Reinforcing Spatial Reasoning in Vision-Language Models with Interwoven Thinking and Visual Drawing
Authors: Junfei Wu
Jian Guan
Kaituo Feng
Qiang Liu
Shu Wu
Liang Wang
Wei Wu
Tieniu Tan
Venue: NeurIPS 2025 poster ()
Keywords: Large Vision-Language Models
Spatial Reasoning
Primary area: applications

Abstract: As textual reasoning with large language models (LLMs) has advanced significant, there has been growing interest in enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning in a straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As a result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial tracking\textemdash capabilities that humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, a novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations including annotating bounding boxes and drawing auxiliary lines, we empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the performance ceiling imposed by specialized perception tools in previous tool-integrated reasoning approaches. To cultivate this capability, we develop a three-stage training framework: cold-start training with synthetic data to establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and reinforcement learning to directly optimize for target rewards. Extensive experiments demonstrate that our model, named \textsc{Spark}, consistently outperforms existing methods across diverse spatial reasoning benchmarks involving maze navigation, static spatial reasoning, video-based reasoning and multi-view-based reasoning tasks, with an average improvement of 11.5\%. Ablation studies reveal the critical role of each training stage, with reflective rejection sampling particularly enhancing the model's self-correction capabilities and reasoning potential.

Reinforeing Spatial Reasoning in Vision-Language Models with Interwoven Thinking and Visual Drawing
Junfei Wu 22 Jian Guan Kaituo Feng", Qiang Liu 12, Shu Wu l2t Liang Wang
Wei Wu Tieniu Tan 125
NLPR, MAIS, Institute of Automation, Chinese Academy of Sciences.
University Chinese Academy of Sciences. 3 AAnt Group.
CUHK MMLab. Nanjing University.
junfei wuccripas iaaiaaaaaa cn, shu wu@nlpr.ia.ac it.ppprriaaa...........mmm...... {jianguanthu, wwwei198503381@@mmal..ccoo
Code: http://ghtaa..cooaattaaaacclllll Model: http:///ggnnnooooe.c..oo//////rr
Abstract
As textual reasoning with large language models (LLMs) has advanced significantly, there has been growing interest enhancing the multimodal reasoning capabilities of large vision-language models (LVLMs). However, existing methods primarily approach multimodal reasoning straightforward, text-centric manner, where both reasoning and answer derivation are conducted purely through text, with the only difference being the presence of multimodal input. As result, these methods often encounter fundamental limitations in spatial reasoning tasks that demand precise geometric understanding and continuous spatial humans achieve through mental visualization and manipulation. To address the limitations, we propose drawing to reason in space, novel paradigm that enables LVLMs to reason through elementary drawing operations in the visual space. By equipping models with basic drawing operations, including annotating bounding boxes and drawing auxiliary lines, empower them to express and analyze spatial relationships through direct visual manipulation, meanwhile avoiding the perfor- mance ceiling imposed by specialized perception tools in previous -oteinteertted reasoning approaches. To cultivate this capability, we develop a three-stage train- ing framework: cold-start training with synthetic data establish basic drawing abilities, reflective rejection sampling to enhance self-reflection behaviors, and re- inforcement learning directly optimize for target rewards. Extensive experiments demonstrate that our model, named VILASR, consistently outperforms existing methods across diverse spatial reasoning benchmarks, involving maze navigation, static spatial reasoning, video-based reasoning, and multi-view-based reasoning tasks, with an average improvement of 18.4%. Ablation studies reveal the critical role of each training stage, where reflective rejection sampling strengthens the model's self-correction capabilities, and reinforcement learning effectively unlocks its reasoning potential.
caaiiniiiaiiiiiiiisss that
Introduction
Large language models (LLMs) have exhibited remarkable reasoning capabilities in complex tasks such as mathematical problem-solving (66, 35] and code generation [6]. particularly through the
Equal Contribution. *Corresponding Author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

---

"slow thinking" paradigm exemplified by OpenAl ol [26] and DeepSeek RI [00], which enables extended reasoning with in-depth self-reflection. Encouraged by the success. growing body of research is now aiming to adapt similar techniques to large vision-language models (LVL.Ms) to enhance their capabilities in image and video reasoning 72
50 13.
While current LVLMs excel at basic visual perception tasks such as object detection [12 and narrative
understanding 40 g they often struggle with spatial reasoning [64 (7), which requires understand-
ing spatial relationships among objects and tracking their dynamic evolution [60] cappabiiliss that are crucial for real-world applications such as robotics 40 and augmented reality [17. Indeed, even when such deep visual understanding is required, LVLMs still rely solely on text-based reason- ing (72), assuming that visual information can be perfectly translated into textual semantic space [23]. Unfortunately, such translation is inherently challenging [33] spatial details are inevitably lost when converting visual information to text, and describing dynamic changes of object positions becomes prohibitively complex in textual space (see examples of GPT-4o in Figure D. Taking inspiration from human cognition, where spatial reasoning relies on mental visualization and dynamic manipula- tion [3) we advocate a vision-centric reasoning paradigm where models actively edit and re-encode visual information at each reasoning step, dynamically supplementing spatial details and relationships This "thinking with images" approach, while validated by OpenAI o3 47 remains underexplored in open-source research.
In parallel with our work, recent studies have begun to integrate visual tools to enable centric However. these approaches exhibit limitations along two key dimensions. First, the reasoning capabilities of LVL.Ms are constrained by black-box perception tools (e.g.. grounding and OCR systems), resulting in not only fixed perception capabilities but also fragmented reasoning composed of disconnected tool invocations that undermine coherence and holistic planning. Second, these methods heavily draw upon reasoning data curated based on human priors, which often exhibit oversimplified logic compared to the complexity of spatial reasoning tasks, with problem decomposition and tool invocation interleaved in a simplistic and linear fashion [8] 5T. Such adherence to prescribed reasoning patterns prevents LVLMs from developing the capacity for critical reflection on tool outputs- a capability that has proven crucial for advanced reasoning [45] These
reasoning 8 51 BT
fundamental limitations call for more flexible and intrinsic approach to vision-centrie reasoning.
In light of these challenges, we propose "drawing to reason in space," novel, versatile reasoning paradigm that empowers LVLMs to reason through elementary drawing operations, as exemplified in Figure [ Through simple yet powerful operations, including bounding boxes for object localization and auxiliary lines for relationship analysis, this paradigm enables direct visual interaction for spatial mroblemssoivnng mirroring human behavior while avoiding the pitfalls of dependence on external perception tools. Based on this paradigm, we develop VILASR. a Vision-LAnguage model that achieves sophisticated Spatial Reasoning through interwoven thinking and visual drawing. To realize this vision, we develop three-stage training framework (Figure 2 First, we introduce cold-star training with synthetic data to establish basic visual drawing abilitics. Second, we design a reflective rejection sampling mechanism that selectively reinforces reasoning paths demonstrating both correct answers and self-correction behaviors, enabling models to revise their visual operations based on intermediate results. Finally, employ reinforcement learning (RL) with carefully designed rewards that balance answer correctness and reasoning format, incentivizing both accurate spatial understanding and coherent visual thinking processes.
Extensive experiments across five diverse spatial reasoning benchmarks demonstrate the effectiveness of VILASR, which achieves substantial improvements over strong baselines by 18.4% on average, involving challenging scenarios that require sequential spatial planning (c.g., maze navigation), tem- poral relationship tracking (c.g., video-bass based reasoning), and information integration from multiple perspectives. Ablation studies reveal the critical role of each training stage. Particularly, reflective rejection sampling significantly enhances the model's 's self-correction capabilities, with the frequency of reflection behaviors doubling compared to models trained without this intermediate stage. Further inference-tine scaling experiments reveal that each training stage progressively enhances the model's s reasoning potential, with the final RL optimization effectively consolidating multi-attempt capabilities while maintaining strong single-attempt performance, significantly narrowing the performance gap compared to earlier training stages.
In summary, contributions are threefold:
2

---

Drawing Reason Space
Reasoning
Video Reasoning
Multi-view Reasoning
Viasal, Irout
Qassttion
Eonite
Detorbi
C antt
Inan rup odll till Vid rugs.
desemina bariin.. optias Solect tumaa.
Adki
O
beeding sningns
aulliry Miniies
Bditted
ViLAsE
acten sepance The tncastents
X
bapanctin
codiheer bitherrd mag
aire waa. st naaid (19985
O0
the unree peodio buti teve zaums Lett gidsaiee
Now like de mnggett
Golter Toege
Capkerarty
TC
share car ditare sperial wiliion. (29880
ANd
HEU par lbbb acundite 37
reasoning, which Image Ressening: The finm destiuation from the starting paint 6 of Hore the des by shep movemion besed on the givzn action sequence ceree Stari at the green point. 6o Moyc to coll D. Go Up Move to the wall (cannot move further but say Move back to cel Right Amonue move cel again The fioal portiio after followiog thi sequence of moves is cel C (Folls eccurstey track postton changes)
preserve spatial details
(highlighard
description):
DJ So Rigic Move to c Go Aptr. Mose cel A Go Dowt More to 8 left Move bock to cel So Down
Video Reasoning: There ard two Jofas in room. One voible image and another con de seen imoge (Muues temporal spatial correletiors acress frames!
Mulli-iew Remoning ... In the dist imgae see Bee bed.... Bon mare froutl view ... In secoed image. Be angle i sdd atened and auch clsser to the ar conditioner sugge Jony the oecervrr moved to the rgnh and deyth spward the al: corditions (Ony coptures coors: spotis releionshis and boll correctly resson ebout perppective monsonnnennn
Figure 1: Top left: Overview of the "drawing reason in space" paradigm, which enables visual reasoning through iterative thinking and drawing operations. Top right: Examples across three spatial reasoning tasks, demonstrating how VILASR decomposes complex problems into interpretable visual reasoning steps. Bottom: Corresponding results from GPT-4o with only textual reasoning.
I. We propose drawing to reason in space, a novel reasoning paradigm that enables LVLMs to perform spatial reasoning through interpretable visual operations;
II. We develop a principled training framework that effectively cultivates models' visual reasoning capabilities through progressive stages;
III. We demonstrate state-of-the-ar performance across multiple spatial reasoning benchmarks and provide insights into the development of visual reasoning abilities in LVLMs.
2
Related works
2.1 Reasoning in LLMs and LVLMs
Instilling advanced reasoning capabilities within LLMs and LVLMs remains significant challenge. Current approaches can be broadly categorized into three directions: (1) Prompt engineering: crafting prompts elicit latent reasoning capabilities in pre-trained models [66, 81] and enable tool usage to complement model capabilities with external knowledge [8] or specialized functionali-
ties [57 19 61 7 These prompt-based approaches heavily depend models' instruction-followin capabilities and often suffer from prompt sensitivity. (2) Supervised fine-tuning: developing tailored
datasets to enhance specific reasoning capabilities 77 67 82) and training models effectively utilize external tools [54] [8
g [5] 51]. Such approaches are inherently bounded by the qual- ity and scale of training data, limiting their potential for advanced reasoning. (3) Reinforcement learning: engineering reward mechanisms to incentivize desired reasoning patterns 29 56 [0]
and optimize tool usage strategies [34]. While promising in textual domains, RL approaches for tool-augmented reasoning have yet to be fully investigated in multimodal scenarios. Current LVLMs either confine their reasoning textual form 72), or rely on specialized perception tools, being constrained by tool capabilities [ 51 and lacking reflective reasoning (55). In contrast, we pioneer staged training recipe that enables models to both express and reflect upon their spatial understanding through iterative drawing operations.
3

---

2.2 Visual spatial reasoning
Visual spatial reasoning, as a crucial component of multimodal intelligence, extends beyond general visual perception to encompass two particularly challenging fundamental capabilities [I5] 777 re- lational reasoning, which involves understanding distances, directions, and spatial common sense between objects 38 [0]]; and perspective transformation, which requires holding and manipulat- ing spatial relationships [42
70]. Despite the remarkable progress of current L.VLMs in basic
visual tasks [24
39 99. numerous benchmarks have revealed significant challenges in spatial reasoning 443 69
36
32 70). This limitation is partly attributed to the nature of current training datasets [2]] which primarily focus visual perception rather than spatial understanding. Recent works have attempted to address this challenge through various approaches. For image-based spatial reasoning, several studies have proposed synthetic datasets [38] 5 7 4. For video-based spatial reasoning, approaches have emerged either by incorporating 3D representations as bridging knowl- edge [83] by tracking objects across frames [37]. However, systematic approaches to enhance LVLMs' spatial reasoning capabilities that can generalize across both images and videos remain largely unexplored. Our work fills this gap by developing principled reasoning framework in LVLMs.
3 Methodology
In this section, we present our approach to advancing spatial reasoning capabilities in LVLMs. Given spatial reasoning question Q and visual input / { n= where each 4n represents a single image, N = 1 corresponds to single image input, and N > 1 denotes video sequence or multiple image inputs, our goal is enable LVLMs to derive the answer A through iterative visual drawing and thinking. We first introduce our reasoning paradigm (3.1) and then detail the training framework (322 that cultivates this reasoning capability.
3.1 Drawing to reason in space
We propose "drawing to reason in space," a reasoning paradigm that empowers LVLMs to decompose complex spatial reasoning tasks into sequence of interpretable visual drawing and thinking steps, as illustrated in Figure]] ! Formally, given the visual input and question Q, the LVLM M generates multi-step reasoning path R to derive the final answer. The reasoning path R can be represented as a T step chain: R = {(re, et, or)) where each step interleaves natural language reasoning rt+ drawing operations et, and observed results o, from executing the drawing operations (74). This iterative process continues until M reaches a conclusive answer in the final reasoning step rr. Next,
elaborate on the core components of the paradigm.
Drawing operations for spatial reasoning. We equip LVLMs with two essential drawing op- erations T = [Toxx: Time] for bounding box annotation and auxiliary line drawing, respectively. These operations are fundamental to spatial reasoning as they enable explicit representation of object locations and their spatial
boundinng boxes anchor object positions while auxiliary lines visualize spatial trajectories and relationshipf Each operation 5 E T accepts three parameters:
the index of the target image from either the original input / or previous drawing outputs {oi}:
single multiple spatial coordinates for annotating bounding boxes drawing auxiliary lines; semantic labels describing the annotated content.
The execution output of each drawing operation is an annotated version of the target image, preserving the original content while overlaying the specified visual elements. While this minimal operation set proves effective for spatial reasoning, it can be readily extended with additional visual manipulation tools in future work.
Per-step spatial reasoning. At the f-th reasoning step. M generates both natural language reason- ing F; and drawing operations e, based on the entire interaction history:
(re, 6 = {el = (kg pl. (m)) = MM[ Re)),
Siine this work focuses on inter-object spatial relationships rather than object-specific details, we adopt only basic drawing operations rather than common visual manipulations like zooming or cropping g 47..

---

Stage Cold-Start Training
Stage 3: Reinforcement Learning
Trajectrsie
Reverds
Advaragee gb
Shvrrage
Stage 2: Reflective Rejection Sampling
Roarrdi
Shouray--
Update
VILASR
Figure 2: Overview of the three-stage training framework of VILASR.
where Et specifies a set m, operations to be executed, eş denote each single operation with three necessary parameters, and Res {rr, Ci2 oi) means the reasoning history before step t. The operations e, can target different images through distinet indices ki. which is crucial for both image and video reasoning as key information may come from multiple previous drawing outputs or different video frames. After execution, these operations output a set of annotated images which are sequentially indexed to maintain order. To enable index-based image retrieval for drawing. M has access to the indices of all available images, including both the original visual input and operation -eeeerrte outputs. The reasoning process terminates under two conditions: reaches final answer, in which case e 0 and 0: or (ii) when the number of reasoning steps reaches predefined maximum maan-
{or 3--
(i) when rt
3.2 Training framework
Our training framework consists of three stages: cold-start training with synthetic offline data to establish basic visual interaction capabilities, reflective rejection sampling cultivate reflection behaviors, and reinforcement learning for incentivizing reasoning potentials, as illustrated in Figure 2 During training, we focus on multiple-choice questions (e.g.. "Which object is to the left of the chair? A. table ...") and numerical questions (c.g.. "How many tables appear in this video?") due to their amenability automated correctness evaluation, strategically excluding free-form answer questions (e.g., describing motion trajectories). In what follows, we first present our reward function design that guides all three stages, followed by detailed descriptions of the stage-wiss wwiee training procedures.
Reward function. For reward design, we propose a rule-based function that combines answer correctness and reasoning format adherence:
S 1(Scomeat B) (Scorret(AA, Á) + Storma(()))
where / is a threshold that ensures format rewards are only granted when minimum correctness threshold is met, preventing reward hacking where the model might optimize for format adherence at the expense of task accuracy. Á is the predicted answer that we extract from the model's 's final reasoning step rr using rule-based parsing. Specifically, we compute Scomect as follows:
1(A A), |C| Enec 1 (I~=a)<
for multiple-choice questions, <1 01) for numerical questions.
Scorroer (A,
(3)
For multiple-choice questions, we simply check the exact match between the predicted and ground- truth answers. For numerical questions, adopt Mean Relative Accuracy (MRA) 770 for reward computation, which provides more robust evaluation than conventional metrics like absolute error or fixed thresholding. Instead, MRA examines the prediction accuracy across multiple confidence C, it checks if the relative error between levels = (0.50, 0.55. 0.95}. For each threshold
predicted value A and ground truth falls below (1 - 0). The final score averages these binary outcomes, effectively measuring the model's precision across different stringency levels.
For Stormats we evaluate the quality of reasoning format based on the structural validity R, assigning score of if all operations in the reasoning path R are executable, and 0 otherwise.
Cold-start training. Prompting alone often fails to elicit effective visual manipulation abilities in LVLMs for reasoning [19 8. Therefore, initialize models' ability to reason in space with
5

