoning trajectory. It estimates BBox confidence from the current policy’s coordinate-token uncertainty, so low-uncertainty BBoxes contribute more to the reward, while high-uncertainty BBoxes contribute less (Figure 2b). To obtain pseudo-ground-truth bounding boxes (pseudo-GT BBoxes), we use a Referring Expression Comprehension (REC) model (e.g. Grounding DINO Liu et al. (2024b)) to localize task-relevant objects. During reward computation, each pseudo-GT BBox is weighted by its REC validity, so a higher-validity localization such as black sedan with validity0.8contributes more than a lower- validity localization such as traffic light with validity 0.6. 4 Preprint 3.2.1CONFIDENCE-AWARE SPATIAL REWARD Pseudo-GT-Guided Spatial Matching. During each trajectoryo i , the LVLM policy generates predicted BBoxes for task-relevant objects referenced in the question and answer options as part of the reasoning trace. These predicted BBoxes are evaluated against precomputed pseudo-GT BBoxes from a REC modelG. For each image-question pair,Glocalizes the extracted objects into tuples (b gt k ,ℓ gt k ,v k ), whereb gt k is the pseudo-GT BBox,ℓ gt k is the corresponding label of a task-relevant object, and v k ∈ [0, 1] is the validity produced byG for the localized pseudo-GT BBox. As illustrated in Figure 2b, each trajectory may generate multiple predicted BBoxes, so matching them to pseudo-GT BBoxes cannot rely on geometric overlap alone. A generated label such as black sedan ahead should match black sedan more strongly than a mismatched label such as traffic sign. We therefore compute a pairwise BBox reward for each predicted BBoxb j with object labelℓ j against each pseudo-GT BBox b gt k , using both geometric overlap and label similarity: R (j,k) BBox = w iou · max 0, IoU(b j ,b gt k )− τ iou + w label · Sim(ℓ j ,ℓ gt k ) · v k ,(3) wherew iou +w label = 1andτ iou is an IoU margin. The clipped IoU term suppresses weak geometric overlap, whileSim(ℓ j ,ℓ gt k ) measures label similarity using cosine similarity between semantic label representations. The pseudo-GT validityv k scales the pairwise BBox reward, assigning a larger weight to higher-validity pseudo-GT BBoxes and reducing the influence of noisier ones. This makes the spatial reward depend more on reliable pseudo-GT BBoxes during matching. We then use Hungarian matching Kuhn (1955) to obtain the optimal one-to-one assignment between predicted BBoxes and pseudo-GT BBoxes: M ∗ i = arg max M i X (j,k)∈M i R (j,k) BBox .(4) The matched pairs inM ∗ i are then used to compute the confidence-weighted spatial reward. BBox Coordinate-Token Uncertainty. We estimate the confidence of generated grounding from the tokens that produce each predicted BBox. A BBox is emitted as"bbox2d": [x1, y1, x2, y2], with each coordinate generated autoregressively as digit tokens that determine its location; their uncertainty therefore estimates confidence in the predicted BBox. LetC =x 1 ,y 1 ,x 2 ,y 2 denote the BBox coordinates andS i,j,c the digit-token positions of coordi- natec∈Cof predicted BBoxb j in trajectoryo i , excluding brackets, commas, and spaces. Leth i,t denote the Shannon entropy ofP θ (·| x i,<t ,I,q)over the full vocabularyV, andD ⊂Vthe set of digit tokens. We define the uncertainty ofb j as the normalized entropy averaged over digits within each coordinate, then over coordinates: H i,j = clip [0,1] 1 |C| log|D| X c∈C 1 |S i,j,c | X t∈S i,j,c h i,t .(5) Full-vocabulary entropy also rises when probability shifts to non-digit tokens, whilelog|D|, the entropy of a uniform choice over digits, sets its scale. Lower H i,j indicates higher confidence in b j . Confidence-Weighted Spatial Reward. We weight each matched predicted BBox by its confidence, estimated from coordinate-token uncertainty H i,j : C i,j = 1− H i,j , ω i,j = β + (1− β)C i,j ,(6) whereC i,j denotes the confidence of predicted BBoxb j ,β ∈ (0, 1)is a confidence floor, and (j,k) ∈ M ∗ i denotes a matched prediction–pseudo-GT pair. The confidence weight gives high- certainty groundings greater contribution while remaining positive even under high uncertainty. The resulting weighted matching scores collectively define a confidence-weighted measure of matching quality, P i = 1 |M ∗ i | X (j,k)∈M ∗ i ω i,j R (j,k) BBox ,(7) whereP i = 0when no match is found. This term evaluates matched prediction–pseudo-GT pairs under the one-to-one assignment, so ambiguous or duplicated assignments cannot inflate the matching quality. 5 Preprint To encourage broader coverage of the pseudo-GT BBoxes for the input(I,q), denoted byP, we define a soft recall term weighted by pseudo-GT validity: Recall i = X k∈P v k ! −1 X k∈P max j R (j,k) BBox , R (i) spatial = F α (P i , Recall i ) = (1 + α 2 )P i Recall i α 2 P i + Recall i . (8) If P k∈P v k = 0or theF α denominator is zero, we setR (i) spatial = 0. Here,Recall i measures how well the pseudo-GT BBoxes are covered by the set of predictions, rewarding each task-relevant object that is localized by at least one predicted BBox. The spatial reward combines matching quality and pseudo-GT coverage through anα-weighted harmonic mean, withα > 1mildly emphasizing coverage and discouraging trajectories that localize only a subset of task-relevant objects. 3.2.2FORMAT AND ANSWER REWARDS Format Reward. We use a format reward to enforce the trajectory structure required for grounded reasoning. As shown in Figure 2b, a trajectory is rewarded for three format properties: a valid reasoning segment, a single final answer token, and a valid grounding format for predicted BBoxes. Malformed outputs, repeated object labels, or BBoxes placed outside the reasoning segment reduce the format reward. Answer Reward. The answer reward assigns a unit reward to a correct final answer and zero otherwise: R (i) ans = 1, if ˆy i = y i , 0, otherwise. (9) 3.3ADAPTIVE REWARD COMPOSITION We integrate the answer, format, and confidence-aware spatial rewards to assign a single reward to each sampled trajectory. The spatial term is adaptively modulated by an answer gate, so the spatial reward remains tied to final-answer correctness (Figure 2c): r i = R (i) ans + λ fmt R (i) fmt + λ s g R (i) ans R (i) spatial ,(10) whereg(1) = 1andg(0) = γ, withγ ∈ (0, 1). When the final answer is correct, the full spatial reward is used; when the final answer is incorrect, positive spatial rewards are reduced byγ. This allows incorrect-answer trajectories to retain partial credit for useful generated grounding. 