MentalThink: Shaping Thoughts in Mental SVG World

# MentalThink: Shaping Thoughts in Mental SVG World
Source: [https://arxiv.org/html/2607.03530](https://arxiv.org/html/2607.03530)
Jisheng YinDingming LiEn YuYana WeiHan ZhouLiang ZhaoHongyu ZhouHongbo PengJianjian SunZheng GeXiangyu ZhangDaxin JiangJingyu Wang

###### Abstract

We introduceMentalThink, a visual\-symbolic reasoning paradigm that equips Multimodal LLMs \(MLLMs\) with an executable mechanism for “mental” visualization\. The core ofMentalThinkis athink\-with\-SVGpipeline, where the model learns to generate, render, and interpretscalable vector graphics\(SVG\) code as an intermediate visual representation for multi\-turn reasoning\. By creating structured vector sketches, the model can externalize spatial hypotheses, inspect them through deterministic rendering, and reason within a constrained geometric space, effectively mimicking the human process of mental imagery\. We instantiate this paradigm through a two\-stage training framework, combining Supervised Fine\-Tuning \(SFT\) for SVG syntactic alignment with multi\-turn Reinforcement Learning \(RL\) to encourage iterative inspection, revision, and refinement of intermediate visual hypotheses\. Extensive evaluations demonstrate thatMentalThinkachieves superior performance on spatial understanding and reasoning benchmarks \(e\.g\.55\.1% on VSIBench, 76\.0% on MindCube\), showing that executable vector graphics provide a verifiable visual workspace for dynamic perspective taking, visual reflection, and compositional scene construction\.

spatial reasoning, multimodal large language models, visual reasoning, mental imagery, scalable vector graphics, chain\-of\-thought, test\-time scaling

![Refer to caption](https://arxiv.org/html/2607.03530v1/x1.png)Figure 1:Conceptual comparisonof different thinking paradigms\.## 1Introduction

> “The soul never thinks without a mental image\.” Aristotle De Anima

The human capacity for reasoning extends far beyond the manipulation of linguistic symbols\(Dinneen,[1995](https://arxiv.org/html/2607.03530#bib.bib6)\)\. Cognitive processes often involvemental imagery\(Kosslyn,[1980](https://arxiv.org/html/2607.03530#bib.bib17)\), where individuals construct and manipulate mental models\(Johnson\-Laird,[1983](https://arxiv.org/html/2607.03530#bib.bib16)\)to understand complex relationships, plan actions, and solve problems\(Shepard & Metzler,[1971](https://arxiv.org/html/2607.03530#bib.bib36)\)\. This cognitive ability serves as a dynamic scratchpad for visualization, allowing us to simulate scenarios, shift perspectives, and ground abstract concepts in aquasi\-physicalspace\. This form of visual thinking is a critical aspect of human cognition and represents a promising frontier for artificial intelligence \(AI\)\. Recent advances in large language models \(LLMs\) have demonstrated strong mental reasoning capabilities through long\-context verbal traces that exhibit structured cognitive behaviors\(Liu et al\.,[2025b](https://arxiv.org/html/2607.03530#bib.bib25); Wei et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib43); Gandhi et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib9)\)\.

Multimodal large language models \(MLLMs\)\(Guo et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib10); Hong et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib12); Wei et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib43)\)have explored diverse mechanisms to incorporate visual inputs into reasoning; however, existing paradigms inevitably incur fundamental trade\-offs\. Language\-centric methods\(Wei et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib43); Huang et al\.,[2026](https://arxiv.org/html/2607.03530#bib.bib14)\)extend Chain\-of\-Thought \(CoT\)\(Wei et al\.,[2022](https://arxiv.org/html/2607.03530#bib.bib42)\)by relying on textual descriptions\. Despite their flexibility, these methods often suffer from weak visual grounding: lacking structured spatial representations, textual reasoning easily drifts from geometric reality, inducing hallucinations that are semantically plausible yet visually unfaithful\(Liu et al\.,[2025a](https://arxiv.org/html/2607.03530#bib.bib24); Li et al\.,[2026](https://arxiv.org/html/2607.03530#bib.bib21)\)\. Conversely, approaches leveraging explicit layout representations \(e\.g\., 2D/3D bounding boxes, cognitive maps\(Yin et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib54)\)\) or external tools\(Zhang et al\.,[2025b](https://arxiv.org/html/2607.03530#bib.bib61)\)attempt to mitigate this issue\. However, these strategies tend to either reduce rich visual scenes into sparse geometric primitives or offload visual imagination to disjoint external modules, consequently compromising the symbolic flexibility and generality inherent to language\-based reasoning\.