---

drawing operations through supervised learning on a synthetic dataset coold The training objective is minimize the average negative lieelkkiioood over all reasoning and operation tokens:
T
Loold =
(
logr(re, ex)t, Q, Ret))
N
where N N =/==((r (1rx| operations. To construct Deold, first collect diverse set of image and video guestion-answering pairs from publicly available datasets, comprising visual inputs 7, questions Q, and ground-truth answers A. We then leverage Qwen2.5-72B-VL [2] generate reasoning paths following our reasoning paradigm described in $3.1 The generated paths are subsequently filtered based on rule- based correctness and format checking in Eq. 2 to ensure high-quality demonstrations of spatial
leel) denotes the total number of tokens in reasoning steps and drawing
reasoning. Appendix shows more details.
Reflective rejection sampling. The success of RL often relies on the model's initial capability to exhibit reflective behaviors [14]. In our case, the ability to reflect on and revise drawing operations define reflective behavior as the
based observed execution output is crucial. Accordingly, recurrence of identical labels across different time steps within the same reasoning process. Formally, for reasoning path R. reflection occurs when:
(5) where (i, and 1/2 represent semantic labels assigned to drawing operations at different reasoning steps, and ef denote the parameters of one drawing operation. However, after cold-start training, observe that the resulting model, denoted as Meold. infrequently exhibits such reflective behavior (see $4.3 for more details), potentially limiting the effectiveness of subsequent RL optimization. To address this limitation, we introduce a novel reflective rejection sampling mechanism. Given a batch of spatial reasoning examples Detfects we first use Meold to sample corresponding reasoning paths, and then continue fine-tune Moold with the following objective:
341,,2, u, v) (H, = 112)) ^ (ct + eit) in R = [(r,, =
Liefect (.I. (r 1 M logplri, ea 1 (,
(6)
where acts as binary filter that equals 1 if and only if the reasoning path R not only yields the correct answer A and meets format criteria, but also satisfies the reflection condition in Eq. 5
This selective training strategy encourages the model learn from high-quality reasoning paths
that demonstrate both reflective thinking and correct reasoning, facilitating the development of
self-correction capabilities crucial for subsequent RL optimization.
Reinforcement learning. We further optimize the model using RL with carefully designed rollout policies. During policy rollout, we monitor the reasoning process and apply early termination to avoid inefficient or circular reasoning patterns. Specifically, the rollout is terminated and the reward set to zero when any of the following conditions operations, i.e., é = 0 while ri has not reached a final answer; (2) the number of accumulated images exceeds predefined threshold o; (3) a drawing operation duplicates a previously executed one, i.e., 34, (2, u, v el = -
met: (1) the model fails to generate any drawing
With the rollout policies defined above and reward functions in Eq. we optimize the policy using GRPO [10] without the KL penalty term [20]:
G
T min (pr,,4, 1 1c (7)
CR.. = E (I..AA)~D
N
[R1 (Pa((11))))))
1=1
Pi. = p(ra,, C1,1 I, Q, Ri,ct)
S mean( [S, (5
A
(8)
(o et, 1, Q, Ra,c))
std( (5;1
where G is the number of rollout reasoning paths, R; = ((ri,) Ct,,, TT+ is the i-th reasoning path, N; denotes the total length of the R, except the tool outputs, S is the reward of R2 and p and Pold represent the current and old policy distributions, respectively. The normalized score Ar, reflects the relative quality of each reasoning path within the rollout group, enabling the model distinguish between learnable and poor reasoning trajectories.

---

140
200
1890
400
893
1300
1200
60.
33.00
1248
200
400
$10
300
1990
1293
(a) Overall reward
(b) Correctness reward Scoeect
(c) Formal reward Stomet
(d) Response length N
Figure 3: RL training curves of VILASR.
4 Experiment
4.1 Experimental setups
Evaluation benchmark and metrics. To evaluate the effectiveness and generalization of VILASR, we conduct experiments on five benchmarks covering three categories:
Image spatial reasoning: focusing on static relationships and sequential planning, including (1)
Maze [25], specifically designed for navigation assessment; (2) SpatialEval-Real 665, demanding
real-world spatial relation understanding.
Video spatial reasoning: requiring temporal relationship tracking, including VSI-Bench [70],
which tests visual spatial understanding over temporal sequences.
Multi-view spatial reasoning: challenging models to integrate information from multiple perspec- tives, including SPAR-Bench [78), MMSI-Bench (71).
These benchmarks consist exclusively of multiple-choice and numerical questions. We evaluate the model performance using accuracy for multiple-choice questions and Mean Relative Accuracy (MRA) [70] for numerical questions. Notably, these metrics follow the same formulation as our training objective (Eq. 3). Appendix
C.2 shows the benchmark statistics.
Implementation details. We implement VILASR based on LWV 2 During the training phase, we process all visual inputs at a maximum resolution of 256 x 28 x 28, with video clips uniformly sampled at 16 frames. In the evaluation stage, we maintain the 16-frame count and the 256 x 28 x 28 frame resolution for VSI-Bench, while increase the resolution to 448 x 28 x 28 for other benchmarks. The training is conducted on cluster of 16 NVIDIA A100 (80G) GPUs For both cold-start training stage and reflective fine-tuning stage, we optimize the model with learning rate of 10-5 for three epochs, requiring approximately 24 and 3 hours, respectively. The subsequent RL optimization is implemented using the VERL framework (58), where we set the training batch size 32 and generate 8 candidate reasoning paths per question. We set the maximum cumulative image number to 42. And the reward threshold ,3 in Eq. 2 is set to 0.0.
The training dynamics are shown in Figure R As illustrated in (a-c), both overall reward S and its components (Scorrect and Stormat) demonstrate steady improvements, validating the effectiveness of our RL optimization. Notably, while achieving better task performance, we observe a decrease in response length N from 2,500 to 1,800 tokens (d). This can be attributed to two factors: First, during cold-start training, we set a minimum of three reasoning steps synthetic data to encourage in-depth reasoning, while RL optimization subsequently drives the model toward more efficient use of drawing operations. Second, the limited training data may not fully expose the model to complex scenarios requiring lengthy reasoning chains. We expect that increasing training data diversity could potentially lead to longer but necessary reasoning steps for more challenging spatial tasks (68] We also present an analysis of the runtime performance in Appendix E.2
Baselines.
We compare VILASR with various representative models and methods as follows:
Proprietary LVLMs: GPT-4o 44
(62). Gemini-2.0-Flash [16), OpenAI o3 and
04-mini [46];
Open-source LVLMs: These models range from small-sized models including Qwen2.5-VV VL- 7B (2), cluding Kimi-VI--A3B-Inse (16B) [X] Qwen2.5-VIL-72 MeVV--NeTT-Vido--77 80
[0 and
[30 to large-sized models in-
LLavi-OOneisioon7722 [30]:
7

---

Table Performance comparison across spatial reasoning benchmarks. Gray- rows represent large-sized models (>7B parameters). For non-shaded rows, bold and underlined numbers indicate the best and second-best results. Italic numbers gray-shaded rows indicate performance below non-shaded best results. Improvement refers to the absolute improvement of VILASR compared with Qwen2.5-VL w/o reasoning. and indicate results from VSI-Bench and VSI-Bench (tiny) set [70] respectively. Results from [63]. Results from 77.. N/A: not support multiple-image
input. OpenAl 04-mini is evaluated on a small subset of benchmarks due to its high cost.
Method
Tool
Reasoning
Image
Mulli-view
MAZE
SpatialEval-Red
VSI-Bench
SPAR-Bench MMSI-Bench
Proprictary LVLMs
GPT-4o
X
48.3
60.7
34.01
33.6
30,3
GPT-4o
Gemini-1.5-Prg
x
45,41
Gemini-2.0-Flaa
x
40.2
45.44
33..4
Scmmini-2.0-Flase
61.7
28.0
OpenAl 03
41.0"
OpenAl oá-mini
Open-source LVLMs
Qwon2.5-VL-7B
X
33.7
58.5
32.7
31.7
26.9
Qwen2.5-VL--7
X
36.5
$4.1
26.2
31.6
27.1
LLaVA-NoXT-Vidoo-BB
68.1
35.6'
26.8
HlVVA-OneVssoon-7
30.8
62.9
32.41
30.6
24.5**
Instruct (16B)
Owen2.5-VL-728
50.5
68.1
36.0
37.4
30.7
LLaVA-NoXT-VVdoo-722
43.2
72.5
28.3
Viaii-One
46.3
68.8
40.21
34.4
28.4*
Representative methods for multimodal reasoning
CocCoM-122 17
51
29.8
49.3
N/A
N/A
N/A
VisCoT-7B 55
26.0
43.2
N/A
N/A
SpaceR-77 7B
48
38.6
62.7
43.5
37.1
28.8
VisPreg
22.6
26.8
NIA
N/A
N/A
ViperGPT
6
27.3
45.9
10.6
23.7
25.4
VILASR
98.2
63.9
45.4
37.6
30,2
Imprevement
M/A
N/A
+64.5
+3.4
+12.7
+3.9
+3.3
Representative models focused on multimodal reasoning: COGCOM [51], which enables step-by-step visual reasoning through image manipulations with specialized perception tools (e.g., grounding) but is limited to single-image inputs; VisCoT [55] which first identifies key regions through bounding box annotations followed by textual reasoning chains on single images; SpaceR [48), which is contemporary work that extends spatial reasoning to video understanding through task-specific optimization on automatically curated video QA data; VisProg [19], which pioneers visual programming by prompting LLM to generate pseudocode orchestrating modular vision APIs for compositional tasks; and ViperGPT [61], which extends this to generate executable Python with richer control flow (e.g., loops, conditionals) for vision language interaction.
Furthermore, we perform ablation studies to evaluate each individual training stage to assess their con- tributions to the final performance. Implementation details of the basclines are show in Appendix C.I
4.2 Main results
As shown in Table VILASR shows strong performance across various spatial reasoning benchmarks, from maze navigation to complex video understanding. Our analysis reveals several key findings:
(1) Limited visual reasoning capabilities in open-source LLMs. Our experiments reveal sig- nificant disparity between proprietary and open- pour-source LLMs their ability to leverage reasoning processes. Proprietary models consistently outperform their non-reasoning counterparts by a substan- margin across different benchmarks (e.g., GPT-4o, Gemini-2.00 2.0--aahh... However, open-source models like Dwe-2.5-VL--BB show minimal or even negative improvements with reasoning enabled, suggesting significant gap their fundamental visual reasoning capabilities. This observation highlights critical direction for future research: enhancing the multimodal reasoning abilities of

---

210
Qwen2.5 78
VRLa
VI.5SR
VILa
Stage
Object
Absolute
Object
Room Size
Relative
Relative
Route
Apperance
Count
Distance
Size
Distance
Direction
Plan
order
(a) Absolute change in scores compared with VILASR on eight (h) Relative change (%) in four key behavioral metrics compared with VILASR.
subsets of VSI-Bench.
Figure 4: Ablation study results on VSI-Bench regarding three training stages: cold-start training (Stage 1), reflective rejection sampling (Stage 2), and reinforcement learning (Stage 3).
open-source models, potentially through improved architectural designs and more sophisticated training strategies that better integrate visual and linguistic information.
(2) Strong performance of VILASR on image- based spatial tasks. VILASR demonstrates ex- ceptional capabilities in both sequential spatial planning (MAZE) and static spatial understanding (SpatialFval). The remarkable performance on maze navigation, in particular, highlights the advan- tage of our "drawing to reason in space" paradigm: through iterative drawing operations, the model effectively breaks down multi-step navigation sequences into interpretable visual steps, thereby captur- ing and tracking spatial state transitions. In contrast, existing methods show limited performance due to various constraints: COGCOM is restricted by the capabilities of its perception tools, and VisCoT lacks the ability to reflect and revise its visual operations since it only performs one-time ground- ing. VisProg and ViperGPT exhibit inferior performance because they often generate malformed or non-executable programs complex questions. Moreover, despite leveraging modular APIs, these methods frequently struggle with basic spatial relationships, consistent with recent findings 44].
(3) Competitive results of VILASR on video and multi-view reasoning. Video and multi-view reasoning present unique challenges beyond static image understanding, as it requires tracking spatial relationships across multiple viewpoints and temporal transitions. While most existing models struggle with this increased complexity, VILASR achieves state-of-the-art performance on all benchmarks, surpassing significantly larger open-source models such as VLa -inionni--7 This success can be attributed to our flexible visual operations that effectively handle dynamic spatial relationships. In contrast, existing approaches face fundamental limitations: COGCOM and VisCoT lack video processing capabilities entirely, while SpaceR's 's text-centric reasoning fails to fully exploit visual temporal information.
4.3 Ablation study
To comprchensively evaluate our training framework, we conduct ablation studies on VSI-Bench's eight spatial reasoning subtasks and analyze four key behavioral metrics. The behavioral metrics include: (1) Reflection Pattern Exhibition, measuring the ratio of examples exhibiting reflection behavior defined in Eq. 5 (2) Number of Reasoning Steps, indicating the average number of reasoning steps (7) required to answer each question; and (3,4) Numbers of Too and Time- reflecting the average number of drawing operations utilized per question. The results shown in Figure J for task performance and Figure for behavioral patterns. We draw the following insights:
(1) Cold-start training: Essential for spatial reasoning foundation. Comparing "VILASR w/o Stage 1&2&3" with "VILASR w/o Stage 2&3", we observe substantial performance improve- ments across all subtasks. Notably, when equipped with only our "drawing reason in space" paradigm without training (i.c., "VILASR w/o Stage 1&2&3"), the model performs even worse than the Qwen2.5-VL-7 backbone. This degradation highlights that sophisticated spatial reasoning capabilities cannot emerge solely with prompting but must be learned through dedicated training.
(2) Reflection sampling: Key to self-correction ability. The comparison between VILASR and "VILASR w/o Stage 2" reveals the crucial role of reflective rejection sampling. Removing this stage leads to 96.5% decrease in reflection pattern exhibition, fundamentally altering the model's behavior and performance. Behaviorally, we observe 33.9% reduction in reasoning steps and dramatically different patterns in drawing operation usage: 85.0% decrease in Trox but 70.5%

---

increase in Time- Such changes particularly affect tasks requiring precise object localization and measurement: "Absolute Distance" (-0.6%), "Room Size" (-0.7%), and "Relative Distance" (-1.0%). In contrast, tasks that primarily rely on directional judgment or categorical reasoning show minimal impact or even slight improvements (e.g., "Object Count": +0.1 %, "Relative Direction": +0.9%), as they can be solved with simpler spatial relationships indicated by lines. This pattern reveals that reflection capability fundamentally shapes how the model builds spatial understanding. Without it, the model shows tendency to make quick spatial judgments through auxiliary lines without sufficient self-verification. Based on this observation, we hypothesize specific mechanisms through which reflection enhances spatial reasoning: re-examining object locations through bbox annotations and carefully evaluating different spatial relationships before making final judgments (see examples in Appendix (D). This verification-drin -rriven approach, rather than making multiple "guessing" attempts through auxiliary lines, appears to be key to accurate spatial reasoning.
(3) RL optimization: Dense rewards enable fine-grained learning. Comparing VILASR with "VILASR w/o Stage 3", we observe consistent performance decreases across most subtasks. The substantial increases in both Toox (+ (+159.4%) and Tiie (+9.1%) usage without RL suggest that RL optimization helps the model learn to use drawing operations more selectively. Moreover, tasks requiring precise numerical answers ("Object Count," "Absolute Distance," "Object Size" and "Room Size") show greater average performance gaps without RL compared to multiple-choice questions (-9.21% % vs. -4.07)). This disparity highlights key advantage of RL optimization: while supervised learning merely maximizes the probability of correct answers, RL provides dense reward signals based numerical proximity to ground truth, enabling more effective learning for precise spatial measurements.
4.4 Inference-time scaling
We further evaluate the effectiveness of our training framework through the lens of inference- time scaling analysis such as pass@ l evaluation (sampling & outputs in parallel and selecting the
best). Prior research has demonstrated: (1) pass@k k serves an empirical upper bound of model
capability with sufficiently large k (59), while pass@) I reflects its single-attempt performance; (2) RL has been shown effectively narrow this gap by consolidating pass @ k capabilities into pass
performance (76]. This motivates our analysis of how each training stage expands model capability.
Inforesce Staling Analya' VSiBeech
Results in Figure reveal the progressive hancement of model capability across training stages: (1) Cold-start training substantially im- proves both the empirical upper bound (pass @ 8) and single-attempt performance (pass @ 1) com- pared to Swen2.55VL-7B: (2) Reflective re-
5.K73
0.531
0,281
0.2
jection sampling further elevates both metries, demonstrating expanded reasoning potential; (3) RI. optimization not only pushes the empirical upper bound (pass@5 but also significantly nar- rows the gap with single-attempt performance (pass@) 1), indicating effective consolidation of multi-attempt capabilities that aligns with previous studies about RL's optimization effects (66
Figure 5: Analysis of inference- time scaling be- havior using pass@1 and pass@8 8 performance.
5
Conclusion
This work presents principled approach to enhancing spatial reasoning capabilities in LVLMs through visual drawing operations. By enabling direct manipulation in the visual space through the "drawing to reason in space" paradigm, we bridge the gap between text-centric reasoning and human- like spatial cognition. Through careful empirical validation, we demonstrate that our three-stage training framework successfully cultivates sophisticated reasoning pattern. Extensive experiments across diverse spatial reasoning benchmarks validate the effectiveness of our approach, showing particular strengths in maze navigation and temporal-spatial understanding tasks. While our results are promising, several important directions remain for future exploration, such as extending our drawing operations to handle more complex 3D spatial relationships, and investigating more efficient training strategies.
10