3.4POLICY OPTIMIZATION The policy is optimized using a GRPO-style clipped objective with KL regularization against a reference policyπ ref . Letρ i (θ) = π θ (o i | I,q)/π θ old (o i | I,q)denote the importance ratio for trajectoryo i , whereπ θ old is the rollout policy used to sample the current group. Using the group- relative advantagesA i G i=1 defined above, we optimize the following objective, whereδis the clipping threshold and η is the KL penalty coefficient: J (θ) =E (I,q)∼D,o i ∼π θ old " 1 G G X i=1 min(ρ i (θ)A i , clip(ρ i (θ), 1− δ, 1 + δ)A i )− η D KL (π θ ∥π ref ) # . (11) 4EXPERIMENTS 4.1IMPLEMENTATION DETAILS We instantiate SpatialCORE with Qwen3-VL-Thinking Bai et al. (2025) backbones: SpatialCORE- 8B uses Qwen3-VL-8B-Thinking, while the lighter SpatialCORE-4B variant uses Qwen3-VL-4B- Thinking. Both are post-trained with LoRA Ding et al. (2023) on all language-model linear layers (r = 32,α = 64, dropout0.05) and the vision encoder (r = 4,α = 8). We train for 3 epochs on the 6 Preprint Table 1: OmniSpatial Jia et al. (2025) results across 10 spatial reasoning task categories. SpatialCORE is compared against proprietary models, general open-source LVLMs, and specialized spatial reasoning models. Proprietary models are included as reference points; the best open-source or specialized result is shown in bold. Average accuracy is weighted by category sample size. MethodAverage Dynamic ReasoningSpatial InteractionComplex LogicPerspective Taking Mani- pulation Motion Anal. Traffic Anal. Loca- lization Geospa. Strategy Pattern Rec. Geometric Reasoning Ego Centric Allo Centric Hypo- thetical Reference Baselines Random Choice24.9824.8626.3025.8823.4327.2721.4424.7722.5524.8425.78 Human Evaluation92.6394.6296.0791.3895.1192.1589.0285.9098.5394.3090.26 Proprietary Models GPT-4.1-mini Open (2025)48.8764.3256.5359.0660.1956.3629.2830.1972.5539.5739.28 Gemini-2.5-flash-preview Team et al. (2023)52.1267.5762.7268.2473.3360.9138.1434.1975.4935.9033.73 o4-mini OpenAI (2025a)52.7772.9759.8360.0073.3361.8234.0236.7773.5340.6940.96 Gemini-2.5-flash Team et al. (2023)53.1670.2764.7461.1872.3858.1835.0536.1374.1240.9632.53 Open-source Models LLaVA-1.5-7B Liu et al. (2024a)34.9754.4631.2335.2936.1933.9429.0124.1855.6034.6636.14 LLaVA-OV-7B Li et al. (2024)35.6843.2438.1532.9429.5241.8228.8722.5847.0636.1737.35 InternVL3-8B Zhu et al. (2025)41.6052.4340.8748.9451.0544.7724.9528.6364.2038.6240.96 InternVL3-14B Zhu et al. (2025)45.9454.3260.1750.3551.8151.4528.0428.2668.0435.3734.46 Qwen2.5-VL-7B Wang et al. (2024)39.1858.3835.0950.1245.3344.0031.1329.4264.5133.1937.35 Gemma-3-12B Gemma Team et al. (2025)43.7154.0554.9154.1247.6245.4516.4930.3263.7336.7033.73 Spatial Reasoning Models SpaceMantis-13B Chen et al. (2024a)36.3647.0336.5940.9434.8633.0922.2724.3949.2238.2539.28 SpaceQwen2.5-VL-3B Chen et al. (2024a)40.2558.1139.8841.1840.9540.9129.9025.8163.7338.8339.76 SpaceThinkerQwen2.5VL-3B Chen et al. (2024a)40.4247.8453.0643.2935.4338.7324.3328.0058.0435.1131.08 RoboPoint-vicuna-v1.5-7B-lora Cai et al. (2025a)35.8557.0328.6134.8237.3340.5529.9022.7150.2038.7240.96 RoboPoint-vicuna-v1.5-13B Liu et al. (2023b)34.6055.6828.1542.8232.1932.5524.1227.7449.0237.6633.49 VST-RL-7B Yang et al. (2025b)41.0956.7543.3944.7546.6642.7225.5128.3872.5432.8943.37 SoFar-Qwen2.5VL-3B Qi et al. (2025b)45.1456.4951.1654.1253.1452.7331.7522.8871.6036.5641.69 SpatialLadder-3B Li et al. (2025)40.5059.4539.0150.5848.5742.7226.8023.8771.5635.1039.75 Backbone and Our Variants SpatialCORE-4B44.6864.6851.7350.5863.8046.3619.5827.7466.6634.8444.57 Qwen3-VL-8B-Thinking (Base) Bai et al. (2025)43.9057.1454.2836.0454.9548.6724.7723.1271.5631.1138.82 Qwen3-VL-8B-Thinking + GRPO45.9261.3254.3055.8858.3346.1825.9025.0072.9236.5742.53 SpatialCORE-8B48.4664.8656.6457.6462.8553.6330.9236.7772.5431.9140.96 Table 2: SpatiaLab Wasi et al. (2026) results across 6 spatial reasoning task categories in the zero-shot setting. SpatialCORE is compared against proprietary models, general open-source LVLMs, and specialized spatial reasoning models. Proprietary models are included as reference points; the best open-source or specialized result is shown in bold. Average accuracy is weighted by category sample size. MethodAverage Question Categories 3D Geom.Dep. & Occu.OrientationRelat. Posit.Size & ScaleSpati. Navig. Reference Baselines Random Choice25.0025.0025.0025.0025.0025.0025.00 Human Baseline87.5793.7074.1391.5891.5188.8987.76 Proprietary Models GPT-4o-mini Hurst et al. (2024)46.5047.0639.0047.0347.1749.6049.79 Gemini-2.5-Flash Team et al. (2023)48.2944.9648.2648.0256.1342.4651.05 Claude 3.5 Haiku Anthropic (2024)42.9342.4442.0846.5346.2335.7145.99 Mistral Medium 3.1 Mistral AI (2025)47.9346.6449.8147.5261.7941.6741.77 Kimi-VL-A3B-Thinking-2506 Team et al. (2025)42.7142.8641.3140.5951.4239.6841.35 Open-source Models InternVL3.5-1B Wang et al. (2025a)31.6433.6132.4323.2737.2631.7530.80 InternVL3.5-2B Wang et al. (2025a)33.7134.0331.6631.6840.5732.5432.49 Qwen2.5-VL-3B-Instruct Wang et al. (2024)41.4341.1835.5246.0440.0947.2239.24 InternVL3.5-4B Wang et al. (2025a)43.2942.8642.8642.0854.7236.5142.19 Gemma-3-4B-it Gemma Team et al. (2025)40.5743.7034.3646.5345.7537.3037.97 LLaVA-1.5-7B Liu et al. (2024a)38.6440.3334.7431.6840.5640.0743.88 Qwen2.5-VL-7B-Instruct Wang et al. (2024)41.0042.8637.8442.5746.2342.0635.44 Llama-3.2-11B-Vision-Instruct30.5026.4730.5020.3042.9230.5632.07 Spatial Reasoning Models SpaceOm Chen et al. (2024a)41.3642.4438.6148.0237.7442.8639.24 SpaceThinker-Qwen2.5VL-3B Chen et al. (2024a)40.6440.3437.8447.0338.2143.2537.97 SpaceQwen2.5-VL-3B-Instruct Chen et al. (2024a)40.1431.5135.1437.6237.7450.7947.26 RoboPoint-vicuna-v1.5-7B-lora Cai et al. (2025a)38.0038.6534.7430.6947.6436.1140.50 