This raises a natural question:Can a reasoning pattern retain linguistic symbolic strengths while being grounded in visual structure?We identify Scalable Vector Graphics \(SVG\) as a compelling solution\. First, as astructured visual language, it offers acomplete and compositional representationof visual layouts, encapsulating object geometry and spatial hierarchies\. Consequently, generating valid vector commands requires genuine structural understanding, transcending the surface\-level pattern matching often observed in pure text generation\. Second, being inherentlycode\-based, this representation aligns natively with the architecture of LLMs\. Since models are extensively pretrained on both large\-scale text corpora and markup or programming languages \(e\.g\., HTML/XML\), they can readily reuse existing hierarchical and compositional priors\(Han et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib11)\)to manipulate visual elements expressed in code form\.

To this end, we introduceMentalThink, a novel reasoning paradigm that enables multimodal LLMs to think visually through explicit and interpretable mental imagery\. At its core,MentalThinkadopts athink\-with\-SVGpipeline \(Figure[1](https://arxiv.org/html/2607.03530#S0.F1)\(d\)\), in which the model generates SVG as an intermediate representation of its internal visual reasoning\. We realize this paradigm through a progressive two\-stage training framework\.\(1\)In the first stage, we perform supervised fine\-tuning \(SFT\) on a curated*think\-with\-SVG*dataset, teaching the model to externalize abstract reasoning into structured SVG representations\.\(2\)In the second stage, we apply multi\-turn reinforcement learning \(RL\) to refine the reasoning process itself, encouraging the model to iteratively inspect, revise, and correct its intermediate visual hypotheses\.

Through comprehensive evaluations,MentalThinkachieves superior performance on spatial understanding and reasoning benchmarks \(e\.g\.55\.1% on VSIBench\(Yang et al\.,[2025b](https://arxiv.org/html/2607.03530#bib.bib50)\), 76\.0% on MindCube\(Yin et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib54)\)\)\. Beyond raw accuracy, our qualitative analysis reveals thatthink\-with\-SVGelicits sophisticated spatial reasoning patterns that are difficult to replicate with pure language, which includes dynamic perspective taking, reflective visual refinement, and compositional scene construction\. These findings suggest thatthink\-with\-SVGconstitutes a promising paradigm that strengthens model cognition through explicit mental imagery, providing an efficient and verifiable abstraction for multimodal reasoning\.

## 2Related Works

Chain\-of\-Thought \(CoT\) Reasoning\. The development of CoT prompting marked a significant milestone in eliciting complex reasoning from LLMs\(Wei et al\.,[2022](https://arxiv.org/html/2607.03530#bib.bib42)\)\. By instructing models to generate a series of intermediate reasoning steps,i\.e\., thinking process, CoT transforms intractable problems into a sequence of manageable sub\-problems\. This decomposition serves as a cognitive bridge, allowing models to maintain logical coherence over long horizons and reducing the likelihood of error propagation, thus dramatically improving performance on tasks requiring complex reasoning\. Such CoT processes are externalized or internalized via SFT\(Yue et al\.,[2023](https://arxiv.org/html/2607.03530#bib.bib58); Yu et al\.,[2023b](https://arxiv.org/html/2607.03530#bib.bib57)\)and further scaled up via RL\(OpenAI,[2024](https://arxiv.org/html/2607.03530#bib.bib28); DeepSeek\-AI et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib5)\), constructing a linear transformation from test\-time compute to performance\.

A natural evolution of CoT is its extension into the multimodal domain\. Pioneering works in multimodal CoT\(Zhao et al\.,[2023](https://arxiv.org/html/2607.03530#bib.bib63); Yu et al\.,[2023a](https://arxiv.org/html/2607.03530#bib.bib55); Zhang et al\.,[2023](https://arxiv.org/html/2607.03530#bib.bib62); Wei et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib43); Meng et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib27); Xiaomi & Team,[2025](https://arxiv.org/html/2607.03530#bib.bib47)\)demonstrate that MLLMs can achieve significantly better results on complex multimodal reasoning tasks when prompted or self\-explored to generate a rationale that interleaves textual explanations with visual features\. However, these methods largely remainlanguage\-centric, where the reasoning process relies on textual descriptions of visual content\. Such approaches often suffer from a lack ofvisual grounding: without a structured spatial representation, the model’s textual reasoning can easily drift from the actual geometric reality of the image, leading to hallucinations that are semantically plausible but visually incorrect\(Liu et al\.,[2025a](https://arxiv.org/html/2607.03530#bib.bib24)\)\. Furthermore, unlike code\-based reasoning which can be executed and verified, pure text lacks a mechanism for rigorous self\-validation\.