---

Acknowledgements
We thank the anonymous reviewers for their insightful comments. This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant Nos. 62141608, 62236010, 62372454, and 62576339, and part by the Ant Group Research Intern Program.
References
[1] Akari Asai, Zeqiu Wu, Yizhong Wang, Avirup Sil, and Hannanch Hajishirzi. Self-RAG: Learning to retrieve, generate, and critique through self-reflection. In The Twelfth International Conference on Learning Representations, 2024.
[2] Shuai Bai, Keqin Chen, Xuejing Liu, Jialin Wang, Wenbin Ge, Sibo Song, Kai Dang, Peng Wang. Shijie Wang, Jun Tang, et al. Qwen2. 5-vl technical report. arXiv preprint w5Xiv22502.13923 2025.
[3] Neil Burgess. Spatial cognition and the brain. Annals of the New York Academy of Sciences, 1124(1):77-97, 2008
[4] Wenxiao Cai, laroslav Ponomarenko, Jianhao Yuan, Xiaoqi Li, Wankou Yang. Hao Dong, and Bo Zhao. Spatialbot: Precise spatial understanding with vision language models, 2025.
[5] Boyuan Chen, Zhuo Xu, Sean Kirmani, Brain Ichter, Dorsa Sadigh, Leonidas Guibas, and Fei Xia. Spatialvim: Endowing vision-language models with spatial reasoning capabilities. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 14465, June 2024.
[6] Mark Chen, Jerry Tworek, Heewoo Jun, Qiming Yuan, Henrique Ponde de Oliveira Pinto, Jared Kaplan, Harri Edwards, Yuri Burda, Nicholas Joseph, Greg Brockman, Alex Ray, Raul Puri, Gretchen Krueger, Michael Petrov, Heidy Khlaaf, Girish Sastry, Pamela Mishkin, Brooke Chan, Scott Gray, Nick Ryder, Mikhail Pavlov, Alethea Power, Lukasz Kaiser, Mohammad Bavarian, Clemens Winter, Philippe Tillet, Felipe Petroski Such, Dave Cummings, Matthias Plappert, Fotios Chantzis, Elizabeth Barnes, Ariel Herbert- Voss, William Hebgen Guss, Alex Nichol, Alex Paino, Nikolas Tezak, Jie Tang, Igor Babuschkin, Suchir Balaji, Shantanu Jain, William Saunders, Christopher Hesse, Andrew N. Carr, Jan Leike, Josh Achiam, Vedant Misra, Evan Morikawa, Alec Radford, Matthew Knight, Miles Brundage, Mira Murati, Katie Mayer, Peter Welinder, Bob McGrew, Dario Amodei, Sam McCandlish, llya Sutskever, and Wojeiech Zaremba. Evaluating large language models trained on code, 2021.
[7] An-Chieh Cheng, Hongxu Yin, Yang Fu, Qiushan Guo, Ruihan Yang, Jan Kautz, Xiaolong Wang, and Sifei Liu. SpatialRGPT: Grounded spatial reasoning in vision-language models. In The Thirty-eight Annual Conference Neural Information Processing Systems, 2024.
[8] Chuanqi Cheng, Jian Guan, Wei Wu, and Rui Yan. From the least the most: Building plug-and-play visual reasoner via data synthesis. In Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen, editors, Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 4941-4957, Miami, Florida, USA, November 2024. Association for Computational Linguistics.
[9] Chuanqi Cheng, Jian Guan, Wei Wu, and Rui Yan. Scaling video-language models to 10k frames via hierarchical differential distillation, 2025.
[10] DeepSeek-AI. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement
learning, 2025.
[11] Yihe Deng, Hritik Bansal, Fan Yin, Nanyun Peng, Wei Wang, and Kai-Wei Chang. Open- vlthinker: An early exploration complex vision-language reasoning via iterative self- improvement. arXiv preprint arXiv:2503. 17352, 2025.
[12] Yu Du, Fangyun Wei, Zihe Zhang, Miaojing Shi, Yue Gao, and Guoqi Li. Learning to prompt for open-vocabulary object detection with vision-language model. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 14084-1409 2022.
11

---

[13] Kaituo Feng, Kaixiong Gong, Bohao Li, Zonghao Guo, Yibing Wang, Tianshuo Peng, Benyou Wang, and Xiangyu Yue. Video-rl: Reinforcing video reasoning milms. arXiv preprint arXiv:2503.21776, 2025.
[14] Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D. Goodman. Cognitive behaviors that enable self-improvinn reasoners, or, four habits of highly effective stars, 2025.
[15] Howard E Gardner. Frames of mind: The theory of multiple intelligences. Basic books, 201 1.
[16] Google. Introducing gemini 2.0: our new ai model for the agentic era, 2024.
[17]
Kristen Grauman, Andrew Westbury, Eugene Byrne, Zachary Chavis, Antonino Furnari, Rohit Girdhar, Jackson Hamburger, Hao Jiang, Miao Liu, Xingyu Liu, Miguel Martin, Tushar Nagara- jan, Iliaa Radosavovic, Santhosh K. Ramakrishnan, Fiona Ryan, Jayant Sharma, Michael Wray, Mengmeng Xu, Eric Z. Xu, Chen Zhao, Siddhant Bansal, Dhruv Batra, Vincent Cartillier, Sean Crane, Tien Do, Morrie Doulaty, Akshay Erapalli, Christoph Feichtenhofer, Adriano Fragomeni, Qichen Fu, Christian Fuegen, Abrham Kahsay Gebreselasie, Cristina González, James M. Hillis, Xuhua Huang, Yifei Huang. Wenqi Jia, Weslie Khoo, Jáchym Kolár, Satwik Kottur, Anurag Kumar, Federico Landini, Chao Li, Yanghao Li, Zhenqiang Li, Karttikeya Mangalam, Raghava Modhugu, Jonathan Munro, Tullie Murrell, Takumi Nishiyasu, Will Price, Paola Ruiz Puentes, Merey Ramazanova, Leda Sari, Kiran K. Somasundaram, Audrey Southerland, Yusuke Sugano, Ruijie Tao, Minh Vo, Yuchen Wang, Xindi Wu, Takuma Yagi. Yunyi Zhu, Pablo Arbeláez, David J. Crandall, Dima Damen, Giovanni Maria Farinella, Bernard Ghanem, Vamsi Krishna Ithapu, C. V. Jawahar, Hanbyul Joo, Kris Kitani, Haizhou Li, Richard A. Newcombe, Aude Oliva, Hyun Soo Park, James M. Rehg. Yoichi Sato, Jianbo Shi, Mike Zheng Shou, Antonio Torralba, Lorenzo Torresani, Mingfei Yan, and Jitendra Malik. Ego4d: Around the world in 3,000 hours of egocentric video. 2022 IEEE/CVF Conference Computer Vision and Pattern Recognition (CVPR), pages 18973-18990, 2021.
[18] Jian Guan, Wei Wu, Peng Xu, Hongning Wang. Minlie Huang, et al. Amor: A recipe for building adaptable modular knowledge agents through process feedback. Advances in Neural Information Processing Systems, 37:1 07:12611 18-126148, 2024.
[19] Tanmay Gupta and Aniruddha Kembhavi. Visual programming: Compositional visual reasoning without training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 11953-14963 2023.
[20] Jingeheng Hu, Yinmin Zhang, Qi Han, Daxin Jiang, Xiangyu Zhang, and Heung- Yeung Shum. Open-reasoner-zero:: An open source approach scaling up reinforcement learning on the base model, 2025.
[21] Yushi Hu, Weijia Shi, Xingyu Fu, Dan Roth, Mari Ostendorf, Luke Zettlemoyer, Noah Smith, and Ranjay Krishna. Visual sketchpad: Sketching as visual chain of thought for multimodal language models. In The Thirty-eightn Annual Conference on Neural Information Processing Systems, 2024.
[22] Drew A Hudson and Christopher D Manning. Gqa: new dataset for real-world visual reasoning and compositional question answering. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 7700-6709, 2019.
[23] Minyoung Huh, Brian Cheung, Tongzhou Wang, and Phillip Isola. Position: The platonic representation hypothesis. In Forty-first International Conference on Machine Learning, 2024.
[24] Aaron Hurst, Adam Lerer, Adam Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Ostrow, Akila Welihinda, Alan Hayes, Alec Radford, et al. Gpt-4o system card. arXiv preprint arXiv:2410.21276 2024.
[25] Michael Igorevich Ivanitskiy, Rusheb Shah, Alex F. Spies, Tilman Räuker, Dan Valentine, Can Rager, Lucia Quirke, Chris Mathwin, Guillaume Corlouer, Cecilia Diniz Behn, and Samy Wu Fung. A configurable library for generating and manipulating maze datasets, 2023.
12

---

[26] Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed EI- El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, Alex Carney, al. Openai ol system card. arXiv preprint SiKiv:2412.167221 2024.
[27] Amita Kamath, Jack Hessel, and Kai-Wei Chang. What's" up" with vision-language models? investigating their struggle with spatial reasoning. arXiv preprint arXiv:2310. 19785. 2023.
[28] Alina Kuznetsova, Hassan Rom, Neil Alldrin, Jasper Uijlings, Ivan Krasin, Jordi Pont-Tuset, Shahab Kamali, Stefan Popov, Matteo Malloci, Alexander Kolesnikov, et al. The open images dataset v4: Unified image classification, object detection, and visual relationship detection at scale. International journal of computer vision, 12807)115561988, 2020.
[29] Hung Lc, Yue Wang, Akhilesh Deepak Gotmare, Silvio Savarese, and Steven Chu Hong Hoi. Coderl: Mastering code generation through pretrained models and deep reinforcement learning. Advances in Neural Information Processing Systems, 35:21314 14-2114--,,28, 2022.
[30] Bo Li, Yuanhan Zhang, Dong Guo, Renrui Zhang, Feng Li. Hao Zhang, Kaichen Zhang, Peiyuan Zhang, Yanwei Li, Ziwei Liu, and Chunyuan Li. Llava-onevision: Easy visual task transfer, 2024.
[31] Chengzu Li, Wenshan Wu, Huanyu Zhang, Yan Xia, Shaoguang Mao, Li Dong, Ivan Vulić, and Furu Wei. Imagine while reasoning in space: Multimodal visualization-of-toogg arXiv preprint arXiv:2501.07544 2025.
[32] Chengzu Li, Caiqi Zhang, Han Zhou, Nigel Collier, Anna Korhonen, and Ivan Vulić. Topviewrs: Vision-language models as tip-view spatial reasoners, 2024.
[33] Songtao Li and Hao Tang. Multimodal alignment and fusion: A survey. arXiv preprint arXiv:2411.17040 2024.
[34] Xuefeng Li, Haoyang Zou, and Pengfei Liu. Torl: Scaling tool-integrated rl, 2025.
[35] Hunter Lightman, Vineet Kosaraju, Yura Burda, Harri Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let's verify step by step. arXiv preprint arXiv:2305.20050, 2023.
[36] Ji Lin, Hongxu Yin, Wei Ping, Pavlo Molchanov, Mohammad Shoeybi, and Song Han. Vila: On pre-training for visual language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 26689-26699, 2024.
[37] Benlin Liu, Yuhao Dong, Yiqin Wang, Zixian Ma, Yansong Tang, Luming Tang, Yongming Rao, Wei-Chiu Ma, and Ranjay Krishna. Coarse correspondences boost spatial-temporal reasoning in multimodal language model, 2024.
[38] Fangyu Liu, Guy Emerson, and Nigel Collier. Visual spatial reasoning. Transactions of the Association for Computational Linguistics. 11:635-651, 2023.
[39] Haotian Liu, Chunyuan Li, Yuheng Li, and Yong Jae Lee. Improved baselines with visual instruction tuning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 26296 22096622666...0 2024.
[40] Muhammad Maaz, Hanoona Rasheed, Salman Khan, and Fahad Khan. Video-chatgpt Towards detailed video understanding via large vision and language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers),
pages 12585-12603 2024.
[41] Damiano Marsili, Rohun Agrawal, Yisong Yue, and Georgia Gkioxari. Visual agentic ai for spatial reasoning with a dynamic api. Proceedings of the Computer Vision and Pattern Recognition Conference, pages 19446-19455, 2025.
[42] Julia McAfoose and BT Baune. Exploring visual-spatial working memory: A critical review of concepts and models. Neuropsychology review, 19:130-142, 2009.
13

---

[43] Roshanak Mirzaee, Hossein Rajaby Faghihi, Qiang Ning, and Parisa Kordjamshidi. SPARTQA: textual question answering benchmark for spatial reasoning. In Kristina Toutanova, Anna Rumshisky, Luke Zettlemoyer, Dilek Hakkani-'Tur, Iz Beltagy, Steven Bethard, Ryan Cotterell, Tanmoy Chakraborty, and Yichao Zhou, editors, Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 4582-4598, Online, June 2021. Association for Computational Linguistics.
[44] OpenAl. Hello gpt-4o. In OpenAl Blog, 2024.
[45] OpenAL. Introducing openai ol-preview. ponedducinn-opnnaaiii -0 o1-preview/ 2024.
https://openai. ctap:://opeaai.commnnoooo com/index/
[46] OpenAl. Introducing openai o3 and 04-mini, 2025.
[47] OpenAl. Thinking with images, 2025.
[48] Kun Ouyang, Yuanxin Liu, Haoning Wu, Yi Liu, Hao Zhou, Jie Zhou, Fandong Meng, and Xu Sun. Spacer: Reinforeing milms in video spatial reasoning, 2025.
[49]
Abby O'Neill, Abdul Rehman, Abhiram Maddukuri, Abhishek Gupta, Abhishek Padalkar, Abraham Lee, Acom Pooley, Agrim Gupta, Ajay Mandlekar, Ajinkya Jain, Albert Tung, Alex Bewley, Alex Herzog, Alex Irpan, Alexander Khazatsky, Anant Rai, Anchit Gupta, Andrew Wang. Anikait Singh, Animesh Garg, Aniruddha Kembhavi, Annie Xie, Anthony Brohan, Antonin Raffin, Archit Sharma, Arefch Yavary, Arhan Jain, Ashwin Balakrishna, Ayzaan Wahid, Ben Burgess-Limerick Beomjoon Kim, Bernhard Schölkopf, Blake Wulfe, Brian Ichter, Cewu Lu, Charles Xu, Charlotte Le, Chelsea Finn, Chen Wang. Chenfeng Xu, Cheng Chi, Chenguang Huang, Christine Chan, Christopher Agia, Chuer Pan, Chuyuan Fu, Coline Devin, Danfei Xu, Daniel Morton, Danny Driess, Daphne Chen, Deepak Pathak, Dhruv Shah, Dieter Büchler, Dinesh Jayaraman, Dmitry Kalashnikov, Dorsa Sadigh, Edward Johns, Ethan Foster, Fangchen Liu, Federico Ceola, Fei Xia, Feiyu Zhao, Freek Stulp, Gaoyue Zhou, Gaurav S. Sukhatme, Gautam Salhotra, Ge Yan, Gilbert Feng, Giulio Schiavi, Glen Berseth, Gregory Kahn, Guanzhi Wang, Hao Su, Hao-Shu Fang. Haochen Shi, Henghui Bao, Heni Ben Amor, Henrik Christensen, Hiroki Furuta, Homer Walke, Hongjie Fang, Huy Ha, Igor Mordatch, Iljja Radosavovic, Isabel Leal, Jacky Liang, Jad Abou-Chakra, Jachhhauaaaaahuunng Kim, Jaimyn Drake, Jan Peters, Jan Schneider, Jasmine Hsu, Jeannette Bohg, Jeffrey Bingham, Jeffrey Wu, Jensen Gao, Jiaheng Hu, Jiajun Wu, Jialin Wu, Jiankai Sun, Jianlan Luo, Jiayuan Gu, Jie Tan, Jihoon Oh, Jimmy Wu, Jingpei Lu, Jingyun Yang. Jitendra Malik, João Silvério, Joey Hejna, Jonathan Booher, Jonathan Tompson, Jonathan Yang. Jordi Salvador, Joseph J. Lim, Junhyek Han, Kaiyuan Wang, Kanishka Rao, Karl Pertsch, Karol Hausman, Keegan Go, Keerthana Gopalakrishnan, Ken Goldberg, Kendra Byrne, Kenneth Oslund, Kento Kawaharazuka, Kevin Black, Kevin Lin, Kevin Zhang, Kiana Ehsani, Kiran Lekkala, Kirsty Ellis, Krishan Rana, Krishnan Srinivasan, Kuan Fang. Kunal Pratap Singh, Kuo-Hao Zeng, Kyle Hatch, Kyle Hsu, Laurent Itti, Lawrence Yunliang Chen, Lerrel Pinto, Li Fei-Fei, Liam Tan, Linxi Jim Fan, Lionel Ott, Lisa Lee, Luca Weihs, Magnum Chen, Marion Lepert, Marius Memmel, Masayoshi Tomizuka, Masha Itkina, Mateo Guaman Castro, Max Spero, Maximilian Du, Michael Ahn, Michael C. Yip, Mingtong Zhang, Mingyu Ding, Minho Heo, Mohan Kumar Srirama, Mohit Sharma, Moo Jin Kim, Naoaki Kanazawa, Nicklas Hansen, Nicolas Heess, Nikhil Joshi, Niko Suenderhauf, Ning Liu, Norman Di Palo, Nur Muhammad Mahi Shafiullah, Oier Mees, Oliver Kroemer, Osbert Bastani, Pannag R Sanketi, Patrick Tree Miller, Patrick Yin, Paul Wohlhart, Peng Xu, Peter David Fagan, Peter Mitrano, Pierre Sermanet, Pieter Abbeel, Priya Sundaresan, Qiuyu Chen, Quan Vuong, Rafael Rafailov, Ran Tian, Ria Doshi, Roberto Martin-Martin, Rohan Baijal, Rosario Scalise, Rose Hendrix, Roy Lin, Runjia Qian, Ruohan Zhang, Russell Mendonca, Rutav Shah, Ryan Hoque, Ryan Julian, Samuel Bustamante, Sean Kirmani, Sergey Levine. Shan Lin, Sherry Moore. Shikhar Bahl, Shivin Dass, Shubham Sonawani, Shuran Song, Sichun Xu, Siddhant Haldar, Siddharth Karamcheti, Simeon Adebola, Simon Guist, Soroush Nasiriany, Stefan Schaal, Stefan Welker, Stephen Tian, Subramanian Ramamoorthy, Sudeep Dasari, Suneel Belkhale, Sungjae Park, Suraj Nair, Suvir Mirchandani, Takayuki Osa, Tanmay Gupta, Tatsuya Harada, Tatsuya Matsushima, Ted Xiao, Thomas Kollar, Tianhe Yu, Tianli Ding, Todor Davehev, Tony Z. Zhao, Travis Armstrong, Trevor Darrell, Trinity Chung, Vidhi Jain, Vincent Vanhoucke, Wei Zhan, Wenxuan Zhou, Wolfram Burgard, Xi Chen, Xiaolong Wang, Xinghao Zhu, Xinyang Geng, Xiyuan Liu, Xu Liangwei, Xuanlin Li, Yao Lu, Yecheng Jason
14