RoboPoint-vicuna-v1.5-13B Cai et al. (2025a)38.6442.0133.9732.6744.3336.9042.19 SpatialLadder-3B Li et al. (2025)35.2839.9134.6139.9038.2025.3933.19 Backbone and Our Variants SpatialCORE-4B44.7146.2246.3342.5753.7736.5143.88 Qwen3-VL-8B-Thinking Bai et al. (2025) (Base)44.7842.0147.1047.0251.8840.4741.35 Qwen3-VL-8B-Thinking + GRPO46.2143.7047.8847.5254.2541.2743.88 SpatialCORE-8B47.9145.3848.6547.5258.4941.6747.22 OmniSpatial Jia et al. (2025) training split using two H100 GPUs, an effective batch size of 32, and G = 4rollout generations. We use AdamW (5× 10 −5 , cosine schedule, 5% warmup,η = 0.01). Pseudo-GT BBoxes are precomputed offline with Grounding DINO Liu et al. (2024b). We manually audit these BBoxes and test robustness to corruption (Section A.3). Reward hyperparameters are λ fmt = 0.2,λ s = 1.0,γ = 0.3,β = 0.1,α = 2.0,w iou = 0.8, andw label = 0.2. Full details appear in Section A.1. 7 Preprint <think> "bbox_2d": [43, 187, 623, 997], "label": "athlete in blue" "bbox_2d": [438, 0, 965, 997], "label": "athlete in white" We have the positions of the relevant objects. Let's think. ... .... .... ... .... .... ... .... .... ... .... .... The correct answer is B. The athlete in white is resting their head on the left arm of the athlete in blue. </think> (b) Left Arm. Question: Which object is the hardest to approach or reach from the chair? Options: (a) Thermostat (b) Scissor (c) Lamp (d) Cup <think> "bbox_2d": [185, 130, 705, 997], "label": "athlete in blue" "bbox_2d": [205, 125, 720, 997], "label": "athlete in white" We have the positions of the relevant objects. Let's think. ... .... .... ... .... .... ... .... .... ... .... .... The correct answer is C. The over- lapping athletes make the supporting arm unclear. </think> (c) Can Not Determine. Question: Based on their body positions, which arm of the athlete in blue supports the athlete in white's head? Options: (a) Right Arm, (b) Left Arm, (c) Can Not Determine SpatialCORE <think> "bbox_2d": [820, 170, 900, 235], "label": "thermostat" ... .... .... "bbox_2d": [430, 80, 610, 255], "label": "cup" We have the positions of the relevant objects. Let's think. ... .... .... ... .... .... ... .... .... ... .... .... The cup is upper in position and farther from the chair's reach. </think> (d) Cup. <think> "bbox_2d": [829, 157, 900, 217], "label": "thermostat" ... .... .... "bbox_2d": [135, 725, 235, 825], "label": "cup" We have the positions of the relevant objects. Let's think. ... .... .... ... .... .... ... .... .... ... .... .... Other objects other than thermostat are either lower in positionor closer to the chair'sreach. </think> (a) Thermostat SpatialCORE Baseline Baseline Figure 3: Qualitative examples from OmniSpatial Jia et al. (2025) (left) and SpatiaLab Wasi et al. (2026) (right). In both cases, the baseline (Qwen3-VL-8B-Thinking Bai et al. (2025)) produces predicted BBoxes that mislocalize the task-relevant objects, leading to incorrect or poorly grounded answers. SpatialCORE generates more accurate predicted bounding boxes and reaches the correct final answer. Bounding boxes are overlaid for visualization; full reasoning traces are in the Appendix Section C. 4.2BASELINES We compare SpatialCORE against the Qwen3-VL-8B-Thinking backbone, its standard GRPO-trained variant, and open-source and specialized spatial reasoning LVLMs; proprietary models serve as references. We evaluate on the held-out OmniSpatial Jia et al. (2025) test set (4 reasoning dimensions, 50 subcategories) and zero-shot on SpatiaLab Wasi et al. (2026) (6 categories, 30 task types in naturalistic scenes) to assess transfer across task designs and visual contexts. Details appear in Section A.5. 4.3RESULTS Spatial Reasoning on Diverse and Challenging Tasks. Table 1 shows that SpatialCORE- 8B achieves the highest weighted-average accuracy among open-source and specialized spatial reasoning models on OmniSpatial, surpassing the GRPO-trained backbone and showing particularly strong gains in categories requiring object-centric spatial comparison. Q1 (lowest) Q2Q3Q4 (highest) Entropy quartile 0 20 40 60 80 Mean matched IoU (%) 8 27 54 35 77 69 61 36 Baseline: = +0.38 SpatialCORE: =0.42 (p = 5 × 10 40 ) BaselineSpatialCORE Figure 4: Mean matched BBox IoU across model-specific coordinate-token entropy quartiles for the unadapted Qwen3-VL-8B-Thinking back- bone (Baseline) and SpatialCORE-8B. Lower en- tropy corresponds to more accurate grounding after SpatialCORE post-training, whereas the baseline shows no consistent relationship. Against specialized spatial reasoning models, the margins are particularly large:SpatialCORE- 8B outperforms VST-RL-7B by7.37%and SpaceThinkerQwen2.5VL-3B by8.04%, suggesting that confidence-aware grounding provides a stronger training signal than grounding supervision alone. Against open-source LVLMs, SpatialCORE-8B outperforms SoFar-Qwen2.5VL-3B by3.32%, InternVL3-14B by2.52%, and Gemma-3-12B by 4.75%. The4.56%gain over its own backbone (2.54%gain over the trained backbone) demonstrates the effectiveness of SpatialCORE, while the matched GRPO ablation in Table 3 isolates the contribution of the spatial reward.Gains are strongest in traffic analysis and localization, tasks that require simultaneously comparing the positions of multiple task-relevant objects, where confident BBoxes provide direct spatial evidence for the final answer. Allocentric and hypothetical reasoning show smaller gains, as they require reasoning across multiple viewpoints, an input-level limitation that predicted BBoxes from a single egocentric view cannot address. Notably, SpatialCORE-8B reaches the 8 Preprint performance range of proprietary models as an open-source system, and SpatialCORE-4B remains competitive at 44.68% average accuracy. Zero-Shot Transfer to Unseen Distributions. On SpatiaLab (Table 2), SpatialCORE-8B leads open-source and specialized models on average and also outperforms the GRPO-trained backbone under zero-shot evaluation. The improvements over specialized models are substantial:12.63% over SpatialLadder-3B,7.27%over SpaceThinker-Qwen2.5VL-3B, and6.55%over