---

Ma. Yejin Kim, Yevgen Chebotar, Yifan Zhou, Yifeng Zhu, Yilin Wu, Ying Xu, Yixuan Wang. Yonatan Bisk, Yoonyoung Cho, Youngwoon Lee, Yuchen Cui. Yue Cao, Yuch-Hua Wu, Yujin Tang, Yuke Zhu, Yunchu Zhang, Yunfan Jiang, Yunshuang Li, Yunzhu Li, Yusuke Iwasawa, Yutaka Matsuo, Zehan Ma, Zhuo Xu, Zichen Jeff Cui, Zichen Zhang. and Zipeng Lin. Open x- embodiment: Robotic learning datasets and rt-x models: Open x-embodiment collaboration). In 2024 IEEE International Conference on Robotics and Automation (ICRA), pages 6892-6903, 2024.
[50] Yi Peng, Xiaokun Wang. Yichen Wei, Jiangbo Pei, Weijie Qiu, Ai Jian, Yunzhuo Hao, Jiachun Pan, Tianyidan Xie, Li Ge, et al. Skywork rlv: pioneering multimodal reasoning with chain-of- thought. arXiv preprint arXiv:2504.05599 2025.
[51] Ji Qi, Ming Ding, Weihan Wang. Yushi Bai, Qingsong Lv, Wenyi Hong, Bin Xu, Lei Hou, Juanzi Li, Yuxiao Dong. and Jie Tang. Cogcom: A visual language model with chain-of of- -ottt--oo-muimaiioonnnom reasoning. In The Thirteenth International Conference on Learning Representations, 2025.
[52] Zhangyang Qi, Zhixiong Zhang, Ye Fang, Jiaqi Wang, and Hengshuang Zhao. Gpt4scene: Un- derstand 3d scenes from videos with vision-language models. arXiv preprint arXiv:2501.01) .01428. 2025.
[53] Yujia Qin, Shihao Liang, Yining Ye, Kunlun Zhu, Lan Yan, Yaxi Lu, Yankai Lin, Xin Cong, Xiangru Tang, Bill Qian, Sihan Zhao, Lauren Hong, Runchu Tian, Ruobing Xie, Jie Zhou, Mark Gerstein, dahai li, Zhiyuan Liu, and Maosong Sun. TooILLM: Facilitating large language models to master 16000+ real-world APIs. In The Twelfth International Conference on Learning Representations, 2024.
[54] Timo Schick, Jane Dwivedi- Yu, Roberto Dessi, Roberta Raileanu, Maria Lomeli, Eric Hambro, Luke Zettemmoyrr Nicola Cancedda, and Thomas Scialom. Toolformer: Language models can teach themselves to use tools. Advances in Neural Information Processing Systems, 36, 2024.
[55] Hao Shao, Shengju Qian, Han Xiao, Guanglu Song, Zhuofan Zong, Letian Wang, Yu Liu, and Hongsheng Li. Visual cot: Advancing multi-modal language models with a comprehen- sive dataset and benchmark for chain-of-the -ffthhought reasoning. Advances in Neural Information Processing Systems, 37:8612-8642. 2024.
[56] Bo Shen, Jiaxin Zhang, Taihong Chen, Daoguang Zan, Bing Geng, An Fu, Muhan Zeng. Ailun Yu, Jichuan Ji, Jingyang Zhao, et al. Pangu-coder2: Boosting large language models for code with ranking feedback. arviv preprint arXiv:2307.14936. 2023.
[57] Yongliang Shen, Kaitao Song, Xu Tan, Dongsheng Li, Weiming Lu, and Yueting Zhuang. Hugginggpt: Solving ai tasks with chatgpt and its friends in huggingface. In Advances in Neural Information Processing Systems, 2023.
[58] Guangming Sheng, Chi Zhang, Zilingfeng Ye, Xibin Wu, Wang Zhang. Ru Zhang, Yanghua Peng, Haibin Lin, and Chuan Wu. Hybridflow: flexible and efficient rihf framework. arXiv preprint arXiv: 19256, 2024.
[59] Charlic Victor Snell, Jachoon Lee, Kelvin Xu, and Aviral Kumar. Scaling LLM test-time com- pute optimally can be more effective than scaling parameters for reasoning. In The Thirteenth International Conference on Learning Representations, 2025.
[60] Chan Hee Song, Valts Blukis, Jonathan Tremblay, Stephen Tyree, Yu Su, and Stan Birchfield. RoboSpatial: Teaching spatial understanding to 2D and 3D vision-language models for robotics. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2025. Oral Presentation.
[61] Didac Surís. Sachit Menon, and Carl Vondrick. Vipergpt: Visual inference via python execution for reasoning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11888-1 1898, 2023.
[62] Gemini Team, Petko Georgiev, Ving Ian I Lei, Ryan Burnell, Libin Bai, Anmol Gulati, Garrett Tanzer, Damien Vincent, Zhufeng Pan, Shibo Wang, et al. Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context. arXiv preprint arXiv:2403.0555 2024.
15

---

[63]
Kimi Team, Angang Du, Bohong Yin, Bowei Xing, Bowen Qu Bowen Wang, Cheng Chen, Chenlin Zhang, Chenzhuang Du, Chu Wei, Congcong Wang, Dehao Zhang, Dikang Du Dongliang Wang. Enming Yuan, Enzhe Lu, Fang Li, Flood Sung, Guangda Wei, Guokun Lai, Han Zhu, Hao Ding, Hao Hu, Hao Yang. Hao Zhang. Haoning Wu, Haotian Yao, Haoyu Lu, Heng Wang, Hongcheng Gao, Huabin Zheng. Jiaming Li, Jianlin Su, Jianzhou Wang. Jiaqi Deng, Jiezhong Qiu, Jin Xie, Jinhong Wang, Jingyuan Liu, Junjie Yan, Kun Ouyang. Liang Chen, Lin Sui, Longhui Yu, Mengfan Dong, Mengnan Dong, Nuo Xu, Pengyu Cheng, Qizheng Gu, Runjic Zhou, Shaowei Liu, Sihan Cao, Tao Yu, Tianhui Song, Tongtong Bai, Wei Song, Weiran He, Weixiao Huang. Weixin Xu, Xiaokun Yuan, Xingcheng Yao, Xingzhe Wu, Xinxing Zu, Xinyu Zhou, Xinyuan Wang, Y. Charles, Yan Zhong, Yang Li, Yangyang Hu, Yanru Chen, Yejie Wang. Yibo Liu, Yibo Miao, Yidao Qin, Yimin Chen, Yiping Bao, Yiqin Wang, Yongsheng Kang, Yuanxin Liu, Yulun Du, Yuxin Wu, Yuzhi Wang, Yuzi Yan, Zaida Zhou, Zhaowei Li, Zhejun Jiang, Zheng Zhang, Zhilin Yang. Zhiqi Huang, Zihao Huang, Zijia Zhao, Ziwei Chen, and Zongyu Lin. Kimi-vl technical report, 2025.
[64] Jiayu Wang. Yifei Ming, Zhenmei Shi, Vibhav Vineet, Xin Wang, Yixuan Li, and Neel Joshi. Is picture worth a thousand words? delving into spatial reasoning for vision language models. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors, Advances in Neural Information Processing Systems, volume 37, pages 75392- 75421. Curran Associates, Inc., 2024.
[65] Jiayu Wang. Yifei Ming, Zhenmei Shi, Vibhav Vineet, Xin Wang, Yixuan Li, and Neel Joshi. Is picture worth a thousand words? delving into spatial reasoning for vision language models. In The Thirty- Hiihtt Annual Conference on Neural Information Processing Systems, 2024.
[66] Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824-24833 2022.
[67] Jiaxin Wen, Jian Guan, Hongning Wang, Wei Wu, and Minlie Huang. Codeplan: Unlocking reasoning potential in large language models by scaling code-form planning. In The Thirteenth International Conference on Learning Representations, 2025.
[68] Tian Xie, Zitian Gao, Qingnan Ren, Haoming Luo, Yuqian Hong. Bryan Dai, Joey Zhou, Kai Qiu, Zhirong Wu, and Chong Luo. Logic-rl: Unleashing Ilm reasoning with sule-based reinforcement learning, 2025.
[69] Yutaro Yamada, Yihan Bao, Andrew K Lampinen, Jungo Kasai, and Ilker Yildirim. Evaluating spatial understanding of large language models. arXiv preprint arXiv:2310. 10. 14540, 2023.
[70] Jihan Yang, Shusheng Yang, Anjali Gupta, Rilyn Han, Li Fei-Fei, and Saining Xie. Thinking in Space: How Multimodal Large Language Models See, Remember and Recall Spaces. arXiv preprint arXiv:2412. 141771 2024.
[71] Sihan Yang. Runsen Xu, Yiman Xie, Sizhe Yang, Mo Li, Jingli Lin, Chenming Zhu, Xiaochen Chen, Haodong Duan, Xiangyu Yue, Dahua Lin, Tai Wang, and Jiangmiao Pang. Mmsi-bench: benchmark for multi-image spatial intelligence, 2025.
[72] Yi Yang, Xiaoxuan He, Hongkun Pan, Xiyan Jiang. Yan Deng, Xingtao Yang. Haoyu Lu, Dacheng Yin, Fengyun Rao, Minfeng Zhu, et al. Rl-onevision: Advancing generalized multimodal reasoning through cross-modal formalization. arXiv preprint arXiv:2503.10615 2025.
[73] Zhengyuan Yang, Linjie Li, Jianfeng Wang, Kevin Lin, Ehsan Azarnasab, Faisal Ahmed, Zicheng Liu, Ce Liu, Michael Zeng, and Lijuan Wang. Mm-react: Prompting chatgpt for multimodal reasoning and action. arXiv preprint arXiv:2303. 1381, 2023.
[74] Shunyu Yao, Jeffrey Zhao, Dian Yu, Nan Du, Izhak Shafran, Karthik R Narasimhan, and Yuan Cao. React: Synergizing reasoning and acting in language models. The Eleventh International Conference on Learning Representations, 2022.
16

---

[75] Longhui Yu, Weisen Jiang, Han Shi, YU Jincheng. Zhengying Liu, Yu Zhang, James Kwok, Zhenguo Li, Adrian Weller, and Weiyang Liu. Metamath: Bootstrap your own mathematical questions for large language models. In The Twelfth International Conference on Learning Representations, 2023.
[76] Yang Yue, Zhiqi Chen, Rui Lu, Andrew Zhao, Zhaokai Wang, Yang Yue, Shiji Song. and Gao Huang. Does reinforcement learning really incentivize reasoning capacity in Ilms beyond the base model?, 2025.
[77] Huanyu Zhang, Chengzu Li, Wenshan Wu, Shaoguang Mao, Yifan Zhang, Haochen Tian, Ivan Vulié, Zhang Zhang, Liang Wang, Tieniu Tan, and Furu Wei. Scaling and beyond: Advancing spatial reasoning in milms requires new recipes, 2025.
[78] Jiahui Zhang, Yurui Chen, Yanpeng Zhou, Yueming Xu, Ze Huang, Jilin Mei, Junhui Chen, Yu-Jie Yuan, Xinyue Cai, Guowei Huang, Xingyue Quan, Hang Xu, and Zhang. From flatland to space: Teaching vision-language models to perceive and reason in 3d, 2025.
[79] Peng Zhang, Can Li, Liang Qiao, Zhanzhan Cheng, Shiliang Pu, Yi Niu, and Fei Wu. Vsr: unified framework for document layout analysis combining vision, semanties and relations. In Document Analysis and Recognition 2021: 16th International Conference, Lausanne, Switzerland, September 5-10, 2021, Proceedings, Part I 16, pages 130. Springer, 2021.
[80] Yuanhan Zhang, Jinming Wu, Wei Li, Bo Li, Zejun Ma, Ziwei Liu, and Chunyuan Li. Video instruction tuning with synthetic data. arXiv preprint arXiv:2410.02713 2024.
[81] Zhuosheng Zhang, Aston Zhang, Mu Li, hai zhao, George Karypis, and Alex Smola. Multimodal Shain-of-thoughi reasoning in language models. Transactions on Machine Learning Research, 2024.
[82] Xueliang Zhao, Wei Wu, Jian Guan, and Lingpeng Kong. Promptcot: Synthesizing olympiad- level problems for mathematical reasoning in large language models, 2025.
[83] Chenming Zhu, Tai Wang, Wenwei Zhang, Jiangmiao Pang. and Xihui Liu. Llava-3d: A simple yet effective pathway to empowering Imms with 3d-awareness, 2025.
17

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: We clearly state its key contributions both abstract and introduction: propos- ing novel "drawing to reason in space" paradigm, developing three-stage training frame- work, and demonstrating state-of-the-ar performance across multiple spatial reasoning benchmarks. These claims are thoroughly supported by detailed methodology descriptions and comprehensive experimental results.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings. It is fine to include aspirational goals as motivation long is clear that these goals are not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
We create a separate "Limitations" section, i.e.,
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution is low or images are taken in low lighting. Or speech-to-text system might not be used reliably provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged
the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
18

---

Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
Justification:
Our paper does not introduce theoretical results.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: The paper provides comprehensive reproducibility information across all key components: (1) detailed description of the three-stage training framework with specific hyperparameters, (2) explicit formulation of reward functions and filtering criteria, (3) clear specification of dataset construction including maze generation parameters and data filtering processes, and (4) complete model architecture details based on the open-source Qwen2.5-VV VL. backbone.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is a specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make clear how reproduce that algorithm. (b) If the contribution is primarily the architecture clearly and fully.
model architecture, the paper should describe
(c) the contribution a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
19

---

(d)
We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility. In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification:
We open-source the data, code, and model, with links provided in this paper.
Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please see the NeurlPS code and data submission guidelines (https://nips.cr cc/
for more details.
While we encourage the release of code and data, we understand that this might not be possible, "No" is acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain exact command and environment needed to run to reproduce the results. See the NeurlPS code and data submission guidelines (https
/ //nips. htap:ss.ccppublicuuuuuuuo htte:/gguudeeeoeeSeuuubbiiiiaiia wst.Summmiiiooooiiooooooooo for more details.
The authors should provide instructions on data access and preparation, including how access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. If only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, to preserve anonymity, the authors should release anonymized versions (if applicable).
Providing as much information as possible in supplemental material (appended the paper) is recommended, but including URLs to data and code is permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (e.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes]
Justification: The paper provides comprehensive experimental details, including: (1) explicit dataset splits and construction process, (2) complete hyperparameters for all three training stages, (3) detailed reward function formulations and thresholds, and (4) specific model configurations based on Qwen2.5-VV VL. Key implementation choices and their rationales are discussed in the main text, with full technical details provided in the appendix.
Guidelines:
The answer NA means that the paper does not include experiments.
The experimental setting should be presented in the core of the paper to a level of detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, in appendix, or as supplemental material.
7. Experiment statistical significance
Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Question:
Answer: [Yes]
Justification: Please
20

---

Guidelines:
The answer NA means that the paper does not include experiments.
The authors should answer "Yes" if the results are accompanied by enror bars, confi- dence intervals, or statistical significance tests, least for the experiments that support the main claims of the paper.
The factors of variability that the error bars capturing should be clearly stated (for example, train/test split, initialization, random drawing of some parameter, or overall
with given experimental conditions).
The method for calculating the error bars should be explained (closed form formula, call to a library function, bootstrap, etc.)
The assumptions made should be given (e.g.. Normally distributed errors).
should be clear whether the eπror bar is the standard deviation or the standard error of the mean.
It is OK to report I-sigma error bars, but should state it. The authors should preferably report a 2-sigma error bar than state that they have 96% CI, if the hypothesis of Normality of errors is not verified.
For asymmetric distributions, the authors should be careful not show in tables figures symmetric error bars that would yield results that are out of range (c.g. negative error rates).
error bars are reported in tables or plots, The authors should explain the text how they were calculated and reference the corresponding figures or tables in the text.
8. Experiments compute resources
Question:
For each experiment, does the paper provide sufficient information on the com- puter resources (type of compute workers, memory, time of execution) needed reproduce the experiments?
Answer: [Yes]
Justification:
The paper specifies compute requirements each training stage in $4.1
Guidelines:
The answer NA means that the paper does not include experiments.
The paper should indicate the type of compute workers CPU GPU, internal cluster, or cloud provider, including relevant memory and storage.
The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.
The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't 't make it into the paper).
9. Code of ethics
Question: Does the research conducted the paper conform, in every respect, with the NeurlPS Code of Ethics httpppp///eurrpp...cpppbbb//////
Answer: [Yes]
Justification:
We have conformed the NeurIPS Code of Ethics.
Guidelines:
The answer NA means that the authors have not reviewed the NeurlPS Code of Ethics.
If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.
The authors should make sure to preserve anonymity (e.g.. there special consid- eration due to laws or regulations in their jurisdiction).
10. Broader impacts
Question: Does the paper discuss both potential positive socictal impacts and negative societal impacts of the work performed?
Answer: [Yes]
21

---

Justification:
We create separate "Broader impact" section, i.e., S
Guidelines:
The answer NA means that there is no societal impact of the work performed.
If the authors answer NA or No. they should explain why their work has no societal impact or why the paper does not address societal impact.
Examples of negatíve societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (c.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.
The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is direct path to any negative applications, the authors should point it out. For example, it is legitimate to point that improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people train models that generate Deepfakes faster.
The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.
If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition attacks, mechanisms for monitoring misuse, mechanisms to monitor how system learns from feedback over time, improving the efficiency and accessibility of ML).
11. Safeguards
Does the paper deseribe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
Question:
Answer: [Yes]
Justification:
We discuss safeguards in G
Guidelines:
The answer NA means that the paper poses such risks.
Released models that have high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model. for example by requiring that users adhere usage guidelines or restrictions to access the model or implementing safety filters.
Datasets that have been scraped from the Internet could pose safety risks. The authors should describe how they avoided releasing unsafe images.
We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make best faith effort.
12. Licenses for existing assets
Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
Answer: [Yes]
The paper properly credits all existing assets. All datasets are used within their license terms, with proper citations to original papers and links to source repositories provided in the appendix.
Justification:
Guidelines:
The answer NA means that the paper does not use existing assets.
The authors should cite the original paper that produced the code package dataset.
22

---

The authors should state which version of the asset is used and, if possible, include URL.
The name of the license (e.g., CC-BY 4.0) should be included for each asset. For scraped data from a particular source (e.g.. website), the copyright and terms of service of that souree should be provided.
assets are released, the license, copyright information, and terms use in package should be provided. For popular datasets, paperswi thcode. com/ datasets has curated licenses for some datasets. Their licensing guide can help determine the license of dataset.
For existing datasets that are re-packaged, both the original license and the license of the derived asset (if it has changed) should be provided. If this information is not available online, the authors are encouraged to reach out to the asset's s creators.
13. New assets
Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
Answer:[Yes]
The paper thoroughly documents new assets through detailed specifications of the three-stage training framework and model architecture and comprehensive documentation of our dataset construction process. We include a README document with our code the supplementary material.
Justification:
Guidelines:
The answer NA means that the paper does not release new assets.
Researchers should communicate the details of the dataset/code/model as part of their submissions via structured templates. This includes details about training, license, limitations, etc.
The paper should discuss whether and how consent obtained from people whose asset used.
At submission time, remember to anonymize your assets (if applicable). You can either create anonymized URL or include anonymized zip file.
14. Crowdsourcing and research with human subjects
Question: For crowdsourcing experiments and research with human subjects, does the paper include full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
Answer: [NA]
Justification:
We do not involve crowdsourcing nor research with human subjects.
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Including this information in the supplemental material is fine, but if the main contribu- tion of the paper involves human subjects, then as much detail as possible should be included in the main paper.
According the NeurIPS Code of Ethics, workers involved in data collection, curation, or other labor should be paid at least the minimum wage in the country of the data collector.
15. Institutional review board (IRB) approvals equivalent for research with human subjects
Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
Question:
Answer: [NA]
23

---

Our research focuses on algorithmic development and model training using existing public datasets, without involving any human subjects or crowdsoureing efforts. Therefore, IRB approval was not required for this work.
Justification:
Guidelines:
The answer NA means that the paper does not involve crowdsoureing nor research with human subjects.
Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
We recognize that the procedures for this may vary significantly between institutions and locations, and we expect authors to adhere to the NeurlPS Code of Ethics and the guidelines for their institution.
For initial submissions, do not include any information that would break anonymity (if applicable), such the institution conducting the review.
16. Declaration of LLM usage
Question: Does the paper describe the usage of LLMs if it is an important, original, or non-standard component of the core methods this research? Note that if the LLM used only for writing, editing, or formatting purposes and does not impact the core methodology, scientific rigorousness, or originality the research, declaration not required.
Answer: [Yes]
Justification: Yes, our work involves LLMs in two significant aspects: (1) we leverage Qwen2.5-VLL -V--22BB to generate initial reasoning trajectories for constructing the VILASR- ColdStart-333 -33k dataset, and (2) method builds upon and fine-tunes the Qwen2.5-VL model architecture. Both uses are explicitly documented in our methodology section, with detailed specifications of how these LLMs contribute training pipeline.
Guidelines:
The answer NA means that the core method development in this research does not involve LLMs as any important, original, non-standard components.
Please refer to our LLM policy /att:s///oarrpssccc/oofffrrreeee for what should or should not be described.
24

---

A
Appendix outline
In these supplementary materials, provide:
Dataset construction (Appendix B):
Experimental setup and full evaluation results (Appendix C
Visualization results (Appendix D
Complexity comparison between VILASR and baselines (Appendix B
Discussion on limitations (Appendix F and broader impact (Appendix of VILASR.
B Dataset construction
We created diverse datasets spanning three categories of spatial reasoning tasks: maze navigation that tests path planning abilities, static image understanding that focuses on spatial relationships, and video comprehension that captures temporal evolution and multi-view spatial reasoning. Building upon basic spatial understanding in static images through bounding box annotation and auxiliary line drawing, our video data further extends these capabilities by incorporating temporal dynamics and multi-view perspectives, leading to more comprehensive spatial reasoning abilities.
Our data collection pipeline leverages multiple public datasets, with careful balancing across different task types to ensure comprehensive coverage. This effort resulted in three primary datasets: VI- supervised dataset containing curated reasoning paths, VILASR-RRS-A specifically designed for the reflective rejection sampling stage, and VILASR-RL-400 optimized construction,
leveraged Qwen2.5-VL. 72B (2 to generate initial reasoning trajectories following our "drawing to reason in space" paradigm detailed in $3.1 A rigorous filtering process based answer correctness and format validity helped identify the most reliable samples. We applied two format criteria: (1) ensuring all drawing operations executable and the final answer can be correctly parsed, and (2) requiring at least three rounds of thinking to ensure sufficient spatial reasoning depth. After cold-start training, we constructed MILASR-RRS-A -8k by selecting instances that generated by the cold-started model and exhibit clear self-correction patterns and correct final answers, providing ideal training examples for cultivating reflective behaviors.
for reinforcement learning. For MILASR-ColdStart-33
Table 2: Dataset distribution across different training stages.
Subset (Modality)
ViL.ASR-ColdStrtt33
VILASS-RRS--L
VILASR-RI-40k
Maze Navigation (Image)
7,000
1,000
10,000
VQA (Image)
10,000
3,000
10,000
GPT4Scene [22] (Video)
6,000
2,000
10,000
SR-9Ik 48 (Video)
10,000
1,800
10,000
Total
33,000
7,800
40,000
Table 2 presents the detailed distribution of these datasets. Our source data encompasses a broad range of spatial reasoning scenarios, drawing from GQA (22). VSR (79), OpenImages (28). OpenSpaces [5] and SpaceLLaVA [5]. For maze navigation tasks, we procedurally generated mazes with varying grid sizes (from 3x3 to 6 6x6) using a depth-first search algorithm") maintaining approximately equal proportions across different grid sizes. Each maze consists a clearly marked starting point and four candidate destinations (labeled as A. B. C, and D). The questions are formulated as multiple-choice problems where the model must determine which destination would be reached by following a given action sequence (e.g., "Determine the final destination from the starting point (green point). Action Sequence: Go up. Go up ..."). This automated generation process ensures diverse maze layouts and action sequences while maintaining problem solvability, creating a controlled environment for evaluating sequential spatial reasoning capabilities.
25

---

Table 3: APIs used for proprietary models evaluation.
Model
API Name
Provider
GPT-4o
gpt-4o-2024-08-06
OpenAl
Gemini-1.5-Fiae
gemini-1.5-flan 1.5-flash
Google
Gemini-1.5-
gemini-1.5-pro
Google
Gemini-2.0-Fi
gemini-2.0-flaat
Google
OpenAI o4-mini
44-min-2025504-111
OpenAl
Table 4: Number of examples in our evaluation benchmark.
Image
Video
Multi-view
MAZE
SpatialEval-Res
VSI-Bench
SPAR-Bench
MMSI-Bench
2,000
135
5,130
7,211
1,000
C Experimental setup and full evaluation results
C.1 Baseline implementation
We evaluate VILASR against various state-of-the-art models and methods.
For closed-source LVLMs, we directly query their official APIs as shown in Table 3 We evaluate these models using zero-shot prompting by directly providing the input images and questions. Under the setting without reasoning, explicitly prompt these models to output answers directly without intermediate reasoning steps, i.e., "Answer with the option's 's letter from the given choices directly" for multiple-choice questions and "Please answer with single numerical value (e.g., 42 or 3.14)" for numerical responses.
For open-source LVLMs ranging from 7B parameters (0wen2.5-VL-77) 22. LLaVA- COE-VA-eeT-Viiiee 7B 80 72B 80 I.L. VA-One Vision-722 (30).
VneVionnn-7B (30) to 72B parameters (QWen2.5-VLL-72B 2 LLaVA-NeXT: -eX----e---- --L-V-L--BB---ttuutn Experts (MoF) architecture with 16.0B total parameters, while dynamically activating 2.8B parameters during inference. We conduct zero-shot evaluation using their standard prompting formats.
(63 leverages Mixture-of-
For specialized reasoning models, we evaluate using their officially released checkpoints and prompts: COGCOM [5I] with its built-in perception tools, VisCoT (55) with its bounding box annotation pipeline, and SpaceR 48 with its video understanding capabilities.
C.2 Benchmark statistics
Table shows the benchmark statistics.
C.3 Detailed results on VSI-Bench
Table provides detailed results on VSI-Bench. VILASR achieves state-of-the-art performance with an average accuracy of 45.4%, outperforming all baseline methods by significant margin (+12.7%) The improvements are particularly pronounced in tasks requiring precise spatial measurements and object localization: "Object Count" (+29.0%), "Absolute Distance" (+15.0%), and "Object Size" (+13.0%). This aligns with our case study observations (see (D) where VILASR demonstrates superior capabilities in systematic measurement and spatial reasoning through drawing operations.
Furthermore, the strong performance in "Relative Distance" (+16.1%) and "Relative Direction" (+20.7%) demonstrates VILASR's 's effectiveness in comparative spatial reasoning. By explicitly drawing auxiliary lines to connect and measure between objects, our model can more accurately assess relative positions and orientations. The significant improvement in "Appearance Order" (+19.8%) further highlights VILASS's s capability temporal-spatial reasoning, where systematic annotation of objects across multiple frames helps track and verify their sequential relationships.
26

---

Table 5: Results on VSI-Bench. Gray-shaded rows represent large-sized models (> parameters).
Results from 70 Results from VSI-Bench (tiny) [7]] Results from
63
Sub-tasks
Method
Numerical questions
Multiple-choice questions
Average
Object Count
Absolute Distance
Object Size
Room Size
Relative
Relative Direction
Route Plan
Apperance Order
Distance
Proprictary LVLMs
GPT-4o
46.2
5.3
43.8
38.2
37.0
41.3
31.5
28.5
34.0"
Gemini-1.5-F7an
53.5
42.17
Gemini-I P-Pro
56.2
30.9
64.1
43.6
51.3
46.3
36.0
34.6
45.41
Gemini-2.0-F 2.0Faah
52.4
30.6
66.7
31.8
56.0
46.3
24.5
55.1
45.4
Open-source LVLMs
Qwen2.5.VI. VL
34.5
19.4
47.6
40.8
32.8
24.5
32.5
29.4
32.7
LLaVA-NeXT-Videe-77
48.5
14.0
47.8
24.2
43.5
42.4
34,0
30.6
35.61
LLaVA-OneVision-72
47.7
20.2
47.4
12.3
42.5
35.2
29.4
24.4
32.41
Kini-VL-AABBnnstruce-BBB
37.4"
Qwen2,5-VL-72B
33.9
27.2
59.3
28.3
47.2
35.3
22.2
34.5
36.0
LLaVA-NecT--vdee-222
48.9
22.8
57.4
35.3
42.4
36.7
35.0
48.6
40.91
LLaVA-OnnVisionn222
43.5
23.9
57.6
37.5
42.5
39.9
32.5
44.6
40.21
Representative methods for multimodal reasoning
SpaceR-77
61.9
28.6
60.9
35.2
38.2
46.0
31.4
45.6
43.5
Ourx
VILASR Improvement
63.5
34,4
60.6
30.9
48.9
45.2
30.4
49.2
45.4
+29.0
+15.0
+13.0
-9.9
+16.1
+20.7
-2.1
+19.8
+12.7
Interestingly, while showing strong performance in most categories, VILASR exhibits slight decreases in "Room Size" (-9.9%) and "Route Plan" (-2.1%). This suggests a limitation tasks requiring holistic reasoning: "Room Size" estimation demands understanding the complete room layout from partial views and reasoning about unseen spaces, while "Route Plan" needs global path planning across multiple viewpoints. Unlike localized spatial measurements that can be solved through explicit drawing operations, these tasks require more sophisticated global inference capabilities to integrate information across different views and time points. This reveals potential directions for extending drawing-baan framework: we could introduce specialized drawing tools for layout reconstruction and space completion. Such extensions would be natural additions to our current drawing operation set, enabling more comprehensive spatial reasoning capabilities.
C.4 Statistical significance analysis
We conduct rigorous statistical significance t-tests, we find that VILASR significantly outperforms the base model (Qwen2.5-VL-7) VL-7BB on MAZE, SpatialEval-Ress VSI-Bench, SPAR-Bas Bench and MMSI-Bench (p < 0.05). These results demonstrate the robust and consistent advantages of our approach across different spatial reasoning scenarios.
validate our experimental results. Using paired
C.5 Prompt template
In this section, we present the comprehensive prompt templates utilized in VILASR, including both the system prompt and user prompt, as illustrated in Figure and Figure respectively. We use these prompt templates for both generating reasoning paths cold start data and inference of VILASR.
C.6 System prompt of VILASR
The system prompt utilized in the VILASR reasoning framework is presented in Figure
C.7
Query prompt template of VILASR
The query prompt utilized in the VILASSR reasoning framework presented in Figure framework utilizes three distinct types of prompts throughout the reasoning process:
Our
27

---

System prompt
Guidance:
You spotial ressaning aesistant with powerful visualization
Your task to break down complex spatial problems and deeratively refine your solution through visualization feedback.
Available tools:
You the following tools visualize. After each usage, you wait for and unalyze the visulization feedback before procoeding.
"*Object Mapper**
Purpose: Identifies and maps key in space
Inpur formar: JSON
""json
[E] "index": i. Image index
"bhox 2d':: (xl,, yl, x2, "label": "object namo namo/leacripioonn H1]
Ouiput: Generates bounding boxcs for visual inspection of the i-th image
**Puth Tracer**
Purpose: Plots movement connections hetween points
.Inpu format: ISON
""json
[t[
"index": f. Image index
"start point 28%: [xl.
"end point 2d" [x2, y2]. "label": "trace description" H]]
Output: Generates paths verification of image
AHW Required Output Format:
ressoning step, you must structure your response
<think> detailed reasoning process] <ithink> Action: [Object Mapper/Path Tracer] ""json
(SSON format coordinates]
After your reasoning and Herrtivvly refine your solution through visualization feedhack, you should arrive final answer and structure your response as follows:
<think> YYou cassoming process] sithink>
<answer> (Your final answer] <tanswer>
following reasoning techniques:
Initial Analysis
Break down the spatial problem
Plan your approach
Reasoning
Stop
Choose appropriate tool
Provide absolutc coordinates JSON format (The top-left cornrr of the image (0, U) and the botton-right corner is [width), (height))
oulput
Reflect visualization:
Is the placement/pall (ath accurate?
Does it align with your rensoning?
adjustments nceded?
Backtmak and Adjust:
If crroes found, backtrack to previous step modify actions decisious as needed
Figure 6: System prompt used in VILASR.
Initial Query Prompt (Image/Video Query Prompt): Initiates the reasoning process by establishing the initial visual context and query.
Follow-up Query Prompt: Guides subsequent reasoning steps by incorporating intermedi- ate results and accumulated context.
Final Answer Prompt: Terminates the reasoning process and enforces answer generation
when either the maximum number of processed images or reasoning steps is reached.
28

---

Video Query Prompt
The index of the given image (width: [width), height: (height)).
of the given image is (number frames) (width: [width), height: [height)).
These are frames from video, numbered from to fuumber frames] in sequence. That index each image is
3, [number frames].
Answer the question with appropriate tools: (Question]
[Output Template)
Begin your reasoning. After each tool use, critically evaluate visualization and adjust nceded:
Image Query Prompt
[Question]
The index given image I.
[Output Template]
Begin your reasoning. After each tool use, critically evaluate the visualization and adjust if needed:
Follow-up Query Prompt
The index of the given image (current image idx3 (width: (width). height: (height)). Continue your reasoning. After each tool critically evaluate the visualization and adjust if needed:
Termination Prompt
The index of the given image (eurrent image idx] (width: (width). height: (height)). Then, you can not invoke the Object Mapper Path Tracer tool. Please answer the initial question and structure your response as required:
Output Template
"Multiple Choice": Answer with the option's letter from the given choices directly. "Numericul": Please the question using single numerical value. "Regression", Please answer question using single numerical value.
Figure Query prompt and output template used in VILASR.
D Visualization results
To illustrate the effectiveness of our approach, we present three representative examples from the MAZE, SPAR-Benche and VSI-Bench benchmarks in Figures 8 9 and 10 respectively. Note that the "Path Tracer" tool refers to drawing auxiliary lines, and the "Object Mapper" tool refers to annotating bounding boxes.
In the maze navigation task (Figure 8). while Qwen2.5- VL-7BB provides incorrect answers directly and GPT-4o attempts textual reasoning but fails accurately track spatial transitions, VILASR successfully decomposes the task into interpretable steps. By using the "Path Tracer" tool to visualize and verify each movement through auxiliary lines, our model ensures accurate navigation through the maze, leading to the correct destination.
For multi-view reasoning (Figure 9. VILASR demonstrates sophisticated spatial understanding by first mapping key objects ("window," "air conditioner") in both images using "Object Mapper", then systematically analyzing their relative positions. Through careful verification using "Path Tracer," correctly determines the observer's position change, while both baseline models struggle with perspective transformations and make incorrect judgments about movement direction.