SpaceOm, with SpatialCORE-8B also surpasses larger open-source LVLMs such as InternVL3.5-4B and Qwen2.5- VL-7B-Instruct. The3.2%gain over its own backbone (1.7%gain over the trained backbone) confirms that confidence-aware grounding transfers to benchmarks with different task designs and visual distributions. Gains are strongest in Relational Positioning, where confident predicted BBoxes over multiple task-relevant objects provide direct evidence for spatial comparisons. Size and Scale estimation show smaller gains, suggesting that confidence-aware grounding primarily benefits object- centric spatial comparisons, while scene-level scale estimation remains a distinct challenge. Notably, on average, SpatialCORE-8B matches the performance range of proprietary systems on a fully unseen benchmark, suggesting that the self-regulating spatial reward instills a grounding behavior that generalizes beyond the training distribution. Figure 5: Bar plots comparing answer accuracy and predicted BBox coordinate-token uncertainty for the unadapted Qwen3-VL-8B-Thinking back- bone (Baseline) and SpatialCORE-8B. Lower un- certainty indicates greater confidence in BBoxes generated during reasoning. Qualitative Analysis. Figure 3 shows representative examples from OmniSpatial and SpatiaLab. In both cases, the baseline produces grounding that fails to support the correct spatial decision, while Spatial- CORE generates more accurate BBoxes and lever- ages them to reach the correct final answer. Notably, the examples reveal distinct failure modes: overlap- ping BBoxes can obscure relative-position reasoning, while mislocalized objects can corrupt reachability judgments. Learning to Ground with Confidence. The self- regulating spatial reward reinforces grounding ac- cording to both its localization quality and the model’s confidence, encouraging confident predic- tions where task-relevant objects are accurately lo- calized. This distinction matters because the base- line often assigns low uncertainty to poorly localized BBoxes (Figure 4). After SpatialCORE post-training, the most confident grounding achieves the highest localization quality: mean matched IoU against pseudo-GT BBoxes reaches77%in the lowest-uncertainty quartile and decreases consistently to36% in the highest. The entropy–IoU correlation correspondingly shifts fromρ = +0.38toρ =−0.42, making lower uncertainty a stronger indicator of accurate localization. This change accompanies improved spatial reasoning on the analyzed OmniSpatial test samples: answer accuracy rises from 44%to48%, while BBox coordinate uncertainty falls from92%to74%relative to Qwen3-VL-8B- Thinking Bai et al. (2025) (Figure 5). Table 3: Ablation study on the spatial interaction subset of OmniSpatial Jia et al. (2025). Average is weighted by category sample size. Best result is bold. VariantAvg. Traffic Anal. Loca- lization Geospa. Strategy SpatialCORE-8B (Full)56.3354.1162.8551.81 w/o vision LoRA53.0050.5958.1050.00 w/o conf. weighting52.3349.4158.0949.09 w/o answer gate54.6752.9460.0050.91 w/o pseudo-GT validity 53.3351.7659.0549.09 Ablation Study. Table 3 tests the defin- ing feature of the self-regulating spatial re- ward: weighting BBox localization quality by confidence in the generated grounding. In separate matched GRPO runs on OmniS- patial’s Spatial Interaction subset, Spatial- CORE reaches 56.33% accuracy; remov- ing confidence weighting while retaining the localization reward lowers it to 52.33%, the largest individual drop. This four-point gap shows the value of learning from confi- dence beyond rewarding localization alone. Vision LoRA and pseudo-GT validity contribute 3.33 and 3.00 points, respectively, while the answer gate contributes 1.66 points by tying rewarded grounding to final-answer correctness. 9 Preprint 5CONCLUSION Spatial reasoning in LVLMs has largely focused on correct answers or accurate localization, over- looking confidence in generated grounding. SpatialCORE uses this confidence as a learning signal through a self-regulating spatial reward. Benchmark gains and controlled ablations demonstrate its value; grounding analyses show stronger alignment between confidence and localization quality. Together, these findings advance confidence-aware spatial reasoning: learning not only to produce grounding, but to reason from it with confidence. Limitations and Future Work SpatialCORE modifies the BBox-based post-training objective, leaving the backbone and input representation unchanged. 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HyperparameterValueNotes Model and architecture Base modelQwen3-VL-8B-ThinkingReasoning backbone LoRA rank32Language-side LoRA LoRA alpha64Language-side LoRA LoRA dropout0.05– LoRA target modulesDefaultArchitecture defaults PrecisionBF16– AttentionFlash Attention 2– Training Number of GPUs2H100 GPUs Epochs3– Per-device batch size2– Rollout generations4GRPO group size G Gradient accumulation steps8– Effective batch size322× 2× 8 Total rollouts per update12832× 4 generations Max completion length3,072 tokens– Optimization OptimizerAdamW– Learning rate5× 10 −5 – LR schedulerCosineMinimum LR = 5× 10 −6 Warmup ratio0.05– KL coefficient0.01KL to reference policy Reward Answer reward weight1.0– Format reward weight0.2– Grounding reward weight1.0– Spatial answer gate0.3Spatial reward scale for incorrect answers Uncertainty floor0.1Floor in confidence weighting ω Grounding F-beta2.0Coverage-weighted harmonic mean IoU weight0.8Pairwise matching score Label weight0.2Pairwise matching score Over-prediction penalty0.3Per unmatched predicted BBox BBox attempt bonus0.05 Added to format reward per valid grounding attempt Uncertainty weightingEnabledActive from step 0 AAPPENDIX: TRAINING CONFIGURATION AND ALGORITHM A.1HYPERPARAMETER SETTINGS Table 4 reports the main hyperparameters used for SpatialCORE-8B post-training, including the GRPO training setup, optimization settings, and reward configuration. A.2TRAINING ALGORITHM Algorithm 1 summarizes one training iteration of SpatialCORE. 