---

Task: Maze Navigation Simalation
Daterming the final destination (A, H, from the starinng (green pain) following the actice sequence. definitions actions below.
Go dpweel-dwwaiight muve one grid space in absolute up/lef//dww/rigg direction.
Full Action Sequence: Go nihtt Go up. Go left Go Go right. Go Go left. Go Go left. Gi left. Go dowa, Gn left. Go
Qwen2.5-VL-7B. B X
GPT-4o (w/ reasoning): <think> Start the green point. right. (Move the column
up.
starting point) (Move into the column up. (Move top row within column B) right. (Move back into column open path above D)Following path, the destination <ithink>
(Move the row directly
up. (Exxi maze through
<answer-D<<answer
cahinAc: To solve this, I'll follow the action soquencz stop-hy-sopp from the starting point (grzen pount)
wthink> The first action (o right!" has heen successfully executed, na shown in lisurlization,
Schlok> The thirceathh "Go upl" as visialization. The path has reached the top- left curner, which curoeponds destination sequence is complete. and the final destiration has been reaclied Therefore, the final answer is sikiikk> Action: Sanawers Kimnsress
successfully
Puth Tracer rool to visuelire each move. This will help confirmm the final right. the puth from the starting point upwards.
aequenee is Vio up 1" To visunlize this I will the Path Tracer tool platting movement posiitio (end of the first action) upwards. Eitkinks Action: Path Tracer.
destination.
sabinsk Action: Path Tracer...
VILASR:
Figure A visualization example of spatial reasoning approaches on the Maze benchmark, including Qwen-2.5-VL-77, GPT-4o, and VILASR.
In the video spatial reasoning task (Figure TOp. VILASR exhibits strong reflection capability and systematic problem-solving. When initial attempts locate and measure the telephone in images 5 and 12 fail, it self-corrects and identifies the correct object in image 13. Furthermore, it shows sophisticated measurement strategy by using reference objects ("monitor," "heaphonees""" establish scale and convert pixel measurements to centimeters. In contrast, baseline models either fail to locate the target object (Qwen2.5-VL-7B) or make rough estimations without proper measurement (GPT-4o).
These cases illustrate how drawing operations enable reliable spatial reasoning grounding abstract relationships in concrete visual representations.
E
Complexity analysis
To thoroughly assess the computational efficiency of VILASR, we present a comprehensive analysis comparing approach with the base model Qwen2.5- model. This analysis encompasses both theoretical complexity bounds and empirical resource utilization, providing insights into the framework's 's scalability and computational characteristics.
E.1 Theoretical time complexity
We analyze the computational complexity across three model variants: the base model (performing direct answer generation), standard reasoning models (generating reasoning chains followed by answer derivation), and our VILASR model (employing iterative visual drawing and thinking). Let M denote the input length (including both image and text tokens), N the answer length, L. the per-step reasoning path length, and S the number of reasoning steps, where = for both base model and standard reasoning approaches. Empirically, VILASR achieves shorter per-step reasoning
30

---

Identify the observer's position in the second imuge relative to the first image. Provide (X. Y) the image plane and depth in meters.
Choose the right answer from the options available.
A. Image Coor: (169. 51), Depth:1.7 moters
Image Coor: (896, 929), Depth meters
Image Coar: (136, 454), 1.pth: meters
Image Coor: (200, 576), Depth: 1.4 meters
Qmen2.5-VL-7::
X
GPT-4o (w/ reasoning): Shink-To To assess the observer's position relative finst image, images. the finst image, we see the bed, redistor cover, and air conditioner from more frontal view, indicating slightly greater distance from the objects. In the second image, the angle side-oriented and much closer to the air conditioner and tissue box, suggesting the observer moved the right and depth observation with given opions, the coerdinates that and lateral movemeni. Option D provides the cvordimates (200, 576) and depth 1.4 meters, aligning with a closer and side-oriented position, sitink? -answerD Image Coc0 576). Depth:144 mansrs/nnswer
analyze the changes perspective between
conditionr.. Comparing
are those that suggest prosimity
Sabloks:
To detennine the observer's pasition in the secoed image relative to the first image, I need to esmalish the observer's perspective
relative positions inferred by looking the relative posilions of the objects and the penspctivv from which the images were taken, winnee'' start by identifying the objects and their relarive positions map the key objects in first image/ nAction: Object Mapperin" "joot'a[( ("index": 1,1 \'boxx 20t": [172, 32, 312, 96),n ("label." "window""sl] Jun
objects
two images. observer's position can
Object Mapger tool/ I'll
Sokinks The window and the air conditioner are correctly identified in the first image. Now, let's map the window conditioner in second image understand the relative position. in5thiikss eAction: Object Mopper'n" "psonin| ('m l"index"" 2/ l'bbox, 2dl": [0,0 0, 252, 108),in ('Ibbll"" "windowi""n]Jee Jin"
Kohinko The window and the air conditioner are correctly identiffed in the second image. Now, let's use the Path Tracer tool to tnace the relutive position of the observer. The observer likely standing fromt of the window the second image. withiink inAciio: Path Thacarlys "jscetaal ('v ("indes 1/m lstarii point 2d" [230, 40)/n l'end point 20:" (100, 1400 ""aabll": ("oburrvrr' puthi" "mn"
image, looking towards the conditioner
The path tracer shows the relative position of the observer inial re-evaluate the observer's position using the relative positions of the objects in the images. The observer likely standing in front the window the first image, looking towards the air cunditioncr the second image. The correct relative position is likely around the coordinatos (169, 51) in the image plane and a depch of 1.7 meturs levikkink 'ncciio:: Answer Allawwer
Sabinks
VILASR: A
Figure 9: A visualization example of spatial reasoning approaches on the SPAR-Bench benchmark, including Qwen-2.5-VL-77, GPT-4o, and VILASR.
Table 6: Complexity analysis of different reasoning approaches.
Model Type
Input Length
Output Length
Time Complexity
Base Model
M
N
O(M -N) O(M (I+ N))
Standard Reasoning
M
L N
O(S L. (L+M)
VILASR (Ours)
M E Mj S L
+S. (L)M(LL
paths (smaller T.) compared to single-step approaches due to its decomposition of reasoning into interpretable visual operations. Ta a comparative analysis of their time complexities.
The total computational complexity is:
5-1
k-1
S-1
T
Σ
[M +
Σ (L++ M,) La] + (M +
Σ (L. + M)) (Us+N).
(9)
31

---

length longest dimension (leygh,, width, height) the telephone, messured cemimeters"
Qwen2.5-V1-7R: The relephone is not viaible in any of the provided images. Therefore, it's not possible to determine its dimensions.
X
GPT-4o reasonlugi: TT desermine the length of loegest dimension of telephonne, need locate telephone the images provided. However, hased the images presented, challenging to identily talephone because photos feature office desks, computeer,, and shelving, there's no clear image a telephone. Typically, landline telephones don't exceed a length of 25 em, but without seeing in these pictures, can't
definitively detenmine longest dimension Since telephones generally their longest dimension as kngth, estimate, <ithink> canewer-estimatee about 20 cn-lanswer>
X
Sahines: determine longest dimensioon of the tolephone, we need visualize telephone in the images and messure its dimensions using the Puth Tracer tool. The relephone is most likely present images 12, and 13, We telephone
elearyy visible and use dimensions, lelnd et' start by idewtifynng the relephone in image 5 and messuring its dimensions V-Stiinke inAction: Object Mapger'n" "json'ul "index"" 5, ''hoox 2d": (282, 282, 378, 328).n "label": ("Ielehhong" "n]
image
tool measure
Kthinke The telephone is not correctlly identified in image The telephone is likely present images 12 and 13. Let's use image 12 to Identity the relephone and measure its dimensions using the Puth Tracer tool, wsakiins 'nAction: Object Mapper'n "jsoola[ ('n Vindex"": l'bbox, 2d:: (22, 282, 112. 328].n Wlabell:: "telephone""" "a]]""
telephone correctly identified image telephone likelly present
use image 13 to identify the telephone and measure dimensions using the Path Tracer tool lithiink nAction: Object Mapporin "joonini ""inde""" 13/n '"boox 2d': 276, 170, 300), '"lbell" ( "telephonn"" "nn
Sahinks The telephone correctly idemified in 13. Now, Puth Tracer tool to the longest dinnension the telephune. We will trace the longest visible side of the telephone in the image iniiiiinke nAstio:: Parh Tracarin" jsownn| ('n ""idex"": 13,0 ('stort point 241 [120, 276],n l'end point 20:": (170, 300).nn "label" MMonggst dimenelon telephone! "ut]j""
Sthinic The path tracer tool shows the longest dimension of the telephone, but the mewarement not centimeters, We need to convert the pixel measurement into centimeters using reference object the messure longest dimension in centimeters. intikinne nnction: Pach Trace''n json'n( ('n ""index"" 13/ua ('strt point 2dit: (250, 168). (end point 2dh: [420, 168) ""label"" loogest dimension the monitor!"
Image, winle''s
monitur
same image estimate the
Kohink> The path tracer tool shoms the longest dimension of monitor, but need the dimeusion of the telephune in centimeters, We should we a reference object with known size the image to estimate the scale, in minLet et's use the headphones in the image mensure the langest dimension the telephone centimeters. wntthtt "essttttt="aAAtiinn nAction:: Path Tracernn" jsoniin V"index": 13/n 'sstrr point 2d" (28. 29 fend read_point__e_e point_2d": [105, 292].z l'labell: (flongest dimension of the headphonesi un]
reforence object with known size estimate the scale
<think- The path tracer tool shows the longest dimension of the hendphunes, but need the longest dimension of the telephome in contimeters, should use the headphones as a refurence ebject with known size estimate the seale wusThe longest dimension of the telephone, messured using the Path Thacer tool and the osimaled scale
headphumes, approcimately 35 centimeters: insikinne nnction:
VILASR:
Figure 10: A visualization example of spatial reasoning approaches on the VSI-Bench benchmark. including Qwen-2.5-VL-77 GPT-4o, and VILASR. We highlight the generated words of VILASR that exhibit reflection behavior in bold.
32

---

Table 7: Average runtime comparison in seconds per sample (VILASR vs. backbone) across different benchmarks.
Average Runtime (s/sample)
Method
Maze
EmbSpatial
VSI-Bench
Qwen2.5-VL-77 (COT)
1.0
0.9
1.9
VILASR
4.4
1.2
7.8
where La is the length of the reasoning path generated at step k, and M2 is the additional multimodal context incorporated at step k:
Assuming each reasoning step has approximately equal length, i.e., L, R L, Mr ~ M for all i, we
can approximate:
T= L. (L L.
+ (L+ (Z
(10)
E.2 Practical runtime
To provide empirical evidence for our complexity analysis, we evaluate the runtime performance of VILASR and compare it against the backbone model, Qwen2.5-VL-7B (CoT), across various benchmarks. Table Filuutriilsssratess the average runtime time per sample.
Limitations
While our work demonstrates promising results in spatial reasoning tasks, several limitations warrant discussion:
First, our training framework primarily focuses on multiple-choice and numerical questions due to their amenability automated evaluation, excluding more complex spatial reasoning scenarios that require free-form textual descriptions (e.g., detailed motion trajectory analysis). This limitation constrains the model's ability handle open-ended spatial reasoning tasks.
Second, a potential risk our reinforcement learning stage the coupling between the reward function and the final evaluation metrics. Since reward is directly tied to achieving the correct final answer on specific benchmarks, the model might learn to exploit dataset-specific shortcuts to maximize its reward, rather than developing truly generalizable spatial reasoning ability. This a common challenge in reward-based optimization that warrants further investigation into more process-oriented reward schemes.
Third, the effectiveness of our drawing operations inherently limited by the 2D nature of the visual interface. Complex 3D spatial relationships and viewpoint changes, which are common in real- world scenarios, may not be adequately captured by our current drawing primitives. This limitation particularly affects the model's performance on tasks involving 3D object relationships or dynamic camera movements.
Finally, the computational cost of our three-stage training pipeline, especially during the reinforcement learning stage, may limit its accessibility to researchers with limited computational resources.
G Broader impact
Our work on enhancing spatial reasoning capabilities in vision-language models has both positive and potential negative societal implications that warrant careful consideration.
the positive side, improved spatial reasoning capabilities could significantly benefit various applications in robotics, autonomous navigation, and assistive technologies. For instance, more accurate spatial understanding could help robots better navigate complex environments and assist people with visual impairments in daily tasks. In educational settings, these models could provide
33

---

interactive tools for teaching spatial concepts and geometric reasoning, Additionally, the interpretable nature of our drawing-buse based reasoning approach enhances model transparency, potentially increasing trust and adoption in critical applications.
However, several potential negative impacts need to be addressed. First, the enhanced spatial reasoning capabilities could be misused for surveillance purposes, enabling more sophisticated tracking and monitoring systems that could infringe on privacy rights. Second, there might be accessibility issues as the drawing-based reasoning approach assumes users have access to and can interact with visual interfaces, potentially excluding certain user groups.
To mitigate these concerns, we recommend: (1) implementing strict usage guidelines and access controls when deploying these models in sensitive applications, (2) exploring alternative interaction modalities to make the technology more accessible. We also encourage future research to focus on developing privacy-preserving spatial reasoning techniques.
To ensure responsible deployment of our technology, we have implemented several safeguards in our release. First, our model access will be gated through an API that requires user agreement to usage guidelines, specifically prohibiting applications in surveillance or privacy-invasive systems. Second, we provide detailed documentation about the model'' capabilities and limitations, along with best practices for responsible implementation in different application scenarios.
34


Reviews:
[{"review_id": "e2SP5a59KE", "reviewer": "Reviewer_Ve3P", "summary": "The paper introduces SPARK, a LVLM that doing multimodal reasoning via interleaved text reasoning and visual drawing. There are two drawing operations, drawing bounding boxes and auxiliary lines, on images and videos. The training recipe includes three stages: (1) cold-start SFT (2) reflective rejection sampling (3) RL. The model, which is fine-tuned over Qwen-2.5 VL, outperform the original model by an average of 11.5%. Ablation shows the effectiveness of each approach.", "questions": "1. The model is getting big improvements on MAZE, but relatively small gains on some other tasks. Can you give more insights on that? What new tools/training strategies do we need to make the approach more effective on these other tasks?\n\n2. As I mentioned in the weaknesses, it would be good to include ablation on each training stage", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n1. The motivation is clear, and the method is reasonable.\n2. The approach effectively gives LVLM the ability to reason with interleaved reasoning trajectories.\n3. Extensive experiments on diverse image and video tasks.\n\nWeaknesses:\n1. More analysis on the inference-time scaling would be helpful. The author only shows the difference of pass@1 and pass@8. However, a more interesting dimension is the number of tokens the model uses to answer the question. It would be great to include, for example, the number of tokens and the number of tool calls during the process of reinforcement learning.\n2. More analysis on the effectiveness of each training stage would be useful. What if we remove one of the stages? How would that affect the final performance?", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable reviews. We provide detailed responses to your questions:\n\n>[W1] More analysis on the inference-time scaling would be helpful. The author only shows the difference of pass@1 and pass@8. However, a more interesting dimension is the number of tokens the model uses to answer the question. It would be great to include, for example, the number of tokens and the number of tool calls during the process of reinforcement learning.\n\nWe appreciate the suggestion to analyze inference-time behavior beyond just pass@k. In response, we provide detailed statistics on the model’s response length and the number of tool calls throughout reinforcement learning (RL) training, as summarized below.\n\nHere, _response length_ refers to the total number of tokens generated **after receiving the input query**, including all model-generated tokens, image tokens used during reasoning, and template tokens.\n\n| **Step** | **Response Length** | **# Tool Calls** |\n|------|------------------|---------------|\n| 0    | 2449.05          | 5.127         |\n| 50   | 2332.45          | 5.114         |\n| 100  | 2292.01          | 5.138         |\n| 150  | 2386.39          | 4.505         |\n| 200  | 2103.77          | 4.916         |\n| 250  | 2083.14          | 4.858         |\n| 300  | 1966.65          | 4.785         |\n\nAs observed, the average response length gradually decreases over the course of RL training, while the number of tool calls first drops significantly and then stabilizes. This suggests that the RL phase helps the model learn to reason more efficiently and use drawing operations more selectively. We attribute this improvement to the fact that the SFT (supervised fine-tuning) phase tends to produce overly verbose or redundant reasoning paths, which RL helps refine.\n\nFurthermore, we analyze different ablations of SPARK on the VSIbench dataset, comparing the average response length and number of tool calls:\n\n| Model                  | Response Length | # Tool Calls |\n|------------------------|------------------|---------------|\n| SPARK                  | 2233.98          | 4.503         |\n| SPARK w/o Stage 3      | 2948.82          | 5.213         |\n| SPARK w/o Stage 2      | 2125.53          | 3.829         |\n| SPARK w/o Stage 2 & 3  | 2834.07          | 5.266         |\n\nCompared to the variants without Stage 3 (RL), SPARK significantly reduces both response length and the number of tool calls, indicating that RL fine-tuning improves the efficiency of reasoning and drawing. \n\nNotably, SPARK w/o Stage 2 (i.e., without the reflective rejection sampling stage) shows a lower number of tool calls than the full model. Our manual inspection found that this variant tends to shortcut reasoning by making quick spatial judgments using auxiliary lines without sufficient self-verification. This highlights the importance of the reflective phase in encouraging deliberate and robust reasoning behaviors. We will add the analysis above in our revision.\n\n>[W2] More analysis on the effectiveness of each training stage would be useful. What if we remove one of the stages? How would that affect the final performance? [Q2] As I mentioned in the weaknesses, it would be good to include ablation on each training stage\n\nThank you for pointing this out. We have included a comprehensive ablation study to evaluate the contribution of each training stage in the submitted version. The results are presented in Table 1 and discussed in Section 4.3 of the current submission, covering the following configurations:\n\n-   w/o Stage 3 (without RL stage)\n-   w/o Stage 2 (without reflective rejection sampling stage)\n-   w/o Stage 2 & 3 (without reflective rejection sampling stage and rl stage)\n-   w/o Stage 1, 2 & 3 (without training)\n\nOur key findings are summarized below:\n\n1. **Stage 1 – Cold-Start Training:**  \nCold-start training establishes a crucial foundation for spatial reasoning, with significant performance gaps observed when omitted, especially on tasks requiring sophisticated reasoning beyond basic spatial relations.\n\n2. **Stage 2 – Reflective Rejection Sampling:**  \nReflection sampling is key to the model's self-correction ability, enhancing its overall reasoning capacity by refining the inference process through reflective rejection mechanisms.\n\n3. **Stage 3 – Reinforcement Learning with Dense Rewards:**  \nReinforcement learning with dense rewards enhances performance and optimizes the decision-making process. Additionally, the use of dense rewards allows for more fine-grained feedback in numerical prediction problems, offering greater improvement on numerical prediction tasks.\n\nThese results validate the necessity of each training stage and highlight their complementary roles in achieving strong overall performance.\n\n\n> [Q1] The model is getting big improvements on MAZE, but relatively small gains on some other tasks. Can you give more insights on that? What new tools/training strategies do we need to make the approach more effective on these other tasks?\n\nThis is an important observation. We attribute the performance gap primarily to differences in task diversity and complexity. The MAZE task is relatively constrained, taking place in a synthetic environment with limited spatial operations (e.g., directional movement) and a relatively small maze size. In contrast, other tasks demand more sophisticated real-world spatial understanding, involving reasoning over varied spatial relations and transformations.\n\nFor instance, VSIbench includes tasks such as object counting, absolute and relative distance estimation, object and room size comparisons, route planning, and appearance order reasoning — all of which introduce significantly higher complexity.\n\nTo enhance performance in these more challenging tasks, we believe several directions are promising:\n\n-   **Spatial pretraining**, to strengthen the model’s foundational understanding of spatial structures and relationships.\n-   **2D/3D reconstruction training**, to enabe the model to develop a genuine understanding of spatial structures by learning to describe and reconstruct 2D or 3D scenes during training.\n-   **Multi-view selection and joint encoding**, to prioritize informative viewpoints and effectively capture spatial relations across diverse perspectives."}, {"review_id": "XXTOcnNu77", "reviewer": "Reviewer_H5eA", "summary": "This paper introduces the SPARK framework, a vision language model that can draw to reason in space. The proposed SPARK has basic drawing operations like annotating bounding boxes and drawing auxiliary lines. Trained with a three-stage paradigm: cold start, reflective rejection sampling, and GRPO-like RL, the model can acquire capabilties to perform spatial reasoning tasks.\n\nEvaluated on multiple spatial reasoning benchmarks spanning maze navigation, static spatial reasoning, video-based temporal tracking, and multi-view scene understanding, the model achieved good performance compared to base VL models.", "questions": "re weaknesses: What if you only perform query-answer (as in standard VQA) fine-tuning? Does the drawing really improve the performance? How does this compare to visual programming-like approaches for solving spatial relationship tasks [A, B]?", "limitations": "yes", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 1, "originality": 2, "strengths_and_weaknesses": "#### Strengths:\n\n- The paper is well-written, and the idea of drawing facilitates visual reasoning is intriguing. This paper successfully makes some good attempts at letting large language models draw auxiliary lines in visual space to help their reasoning. \n\n- The three-stage paradigm is up-to-date with contemporary advances in RL for LLM reasoning. It's good to see that it can be scaled to more operators.\n\n#### Weaknesses:\n\n- The drawing concept is a bit bluffing. Here, the drawing defined in this paper is merely bounding boxes and simple lines -- which have limited usage cases beyond simple spatial reasoning.\n\n- Lacking baseline comparisons for spatial reasoning involving tool use: how does this compare to visual programming-like approaches for solving spatial relationship tasks [A, B]?\n\n- Ablations: It seems that stage 1 is the most important stage. I suspect that the first step is more like some fine-tuning on the spatial reasoning tasks, making it unfair to compare to other base VL models. What if you only perform query-answer (as in standard VQA) fine-tuning? Does the drawing really improve the performance?\n\nref:\n\n[A]. Gupta, T., & Kembhavi, A. (2023). Visual programming: Compositional visual reasoning without training. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (pp. 14953-14962).\n\n[B]. Surís, D., Menon, S., & Vondrick, C. (2023). Vipergpt: Visual inference via python execution for reasoning. In Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 11888-11898).", "was_revised": true, "final_justification": "After reading the authors' response, I have decided to increase my score by one.", "rebuttal": "Thank you for your valuable reviews. We first address Weakness 2 and Weakness 3, and then respond to Weakness 1. Below are our detailed responses:\n\n> [W2] Lacking baseline comparisons for spatial reasoning involving tool use: how does this compare to visual programming-like approaches for solving spatial relationship tasks [A, B]?\n\nWe appreciate this suggestion. We have incorporated the two recommended baselines — **VisProg** and **ViperGPT** — into our experiments. The results are summarized below:\n\n| Method     | Maze | SpatialEval | EmbSpatial | VSIbench | Spar-Bench |\n|------------|------|-------------|------------|----------|------------|\n| VisProg    | 22.6   |     18.0    |  13.5    |    -     |    -       |\n| ViperGPT   |  27.3   |    34.1        |    39.0       |    10.6    |    23.7      |\n| SPARK      | 89.0 | 63.4        | 64.9       | 42.9     | 34.9       |\n\nNote: VisProg does not support multi-image inputs, making it inapplicable to video-based (VSIbench) and multi-view (Spar-Bench) tasks.\n\nAs shown, SPARK achieves significantly stronger and more stable results across benchmarks compared with VisProg and ViperGPT. Furthermore, during our reimplementation of **VisProg** and **ViperGPT**, we observed their following limitations:\n\n-   **Dependency on Black-box Perception Tools:** VisProg and ViperGPT rely heavily on black-box perception modules (e.g., object detection and localization systems), whose capabilities are fixed and cannot be optimized through end-to-end training. These predefined tools not only limit the system's ability to handle complex spatial relationships, but also lead to fragmented reasoning processes through disconnected tool invocations.\n-   **Limited Robustness and Generalization**: Both methods exhibit significant brittleness in handling complex scenarios:\n\n\t- **Heavy reliance on carefully crafted prompts**, leading to format errors and unexecutable programs when facing unseen tasks, especially in tasks like **MAZE**, which demand multi-step planning and reasoning. Many samples failed due to parsing or planning issues.\n\t-   **The tendency to fall back to simple VQA tool calls** even for complex questions and **confusion with basic spatial relationships** (e.g., above-behind vs. below-in front), aligning with the observation of recent research [1].\n\n\nIn contrast, SPARK provides several key advantages:\n\n1.  **Direct Visual Manipulation**: Through elementary drawing operations, SPARK avoids the limitations of black-box perception tools, enabling more trainable and interpretable spatial reasoning.\n2.  **Coherent Reasoning Process**: Our approach allows for coherent reasoning processes that can be iteratively refined through self-reflection and effectively optimized through RL.\n3.  **General and Extensible Framework**: While our current implementation focuses on basic drawing operations, the framework is readily extensible to incorporate additional visual operations for different types of spatial reasoning tasks. This flexibility is evidenced by our strong performance across diverse tasks, from single-image spatial relationship understanding to complex video-based reasoning.\n\nWe will incorporate these comparisons and a more detailed discussion into the revised manuscript.\n\n[1] Visual Agentic AI for Spatial Reasoning with a Dynamic API. CVPR 2025\n\n> [W3] Ablations: It seems that stage 1 is the most important stage. I suspect that the first step is more like some fine-tuning on the spatial reasoning tasks, making it unfair to compare to other base VL models. What if you only perform query-answer (as in standard VQA) fine-tuning? Does the drawing really improve the performance?\n\nWe appreciate the reviewer’s insightful question. To address this concern, we conducted a controlled ablation study in which we fine-tuned the same base model using only question-answer pairs, without any intermediate reasoning supervision—constructing a standard VQA-style fine-tuning pipeline. The results are shown below:\n\n| Method               | Maze | SpatialEval | EmbSpatial | VSIbench | Spar-Bench |\n|----------------------|------|-------------|------------|----------|------------|\n| Qwen2.5-VL-7B+ SFT     | 73.8 | 60.4        | 61.3       | 39.1     | 33.7       |\n| SPARK                | 89.0 | 63.4        | 64.9       | 42.9     | 34.9       |\n\nThese results clearly show that incorporating the \"drawing to reason in space\" paradigm leads to substantial improvements across all benchmarks, particularly on tasks like Maze and VSIbench, which demand explicit modeling of spatial layout and sequential planning. \n\nThese results demonstrate that **drawing operations play a crucial role in spatial reasoning beyond what can be achieved through standard fine-tuning**. While both approaches were trained on the same dataset, SPARK's ability to dynamically introduce novel spatial relationships through drawing operations leads to substantial improvements. This validates our core thesis that effective spatial reasoning requires direct visual manipulation rather than purely textual reasoning.  \nWe will include the comparison in our revised revision.\n\n> [W1] The drawing concept is a bit bluffing. Here, the drawing defined in this paper is merely bounding boxes and simple lines -- which have limited usage cases beyond simple spatial reasoning.\n\nWe appreciate the reviewer's thoughtful comment. We would like to clarify several important points:\n\n-   **Operation Choice:** The basic operations (frame selection, bounding boxes, and auxiliary lines) are an intentional design choice that prioritizes interpretability and controllability while maintaining sufficient expressiveness for spatial reasoning. The visual drawing elements are extensively present in pre-training data of LVLMs, making them natural building blocks for enhancing spatial understanding. The simplicity and familiarity of these operations enable the model to focus on the core task of spatial reasoning without being distracted by complex visual manipulations.\n-   **Demonstrated Effectiveness:** Our experimental results show that these elementary operations, when strategically combined, serve as a powerful mechanism for complex spatial reasoning. SPARK achieves significant improvements across diverse challenging tasks, from maze navigation to video-based spatial relationship tracking, demonstrating that simple operations can effectively capture sophisticated spatial relationships.\n-   **Advantages Over Existing Approaches:** Current approaches to multimodal reasoning broadly fall into two categories, each with significant limitations:\n\n\t-   **Text-centric reasoning and reasoning-free approaches:** While these approaches excel at basic visual tasks, they merely add multimodal input to traditional language model reasoning. This approach assumes visual information can be perfectly translated into textual space. However, **converting visual information to text inevitably loses critical spatial details and makes it prohibitively difficult to track dynamic spatial relationships**.\n\t-   **Tool-based reasoning approaches:** These works like VisProg and ViperGPT attempt to enable vision-centric reasoning through external tools. However, they are limited by: (1) Dependency on black-box perception tools, resulting in **fixed perception capabilities and fragmented reasoning processes**; (2) **Limited ability for deep reasoning with reflection on tool outputs** due to their reliance on prompting engineering. In contrast, SPARK's drawing-based reasoning provides a more flexible and intrinsic approach to spatial understanding. leading to significant improvements over VisProg, ViperGPT, and standard VQA training as shown in the results above. \n-   **Future Extensibility:** While our current implementation focuses on two fundamental operations, this work represents an innovative first step towards vision-centric reasoning. The framework is readily extensible to incorporate additional drawing operations based on specific task requirements, while maintaining the benefits of interpretability and direct visual manipulation.\n\nOur results demonstrate that these basic operations, when properly integrated into a learning framework, can achieve sophisticated spatial reasoning capabilities while maintaining simplicity and interpretability."}, {"review_id": "ctsfYXhcP2", "reviewer": "Reviewer_nXQB", "summary": "This paper introduces SPARK to enhance the spatial reasoning capabilities of LVLMs. Moving beyond the direct application of text-based reasoning to visual tasks, SPARK proposes a \"drawing to reason in space\" paradigm. By employing tools in a manner analogous to LLM agents, SPARK generates visual and textual reasoning paths. The progressive three-stage training framework—comprising cold-start training, reflective rejection sampling, and reinforcement learning—enables substantial performance improvements across multiple spatial reasoning benchmarks.", "questions": "- Q1. The Reasoning Process: Are the reasoning steps generated autonomously by the model? If so, what termination conditions are in place to prevent infinite or non-productive reasoning loops?\n- Q2. The Attribution of Performance Gains: Given that SPARK was fine-tuned on specialized data while the baselines were not, how can the performance gains be attributed specifically to the \"drawing to reason\" paradigm versus the data advantage? Can the ablation study be used to help disentangle these two factors?\n- Q3. The Cost-Benefit of the Iterative Method: Considering the high computational cost of SPARK's iterative process, what are its specific advantages over simpler strategies that also use a larger compute budget (e.g., textual self-correction, sample-and-vote)? What justifies the added complexity of the visual iteration mechanism?\n- Q4. Code and Data Reproducibility: The paper's checklist states that code and data are in the supplementary material, but they could not be located. Could the authors please clarify the access method to ensure reproducibility?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n- S1. Paradigm Innovation: The paper's \"drawing to reason in space\" paradigm innovates upon previous methods that apply text-centric reasoning to visual tasks by empowering the model to reason through direct drawing operations in the visual space.\n- S2. High Interpretability: The method generates a \"visual chain of thought,\" presenting the reasoning process as a transparent sequence of interleaved images and text. This significantly enhances interpretability and trustworthiness.\n\nWeaknesses\n- W1. Limited Technical Novelty of Training Framework: The proposed three-stage training framework is primarily a sequential application of existing, widely-used methods (cool-start and RL) and may lack sufficient novelty to be a core contribution.\n- W2. Confounding Factors in Performance Gains: It is difficult to attribute the model's strong performance solely to the \"drawing to reason\" paradigm, as it benefits from specialized fine-tuning data that most baseline models did not have access to.\n- W3. Lack of Comparisoin on Computational Cost: The method's high iterative cost creates an unfair comparison against the single-pass baseline models. The experiments lack a control group under an equivalent computational budget (e.g., allowing for multi-sample voting), which makes it difficult to assess the intrinsic effectiveness of the paradigm itself.", "was_revised": true, "final_justification": "The visual drawing-based reasoning is sound and effectively verfied by experiments.", "rebuttal": "Thank you for your valuable reviews. We provide detailed responses to address your concerns:\n\n> [W1] Limited Technical Novelty of Training Framework: The proposed three-stage training framework is primarily a sequential application of existing, widely-used methods (cool-start and RL) and may lack sufficient novelty to be a core contribution.\n\nWe respectfully disagree with this assessment. Our work makes several significant contributions:\n\n-   Analysis of Current Limitations: Through careful analysis, we identify a fundamental flaw in existing multimodal reasoning approaches: while current LVLMs excel at basic visual tasks like object detection and narrative understanding, they rely solely on text-based reasoning chains, with the only difference from text-only tasks being the presence of multimodal input. This text-centric approach assumes that visual information can be perfectly translated into textual semantic space. However, such translation may inevitably lose critical spatial details - geometric relationships become ambiguous when described in text, and tracking dynamic changes of object positions becomes prohibitively complex, as evidenced by the poor performance of current systems.\n-   Novel Vision-Centric Reasoning Paradigm: To address the limitations of current LVLMs, we propose that multimodal reasoning should dynamically incorporate new visual features throughout the reasoning process, leading to our \"draw to reason in space\" framework. While this conceptually aligns with OpenAI's recent \"thinking with images\" paradigm (April 2025), our work was conducted independently and addresses more challenging scenarios that require understanding spatial relationships across multiple video frames. Moreover, unlike recent tool-based approaches that rely on black-box perception tools (e.g., grounding and OCR systems) or heavily draw upon offline-curated reasoning data, our framework enables more flexible and intrinsic visual reasoning.\n-   Technical Innovation in Training: While our framework builds on established methods like cold-start training and reinforcement learning, we introduce a novel reflective rejection sampling stage. This innovation significantly enhances the model's self-reflection capabilities (from 4.3% to 12.5% reflection rate) and improves the potential for subsequent RL optimization, as demonstrated in our ablation studies.\n-   Strong Empirical Validation: Our comprehensive experiments demonstrate substantial improvements over text-only reasoning baselines across diverse spatial tasks, with an average improvement of 11.5% compared wtih the backbone model. This empirical evidence strongly supports our core thesis that vision-centric reasoning is essential for effective spatial understanding.\n\nIn summary, while individual components may build on existing techniques, our work's novelty lies in identifying a critical limitation in current approaches and proposing a principled solution supported by both theoretical analysis and strong empirical results.\n\n>[W2] Confounding Factors in Performance Gains: It is difficult to attribute the model's strong performance solely to the \"drawing to reason\" paradigm, as it benefits from specialized fine-tuning data that most baseline models did not have access to. [Q2] The Attribution of Performance Gains: Given that SPARK was fine-tuned on specialized data while the baselines were not, how can the performance gains be attributed specifically to the \"drawing to reason\" paradigm versus the data advantage? Can the ablation study be used to help disentangle these two factors?\n\nWe appreciate the reviewer’s insightful question. To address this concern, we conducted a controlled ablation study in which we fine-tuned the same base model Qwen2.5-VL-7B using only question-answer pairs, without any intermediate reasoning supervision—constructing a standard VQA-style SFT pipeline. The results are shown below:\n\n| Method               | Maze | SpatialEval | EmbSpatial | VSIbench | Spar-Bench |\n|----------------------|------|-------------|------------|----------|------------|\n| Qwen2.5-VL-7B + SFT     | 73.8 | 60.4        | 61.3       | 39.1     | 33.7       |\n| SPARK                | 89.0 | 63.4        | 64.9       | 42.9     | 34.9       |\n\nThese results clearly show that incorporating 'drawing to reason in space' leads to substantial improvements across all benchmarks—particularly on tasks like Maze and VSIbench, which demand explicit modeling of spatial layout and sequential planning. \n\nThese results demonstrate that **drawing operations play a crucial role in spatial reasoning beyond what can be achieved through standard fine-tuning**. While both approaches were trained on the same dataset, SPARK's ability to dynamically introduce novel spatial relationships through drawing operations leads to substantial improvements. This validates our core thesis that effective spatial reasoning requires direct visual manipulation rather than purely textual reasoning. \n\nWe will include the comparison in our revised revision.\n\n> [W3] Lack of Comparisoin on Computational Cost: The method's high iterative cost creates an unfair comparison against the single-pass baseline models. The experiments lack a control group under an equivalent computational budget (e.g., allowing for multi-sample voting), which makes it difficult to assess the intrinsic effectiveness of the paradigm itself. [Q3] The Cost-Benefit of the Iterative Method: Considering the high computational cost of SPARK's iterative process, what are its specific advantages over simpler strategies that also use a larger compute budget (e.g., textual self-correction, sample-and-vote)? What justifies the added complexity of the visual iteration mechanism?\n \nWe incorporated the two suggested baselines: **Self-Correction** and **Multi-Sample Voting**, with implementation details as follows.\n\nIn **Self-Correction** [1], the model first generates an answer with reasoning, then critiques and refines it based on its own output. This cycle repeats until no further changes are made, allowing for iterative self-improvement.\n\nIn **Multi-Sample Voting** [2], we sample five reasoning trajectories and answers independently, and then adopt majority voting to determine the final answer.\n\n**Performance Comparison**\n\n| Method             | Maze | SpatialEval | EmbSpatial | VSIbench | Spar-Bench |\n|--------------------|------|-------------|------------|----------|------------|\n|Qwen2.5-VL-7B| 33.7|58.5 | 47.9 | 32.7  | 31.2 | \n| Qwen2.5-VL-7B w/ Reasoning  | 36.5  |    56.3    |  52.7   | 26.2  |  31.6  |\n| Self-correction | 36.9  |    59.8    | 55.8    | 26.6   |  31.5    |\n| Multi-Sample Voting | 32.5  |    55.3    | 57.2    | 25.8   | 30.4     | \n| SPARK  | 89.0 | 63.4        | 64.9       | 42.9     | 34.9       |\n\nAs shown, both self-correction and multi-sample voting improve upon standard prompting by leveraging additional computation through error correction or output aggregation, respectively. However, these methods are fundamentally limited to textual processing and cannot incorporate visual feedback across iterations.\n\nSPARK's iterative visual reasoning framework refines spatial understanding through repeated visual grounding and feedback loops, consistently outperforming baselines across diverse spatial reasoning benchmarks. \n\n**Computational Overhead Analysis**\n\nWe also report the computational overhead for SPARK and the text-based baselines in terms of average wall-clock runtime per sample:\n\n| | Maze | EmbSpatial | VSIbench |\n|---------------|------|------------|----------|\n|**Avg. Runtime of Qwen2.5-VL-7B w/ Reasoning**| 1.0|0.9|1.9|\n|**Avg. Runtime of Self-Correction**| 3.5|2.1| 5.3|\n|**Avg. Runtime of Multi-Sample Voting**|2.0|1.5|3.4|\n| **Avg. Runtime of SPARK** | 4.4  | 1.2        | 7.8      |\n\nWhile SPARK introduces higher computational cost due to its iterative drawing to reason, this overhead is justified by the significant performance gains. Importantly, SPARK is orthogonal to both Self-Correction and Multi-Sample Voting, and can be integrated with these approaches for further improvement.\n\n[1] Self-Refine: Iterative Refinement with Self-Feedback. NIPS 2023\n\n[2] Self-Consistency Improves Chain of Thought Reasoning in Language Models. ICLR 2023\n\n> [Q1] The Reasoning Process: Are the reasoning steps generated autonomously by the model? If so, what termination conditions are in place to prevent infinite or non-productive reasoning loops?\n\nYes, the reasoning process in SPARK is fully autonomous. It proceeds iteratively, with the model generating intermediate steps until it produces a final answer enclosed within the special tokens `<answer>` and `</answer>`, which serves as an explicit termination signal, as exemplified in Figure 1 of the current submission. Additionally, we also impose predefined upper bounds on both the **number of reasoning iterations** and the **number of accumulated sketches/images**. If either threshold is reached before an answer is generated, the process is forcefully terminated.\n\nThe details of this temination condition can be found in specifically lines 158–159 and lines 214–217. We will revise and clarify the relevant descriptions in the final version.\n\n> [Q4] Code and Data Reproducibility: The paper's checklist states that code and data are in the supplementary material, but they could not be located. Could the authors please clarify the access method to ensure reproducibility?\n\nWe sincerely apologize for the confusion. We failed to prepare the anonymized code and data package in time for inclusion in the supplementary material.\n\nAs the rebuttal phase prohibits the inclusion of external links, we are currently unable to provide access to the code and data. However, we are fully committed to releasing the complete code and data, to ensure full reproducibility and facilitate future research."}, {"review_id": "XH9hcVAfLv", "reviewer": "Reviewer_ZTi9", "summary": "This paper introduces a new model called SPARK, leveraging ‘drawing to reason in space’, a vision centric alternative to the tex-only chain of thought that current large vision-language models (LVLMs) use. SPARK is a VLM (built on a Qwen-2.5-VL-7B backbone) that combine natural language thinking with 2 explicit visual operations: i) drawing bonding boxes and ii) drawing auxiliary lines. With the 2 additional mechanisms, SPARK can externalize spatial hypothesis directly on the image (or video frames). SPARK is trained in 3 steps: i) Cold start supervised fine-tuning (to teach basic drawing skills), ii) reflective rejection sampling and iii) a Reinforcement Learning training. SPARK is evaluated in 5 benchmarks covering static images, videos and multi-view scenes. SPARKS consistently outperforms open-source LVLMs (up to 72B) and specialized reasoning systems.", "questions": "1. Do you think it would be possible to extend the operation set (e.g. drawing polygone, heat maps) without retraining from scratch ? If so, please discuss and what kind of tasks you expect improvement\n2. There is no systematic study on how SPARK is sensitive to video length (or image resolution) ? Does it scale well to long video sequence (or very high resolution images)\n3. Have you tried different backbone (e.g. larger backbone like Qwen 72B). Do you think SPARK could easily scale up ? And also do you think it will work with vision encoder (e.g. CLIP-VIT)\n4. What is the average wall-clock latency per chain-of-thought compared with classical text-only models ? \n5. Does reflective rejection hurt exploration by discarding partially correct, but creative trajectories ?", "limitations": "The main limitation lies in the fact that evolution is restricted to categorical (and numerical) QA. There is no assessment of free-form explanations or open-ended planning tasks.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths: The Vision-centred reasoning paradigm is novel and well motivated: by allowing the model to draw spatial artifacts, the model aligned more closely with human spatial cognition. The 3 stages curriculum is well motivated and also empirically validated (thrgouht ablation studies). The benchamarks are broad enough to convincingly demonstrate the performance of SPARK. I have appreciated the interpretable outputs: the drawn artifacts make the model’s reasoning chain verifiable by humans, which is a useful property for safety and debugging.\n\nWeaknesses: \n1. Only boxes and straight lines are supported; many spatial tasks (3D rotation, occlusion…) might need richer geometric primitives to be solved.\n2. The training and the evaluation avoid free-form answers; realisms and linguistic generalization remain untested.\n3. Concerning the reward design, it seems that the same correctness/MRA formula drives both the optimisation and the test evaluation… I am concerned because there is a huge risk of overfitting…\n4. There is not quantification of the computation overhead: drawing and image re-encoding each step adds inference latency and memory, would be good to at least quantify what it the additional compute/overhead.", "was_revised": true, "final_justification": "I still think this article deserves to be accepted : strong methodology, real innovation, an potential high impact !\nI keep my rating (5/6)", "rebuttal": "> [W1] Only boxes and straight lines are supported; many spatial tasks (3D rotation, occlusion…) might need richer geometric primitives to be solved. [Q1] Do you think it would be possible to extend the operation set (e.g. drawing polygone, heat maps) without retraining from scratch ? If so, please discuss and what kind of tasks you expect improvement\n\nWe appreciate the reviewers' insightful questions. Boxes and straight lines are currently used as lightweight yet effective primitives to support spatial reasoning. To further enhance SPARK’s capability, we consider **two categories of extended operations**:\n\n1.  **Operations that provide additional spatial cues**, such as magnification, heatmaps, or depth maps. These can often be incorporated **without retraining**, by directly integrating them as new tools in the drawing pipeline.\n    \n2.  **Operations that require the model to reason with new geometric representations**, such as 3D bounding boxes. These do not introduce external information but guide the model to **focus on important regions** and perform **spatial exploration and grounded reasoning**. Such capabilities typically require **continued fine-tuning** with additional demonstrations to be used effectively.\n    \nWe expect such extensions to be especially beneficial for **complex 3D spatial reasoning tasks**, including mental rotation, occlusion handling, and perspective inference. \n\n\n> [W2] The training and the evaluation avoid free-form answers; realisms and linguistic generalization remain untested. [W3] Concerning the reward design, it seems that the same correctness/MRA formula drives both the optimisation and the test evaluation… I am concerned because there is a huge risk of overfitting…\n\nWe appreciate the comment. Most benchmark tasks use structured outputs (e.g., choices or numbers) to enable **objective and reproducible evaluation**, and to focus on **core spatial reasoning** rather than linguistic variability. This design is aligned with existing spatial benchmarks, which emphasize **decision-making over language generation**.\n\nWe agree that assessing **linguistic generalization** is valuable, and our framework is compatible with extensions to free-form tasks (e.g., spatial description or explanation), which we plan to explore in future work.\n\n\n> [W4]  There is not quantification of the computation overhead: drawing and image re-encoding each step adds inference latency and memory, would be good to at least quantify what it the additional compute/overhead. [Q4] What is the average wall-clock latency per chain-of-thought compared with classical text-only models ?\n\nWe thank the reviewers for raising this important point. We provide a quantification of SPARK’s computational overhead across benchmarks, including both average wall-clock runtime per sample and average number of reasoning steps:\n\n| | Maze | EmbSpatial | VSIbench |\n|---------------|------|------------|----------|\n| **Avg. Runtime of Qwen2.5-VL-7B w/ Reasoning** | 1.0  | 0.9        | 1.9     |\n| **Avg. Runtime of SPARK** | 4.4  | 1.2        | 7.8      |\n\nCompared to classical text-only CoT models, SPARK introduces additional latency primarily due to drawing and image re-encoding at each step. The runtime grows with reasoning depth and task complexity.  \nRelevant results are presented in Appendix C.2 of the supplementary material. We will ensure that the appendix is clearly organized to facilitate understanding for readers.\n\n> [Q2] There is no systematic study on how SPARK is sensitive to video length (or image resolution) ? Does it scale well to long video sequence (or very high resolution images)\n\nwe examined how variations in maximum image/frame resolution and the number of frames impact the model's performance. The results are summarized in the table below:\n\n| Max Resolution  | Number of Frames | VSIbench|\n|--------|----------|----------|\n|256\\*28\\*28| 16 | 42.9|\n|448\\*28\\*28|16| 43.3 |\n|256\\*28\\*28|32| 43.7|\n\nAs shown, increasing either the number of frames or the resolution results in a slight performance improvement. This suggests that higher frame resolution and a greater number of frames contribute positively to the model's reasoning ability.\nWe will include these new experimental results in our revised manuscript.\n\n\n> [Q3] Have you tried different backbone (e.g. larger backbone like Qwen 72B). Do you think SPARK could easily scale up ? And also do you think it will work with vision encoder (e.g. CLIP-VIT)\n\nThank you for your question. Our reasoning paradigm is architecture-agnostic and can be directly scaled across various LVLMs **without fundamental modifications**. While we have not yet trained SPARK on the Qwen2.5-VL-72B backbone due to computational resource constraints, we have utilized Qwen 72B for inference and cold-start data construction. We anticipate that performance will improve steadily with scale, as observed in many spatial reasoning tasks.\n\nOur reasoning paradigm modifies only the inference procedure, without altering the model architecture itself. Therefore, it is generally applicable to **other LVLM architectures**, and is **agnostic to the specific choice of LLM or vision encoder**. As for the specific vision encoder mentioned (e.g., CLIP-ViT), we are not certain about its exact integration details within a given LVLM pipeline, but in principle, SPARK can operate with any LVLMs.\n\n> [Q5] Does reflective rejection hurt exploration by discarding partially correct, but creative trajectories ?\n\nWe appreciate this insightful question about the potential impact of reflective rejection sampling on exploration and creativity. However, we argue that our approach does not hurt exploration diversity because our rejection mechanism only filters based on the presence of self-correction behaviors, not their specific forms or reasoning paths. This allows the model to discover diverse ways of revising its reasoning while maintaining accuracy.\n\nFurthermore, our quantitative analysis suggests that our approach actually enhances trajectory diversity. Specifically, we analyze the diversity of reasoning trajectories over 500 generated examples on VSIBench using the **distinct-3/4 scores**, which increased from 0.2134/0.3262 to 0.2148/0.3359 after the reflective rejection sampling stage. These results suggest that reflective rejection sampling not only **preserves exploratory behavior** but also leads to **a modest improvement in trajectory diversity**."}]