16 Preprint Algorithm 1 Training SpatialCORE with self-regulating spatial reward Require:LVLM policyπ θ , reference policyπ ref , training setD, rollout sizeG, precomputed pseudo-GT grounding BBoxes 1: for each training step do 2:Sample batchB ⊂D 3:for each (I,q,y)∈B do 4:Retrieve pseudo-GT BBoxes(b gt k ,ℓ gt k ,v k ) 5:Rollout: o i G i=1 ∼ π θ (·| I,q) 6:for each trajectory o i do 7:Generated grounding: parseb j ,ℓ j ,S i,j from o i 8:Matching: compute pairwise R (j,k) BBox andM ∗ i 9:Uncertainty: compute H i,j from BBox coordinate tokens 10:Confidence: compute C i,j = 1− H i,j and ω i,j 11:Spatial reward: compute R (i) spatial from R (j,k) BBox ,M ∗ i , and ω i,j 12:Format/answer rewards: compute R (i) fmt and R (i) ans 13:Adaptive reward: compose r i from R (i) ans , R (i) fmt , and answer-gated R (i) spatial 14:end for 15:Advantage: computeA i G i=1 fromr i G i=1 16:end for 17:Update: optimize θ with GRPO and KL regularization to π ref 18: end for A.3PSEUDO-GT SUPERVISION AND RELIABILITY BBox Construction. The spatial reward compares generated BBoxes with reference locations for task-relevant objects. We construct these pseudo-GT annotations offline, before policy optimization. Each retained annotation is represented as(b gt k ,ℓ gt k ,v k ), whereb gt k is a BBox in the LVLM’s nor- malized image coordinates,ℓ gt k is its object label, andv k ∈ [0, 1]is the pseudo-GT validity used in reward computation. We first identify the entities to localize. Given an image-question pair, a fixed GPT-4o-mini Hurst et al. (2024) prompt extracts physical objects and persons mentioned in the question and answer options. It preserves modifiers that distinguish instances, such asboy in orange clothes,blue gear, andgray vehicle. We filter non-visual terms and relational or directional expressions, including left,right,front,distance, anddirection, because they do not define object BBoxes. 8090100 Audited BBox precision (%) 0.30-0.49 (n=74) 0.50-0.69 (n=61) 0.70-0.89 (n=69) ≥ 0.90 (n=58) Grounding DINO confidence Overall: 95.8% Figure 6: Manual audit precision of pseudo- GT BBoxes across Grounding DINO confidence ranges. Points show precision and whiskers show 95% confidence intervals; labels give audited BBox counts. The dashed line marks overall preci- sion. When no suitable object or person is identified, the phrase list remains empty. Otherwise, the extracted phrases become queries for the grounding model. We then localize those phrases with Grounding DINO Liu et al. (2024b). For each sample with non- empty queries, we concatenate the phrases into a text prompt and run zero-shot detection on the image. From the candidate BBoxes, labels, and detection scores, we retain the highest-scoring BBox per re- turned label and discard detections below the0.3 confidence threshold. BBox coordinates are scaled to the LVLM’s[0, 1000]image-coordinate convention, and each retained detection score becomes its validity v k . We omit pseudo-GT construction for task types where object-level generated grounding is not mean- ingful. Finally, we save the sample-level phrases and BBoxes in a JSON file for reward computation. Quality Audit.The spatial reward uses pseudo-GT BBoxes as localization targets, so their reliability 17 Preprint matters to the learning signal. We manually audited 262 retained BBoxes from 200 randomly sampled training examples, counting a BBox as correct if it localized the intended task-relevant object. Overall, 251 were correct (95.8%). All 11 observed errors occurred in the two lower Grounding DINO confidence ranges; every audited BBox with confidence at least0.70was correct (Figure 6). This pattern motivates retaining detector confidence as pseudo-GT validityv k , giving less reliable references less influence on the spatial reward. The matched ablation reinforces this choice: removing validity weighting reduces accuracy from 56.33% to 53.33% (Table 3). Pipeline Coverage.We trace pseudo-GT construction across the full OmniSpatial training split. Of 5,643 samples containing BBox-localizable task-relevant objects, phrase extraction yields queries for 4,063, and 4,007 receive at least one valid Grounding DINO BBox above the0.3confidence threshold. The resulting coverage is71.0%of these samples and98.6%of those with phrase queries. Samples without a valid reference often belong to Complex Logic or Dynamic Reasoning tasks, where paths, sequences, or spatial relationships may matter more to the answer than object localization alone. The spatial reward applies only when grounding can be evaluated against a valid reference. If no pseudo-GT BBox is available, the spatial reward is zero; training continues with the answer and format rewards, and generated BBoxes are neither rewarded nor penalized. If a valid reference is available but the model generates no BBox, it receives a negative spatial reward with coefficient0.3, scaled by pseudo-GT validity. This distinguishes the absence of a reference from failure to ground an available target. Robustness to Corrupted Pseudo-GT. The quality audit assesses the pseudo-GT BBoxes pro- duced by our pipeline. To test how strongly SpatialCORE depends on their accuracy, we retrain SpatialCORE-8B after corrupting40%of valid pseudo-GT BBoxes. Each selected BBox is randomly removed, assigned the label of a different valid object in the same sample, or displaced until its IoU with the original BBox falls below0.6. These interventions either remove spatial supervision or introduce a misleading grounding target. We evaluate the resulting model on the full OmniSpatial test set. Table 5: Robustness to pseudo-GT corruption on the full OmniSpatial test set. Base denotes Qwen3-VL-8B-Thinking. Training settingAcc. (%) Base43.90 SpatialCORE-8B (40% corrupted)46.70 SpatialCORE-8B (original)48.46 Even with two in five reference BBoxes corrupted,SpatialCORE-8B reaches 46.70%accuracy, remaining2.80per- centage points above the unadapted backbone (Table 5). Relative to training with original pseudo-GT, accuracy falls by1.76points, showing that reference quality contributes to the gain. At the same time, the improvement persists when spatial supervision is partly missing or