Author rebuttal:

Meta-review: The paper proposes SPARK, a vision-language model that interleaves natural-language reasoning with simple visual drawing operations (boxes, lines) to perform spatial reasoning across images and videos. A three-stage training recipe (cold-start SFT, reflective rejection sampling, RL) yields consistent gains on five spatial reasoning benchmarks and produces an interpretable “visual chain of thought.”

Reviewers found the motivation clear, the paradigm shift to vision-centric reasoning interesting, and the empirical coverage broad; they also appreciated the interpretability benefits. Main weaknesses raised early on were limited novelty in the training stack, unclear attribution of gains vs. specialized training data, missing comparisons to visual-programming baselines, compute/latency overhead, restricted drawing primitives, and lack of free-form evaluation.

In rebuttal, the authors added several baselines/controls, and analyses of inference-time scaling, termination conditions, and runtime overhead; they also reported limited sensitivity studies and clarified extensibility of the operator set and plans to release code/data upon acceptance. These additions addressed most factual concerns; some open issues remain around compute cost, the narrow operator set, and the absence of free-form outputs.

After discussion, two reviewers maintained clear “accept” positions, one moved from borderline-accept to stronger support, and one reviewer raised their score but remains below the accept threshold, primarily on novelty/scope grounds. Importantly, no fundamental methodological flaws or correctness issues were identified, and the missing baselines/controls were added, which favored the method.

Given all this, the AC recommends the paper be accepted. The authors should, in the camera-ready, (i) release code/models/data, (ii) quantify compute/latency more prominently, (iii) discuss reward-evaluation coupling risks, and (iv) outline/validate richer drawing primitives and, when feasible, a free-form evaluation.
Decision: Accept (poster)