misleading:60%of the BBoxes remain intact, and the answer and format rewards continue to provide learning signals for every sample. Together with the quality audit, this experiment establishes both the value of reliable pseudo-GT and the resilience of SpatialCORE to substantial corruption of its grounding targets. A.4REWARD AND IMPLEMENTATION DETAILS Pseudo-GT Matching. Generated grounding in a rollout may not align one-to-one with the pre- computed pseudo-GT BBoxes. The policy can produce a different number of BBoxes than the pseudo-GT set, and its labels may use different but compatible wording. For example, a generated labelblack sedan aheadshould still match a pseudo-GT labelblack sedan. Conversely, geometric overlap alone is insufficient: a predicted BBox labeledtraffic signmay overlap a pseudo-GT BBox fortraffic light, but the semantic mismatch should make this assignment weaker. We therefore match predicted and pseudo-GT BBoxes using both geometric overlap and label similarity. For a predicted BBox with object label(b j ,ℓ j )and a pseudo-GT BBox(b gt k ,ℓ gt k ,v k ) , we define the pairwise BBox reward as R (j,k) BBox = w iou max 0, IoU(b j ,b gt k )− τ iou + w label Sim(ℓ j ,ℓ gt k ) v k ,(12) 18 Preprint wherew iou +w label = 1andτ iou is an IoU margin. The clipped IoU term suppresses weak geometric overlap, while the label-similarity term favors assignments between semantically compatible object phrases. This prevents overlapping but mismatched BBoxes from being treated as strong matches. We compute label similarity through semantic label representations i.e., a lightweight bag-of-words representation. Each label is tokenized into words and represented by a binary word-presence vector. For example,black sedan aheadandblack sedanshare the key wordsblackand sedan, yielding high cosine similarity, whereastraffic signandtraffic lightshare onlytrafficand receive lower similarity. Formally, letφ(ℓ)denote the bag-of-words vector for label ℓ. We compute Sim(ℓ j ,ℓ gt k ) = φ(ℓ j ) ⊤ φ(ℓ gt k ) ∥φ(ℓ j )∥ 2 ∥φ(ℓ gt k )∥ 2 .(13) This lexical similarity is sufficient for our setting because labels are short object phrases extracted from questions, answer options, and generated grounding. It also avoids adding an external embedding model to reward computation. The pseudo-GT validityv k scales the pairwise reward by the reliability of the grounding-model localization. High-validity pseudo-GT BBoxes therefore have a stronger effect on matching, while lower-validity or noisier BBoxes contribute less to the spatial reward. After computing all pairwise rewards, we use Hungarian matching Kuhn (1955) to obtain a maximum- reward one-to-one assignment: M ∗ i = arg max M i X (j,k)∈M i R (j,k) BBox .(14) The one-to-one constraint prevents a single predicted BBox from matching multiple pseudo-GT BBoxes and prevents multiple predictions from claiming the same pseudo-GT BBox. The matched pairs inM ∗ i are then used to compute the confidence-weighted spatial reward. Additional Reward Shaping. We use two lightweight shaping terms for training stability. First, the format reward includes a BBox attempt bonus of0.05when pseudo-GT BBoxes are available and the trajectory contains at least one valid predicted BBox whose label overlaps with the question or answer options. This reduces the incentive to avoid BBox generation while filtering out irrelevant grounding attempts. Second, the spatial reward applies an over-prediction penalty of0.3to valid predicted BBoxes that remain unmatched after one-to-one assignment with pseudo-GT BBoxes, limiting extra generated grounding beyond the task-relevant objects. These auxiliary terms stabilize the grounded format during post-training, while the main spatial supervision is provided by the confidence-weighted matching reward. SFT Cold Start. Before GRPO post-training, we perform a supervised cold-start stage on 1,000 OmniSpatial Jia et al. (2025) training samples. This stage initializes the policy with the required grounded reasoning format and teaches the distinction between boxable task-relevant objects and non-boxable spatial terms. When reliable pseudo-GT BBoxes are available, the target completions include BBox lines, followed by a reasoning trace and final answer in the same format used during re- inforcement learning. We train a LoRA adapter with completion-only cross-entropy, masking prompt tokens while freezing the visual encoder and updating only language-side adaptation parameters. The resulting adapter initializes the GRPO policy, after which SpatialCORE optimizes the self-regulating spatial reward described in the main method. To assess the necessity of this initialization, we additionally train the base model with GRPO for one full epoch without the 1,000-sample SFT cold start. Without SFT, the model does not converge to the grounded format: the grounding reward remains between−0.125and+0.003, ends at0.000, and the model ultimately stops generating BBoxes. Its general reasoning and final-answer format remain stable, indicating that the collapse is specific to generated grounding. In contrast, with the cold start, SpatialCORE maintains a positive grounding reward between0.15and0.33and generates BBoxes in95–100%of training responses throughout GRPO. These dynamics indicate that the cold start primarily establishes the grounded output structure; once this structure is maintained, the spatial reward drives subsequent improvement. 19 Preprint System Prompt Design. We use the fixed system prompt in Figure 7 during training to enforce a consistent grounded reasoning format. Since Qwen3-VL-Thinking Bai et al. (2025) automatically prefills the opening<think>token after the user message, the prompt does not ask the model to generate<think>; it only requires the model to close the reasoning segment with</think>. The prompt further instructs the model to output relevant BBoxes before the reasoning trace and produce a single final answer letter after</think>, allowing the training pipeline to parse generated grounding, reasoning, and final answers consistently across sampled trajectories. Compute Resources.The main training configuration is described in Section 4.1 and Table 4. The final SpatialCORE GRPO run was performed on 2 NVIDIA H100 GPUs using BF16 precision and vLLM-based rollout generation. Training required approximately 31 hours, corresponding to about 62 H100 GPU-hours. This includes rollout sampling, reward computation, and policy optimization for the final reported model. Runtime may vary depending on the generation backend, rollout length, decoding settings, batching efficiency, and system load. The reported estimate is therefore intended as a practical reference for reproducing the main training run rather than an exact hardware-independent cost. It excludes preliminary debugging, hyperparameter exploration, failed runs, and additional baseline or ablation experiments. A.5BENCHMARK DETAILS OmniSpatial.OmniSpatial Jia et al. (2025) contains more than 8.4K question–answer pairs cover- ing four spatial reasoning dimensions: dynamic reasoning, spatial interaction, complex spatial logic, and perspective taking. These dimensions are further divided into 50 fine-grained task subcategories. We use the official training split of 6,902 samples for SpatialCORE post-training and evaluate on the official held-out test split of 1,533 samples. SpatiaLab.SpatiaLab Wasi et al. (2026) contains 1,400 visual question–answer pairs from realistic, unconstrained scenes. It covers six spatial reasoning categories: relative positioning, depth and occlusion, orientation, size and scale, spatial navigation, and 3D geometry, with five task types per category. We evaluate SpatialCORE in the multiple-choice setting. No SpatiaLab samples are used during post-training. We evaluate SpatialCORE on OmniSpatial Jia et al. (2025) and SpatiaLab Wasi et al. (2026). OmniS- patial is used for post-training and held-out evaluation, while SpatiaLab is used only for zero-shot evaluation. Evaluation Protocol.For both benchmarks, we report accuracy. A prediction is counted as correct if the selected option matches the ground-truth answer. Category-level scores are computed over the samples in each category. Overall accuracy is computed over the full evaluation set and is equivalently reported as a sample-weighted average across categories. BAPPENDIX: RATIONALE FOR CONFIDENCE-GUIDED GROUNDING We provide an optimization-based rationale for confidence-guided generated grounding in Spatial- CORE, using the GRPO policy optimization framework Shao et al. (2024). Under answer-only rewards, trajectories that produce the same final answer receive the same reward signal, even if their generated grounding differs in confidence. This can make the objective insensitive to whether predicted BBoxes are confidently localized. The confidence-weighted spatial reward reduces this indifference by incorporating predicted BBox coordinate-token uncertainty into the reward signal. B.1GRADIENT INDIFFERENCE UNDER ANSWER-ONLY SUPERVISION Under standard GRPO, the policy objective over a group of G trajectories is: J(θ) =E (I,q)∼D,o i ∼π θ old " 1 G G X i=1 min(ρ i (θ)A i , clip(ρ i (θ), 1− δ, 1 + δ)A i )− η D KL (π θ ∥π ref ) # , (15) 20 Preprint whereρ i (θ) = π θ (o i | I,q)/π θ old (o i | I,q)is the importance ratio andA i is the group-relative advantage. Under answer-only supervision,r i = R (i) ans , and the advantageA i depends only on whether the final answer is correct. Consider two trajectorieso i ando i ′ that produce the same correct final answer but differ in predicted BBox coordinate-token uncertainty:o i produces low-uncertainty generated groundingH i,j ≈ 0, whileo i ′ produces high-uncertainty generated groundingH i ′ ,j ≈ 1. Since R (i) ans = R (i ′ ) ans = 1 , their answer-only rewards are identical, and their group-relative advantages provide no preference between confident and uncertain generated grounding. For the unclipped policy-gradient term, coordinate tokens from these trajectories therefore receive the same advantage whenever the final answers match: A i = A i ′ ⇒ ∇ θ logπ θ (x i,t | x i,<t ,I,q)A i and∇ θ logπ θ (x i ′ ,t | x i ′ ,<t ,I,q)A i ′ (16) are weighted by the same trajectory-level advantage, forx i,t ∈S i,j andx i ′ ,t ∈S i ′ ,j . Thus, answer- only supervision provides no gradient signal that separates low-uncertainty generated grounding from high-uncertainty generated grounding. As a result, uncertain generated grounding may still be reinforced when it co-occurs with a correct final answer. B.2CONFIDENCE-WEIGHTED REWARDS BREAK THIS INDIFFERENCE SpatialCORE introduces a spatial reward R (i) spatial that depends on the confidence weight ω i,j = β + (1− β)(1− H i,j ),(17) whereH i,j is the normalized predicted BBox coordinate-token uncertainty andβis the confidence floor. This makes the spatial reward sensitive to generated grounding confidence. For trajectories with the same answer and format rewards, the composite reward in Equation (10) can still differ through the spatial term: r i − r i ′ = λ s g(R (i) ans )R (i) spatial − g(R (i ′ ) ans )R (i ′ ) spatial .(18) When two trajectories have comparable matched BBox quality but different coordinate-token un- certainty, the lower-uncertainty trajectory receives a larger confidence weightω i,j and therefore a larger spatial reward. This creates an advantage gap that favors confident generated grounding over uncertain generated grounding, even when both trajectories reach the same final answer. B.3ANSWER GATE PRESERVES GENERATED GROUNDING SIGNAL ON INCORRECT TRAJECTORIES A further concern is whether the spatial reward is lost when the final answer is incorrect. Under answer-only supervision, incorrect trajectories receiver i = 0regardless of whether their generated grounding is useful. SpatialCORE addresses this through the answer gateg(·)in Equation (10), which keeps a reduced spatial reward when the final answer is incorrect: r i = λ fmt R (i) fmt + λ s γR (i) spatial ,if R (i) ans = 0,(19) whereγ ∈ (0, 1). Thus, trajectories with incorrect final answers can still retain partial credit for useful generated grounding. This allows generated grounding to improve before the model consistently predicts the correct final answer. CAPPENDIX: ADDITIONAL QUALITATIVE RESULTS Figure 8 presents a complete SpatialCORE trajectory. The example includes the predicted BBoxes generated in the reasoning trace, the subsequent spatial reasoning, and the final answer. It shows how SpatialCORE makes generated grounding part of the reasoning process, using localized task-relevant objects as evidence for the final spatial decision. 21 Preprint You are a spatial-reasoning assistant for visual multiple-choice questions. Your task is to answer a question about one image by grounding relevant visible entities, reasoning over the image, and outputting exactly one final answer letter. IMPORTANT CONTEXT: - You are given one image and one question about that image. - Answer options may be provided in the text, or they may appear inside the image. - If the options are not fully written in the text, identify them from the image. - Use the image as the primary source of truth. - Do NOT hallucinate objects, text, or spatial relations. - Do NOT refuse. If uncertain, choose the most plausible answer based on the image. OUTPUT PROCEDURE: Step 1 — Inside thinking, first output bbox lines for relevant visible entities, if any are boxable. Step 2 — Each bbox line must use exactly this JSON format: "bbox_2d": [x_min, y_min, x_max, y_max], "label": "descriptive noun phrase" Step 3 — After the bbox lines, output this exact transition sentence: We have the positions of the relevant objects. Let's think. Step 4 — After that sentence, continue with reasoning. Step 5 — Then close thinking with: </think> Step 6 — Immediately after </think>, output exactly one capital letter: A, B, C, or D Step 7 — Output nothing after that answer letter. Figure 7: System prompt used to standardize generated grounding trajectories during SpatialCORE training. Continued on the next page. 22 Preprint GROUNDING RULES: - Bounding boxes must correspond ONLY to objects or entities explicitly mentioned in the question or answer options. - Do NOT generate boxes for any other visible objects. - Do NOT introduce new object names, inferred descriptions, or scene elements. - The bbox label must be a short object name or descriptive noun phrase extracted from the question or answer options. - Never use a full sentence or action phrase as a bbox label. BBOX RULES: - Only output bbox lines for visible, boxable noun phrases. - Actions, decisions, and abstract concepts are not boxable. - Output at most one bbox per referenced object or phrase. - Do not repeat, refine, or split the same object into multiple boxes. - Coordinates must be integers from 0 to 1000. - x increases from left to right; y increases from top to bottom. - Only include boxes for entities that are actually visible. - If nothing is boxable, output no bbox lines and continue directly. - If the same noun phrase refers to multiple instances, select only the single most relevant instance. - Do NOT output multiple bounding boxes with the same label. - Each label may appear at most once. REASONING RULES: - Use visible evidence such as position, distance, depth, ordering, overlap, perspective, and text in the image. - Refer to grounded objects when present. - Base the answer on visual evidence from the image. FORMAT CONSTRAINTS: - Do not start with conversational filler. - If bbox lines are present, they must be the first content inside <think>. - Do not place bbox JSON after </think>. - Do not place any text between </think> and the final answer. - After </think>, output only a single capital letter: A, B, C, or D. - Do not output anything after that letter. FINAL REQUIREMENT: Your response must follow the exact output order above. The final output after must be exactly one capital letter. Figure 7: System prompt used to standardize generated grounding trajectories during SpatialCORE training, continued. 23 Preprint <think> "bbox_2d": [829, 157, 900, 217], "label": "thermostat" "bbox_2d": [705, 277, 755, 342], "label": "scissor" "bbox_2d": [635, 75, 755, 300], "label": "lamp" "bbox_2d": [135, 725, 235, 825], "label": "cup" We have the positions of the relevant objects. Let's think. The thermostat is located at x: 829–900, y: 157–217, placing it on the upper-right side of the image. The scissor is at x: 705–755, y: 277–342, also on the right side but slightly lower than the thermostat. The lamp is at x: 635–755, y: 75–300, spanning a larger vertical area on the right side. The cup is at x: 135–235, y: 725–825, positioned on the lower-left side of the image. To determine which object is the hardest to reach from the chair, we need to consider the spatial relationship between the chair and each object. The chair appears centrally located and oriented toward the desk area where the objects are placed. The thermostat is positioned high on the right side, likely mounted on the wall, so reaching it would require stretching upward. The scissor is lower than the thermostat, making it easier to reach. The lamp is also on the right side but extends downward toward the desk area, making it more accessible than the thermostat. The cup is on the left side near the lower desk area, closer to the chair's reach. Considering these positions, the thermostat is the hardest object to approach or reach from the chair. The other objects are either lower in position or closer to the chair's reach. Therefore, the correct answer is A. Thermostat. </think> (a) Thermostat SpatialCORE: Question: Which object is the hardest to approach or reach from the chair? Options: (a) Thermostat (b) Scissor (c) Lamp (d) Cup Figure 8: Qualitative example of confidence-aware grounded spatial reasoning with SpatialCORE. The model first generates predicted BBoxes for the task-relevant objects, includingthermostat,scissor,lamp, and cup, and then reasons over their localized positions relative to the chair. By producing confident generated grounding during the reasoning trace, SpatialCORE identifies the wall-mounted thermostat as the hardest object to reach and selects the correct final answer. Bounding boxes are overlaid only for visualization. 24