Think\-with\-Image\. To address the limitations of language\-centric reasoning, several recent methods\(Hu et al\.,[2024](https://arxiv.org/html/2607.03530#bib.bib13); Wu & Xie,[2024](https://arxiv.org/html/2607.03530#bib.bib46); OpenAI,[2025](https://arxiv.org/html/2607.03530#bib.bib29)\)have emerged to “think\-with\-image”\. One strategy leverages SFT or RL technology to enable models to call external tools for image manipulation,e\.g\., zoom\-in/out\(Sarch et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib34); Zheng et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib64)\)or generating auxiliary visuals\(Chern et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib3); Qin et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib31)\), as an intermediate reasoning step\. However, the utility of this approach is often constrained by the rigid API of external tools, which breaks the end\-to\-end differentiability of the reasoning chain\. An alternative strategy focuses on internal visual representations, such as generatingcognitive maps\(Yin et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib54)\)orbounding box layouts\(Li et al\.,[2025a](https://arxiv.org/html/2607.03530#bib.bib19); Yang et al\.,[2025e](https://arxiv.org/html/2607.03530#bib.bib53)\)to explicitly model spatial relationships\. While these methods improve localization, they often oversimplify complex visual details into sparse primitives \(e\.g\., boxes\), losing the fine\-grained shape information required for detailed reasoning\. In this work, we propose a novel “think\-with\-SVG” pipeline\. By generating a structured, machine\-readable format that is inherently visual yet compositionally precise, we bridge the gap between abstract symbolic reasoning and concrete visual grounding without relying on black\-box external tools\.

SVG in LLM & MLLM\. Traditionally, Scalable Vector Graphics \(SVG\) in the context of LLMs has been utilized primarily as ageneration target\(Xing et al\.,[2024](https://arxiv.org/html/2607.03530#bib.bib48)\)or abenchmark\(Yang et al\.,[2025d](https://arxiv.org/html/2607.03530#bib.bib52)\)for evaluating spatial understanding\. Recent works have explored utilizing LLMs to generate SVG code for creating icons, charts, and artistic designs\(Rodriguez et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib33); Xing et al\.,[2024](https://arxiv.org/html/2607.03530#bib.bib48)\), or used SVG\-rendering tasks to assess the code\-generation capabilities of models regarding spatial coordinates\(Wu & Xie,[2024](https://arxiv.org/html/2607.03530#bib.bib46)\)\. However, these approaches treat SVG as the final output, the “result” of the thought process, rather than the medium of thought itself\. To the best of our knowledge,MentalThinkis the first to leverage SVG as anintermediate reasoning modality, enabling the model to construct, inspect, and refine a “mental sketch” to guide its decision\-making process for complex multimodal tasks\.

![Refer to caption](https://arxiv.org/html/2607.03530v1/x2.png)Figure 2:Think\-with\-SVG Pipeline\. MentalThink trains MLLMs to natively use SVG code to render “mental images” during multi\-turn thinking process with SVG environment, enabling more advanced and effective reasoning for complex problem\-solving\.
## 3Think\-with\-SVG Reasoning Framework

### 3\.1Preliminaries: Multimodal CoT

Building upon recent theoretical foundations\(Zhang et al\.,[2025a](https://arxiv.org/html/2607.03530#bib.bib59); Chen et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib2); Gan et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib8)\), we begin by establishing formal definitions for Chain\-of\-Thought reasoning\(Wei et al\.,[2022](https://arxiv.org/html/2607.03530#bib.bib42)\)paradigm, which structures problem\-solving as a sequence of intermediate, human\-readable steps\.

Definition 3\.1\(Chain\-of\-Thought State\)\. Given a queryq∈𝒬q\\in\\mathcal\{Q\}and a sequence of intermediate reasoning stepsξ=\{ξ1,ξ2,…,ξt\}\\xi=\\\{\\xi\_\{1\},\\xi\_\{2\},\\ldots,\\xi\_\{t\}\\\}, we define a CoT state as the tuples=\(q,ξ\)s=\(q,\\xi\), where eachξi∈ℒ\\xi\_\{i\}\\in\\mathcal\{L\}represents a semantic unit advancing toward the solution in the linguistic spaceℒ\\mathcal\{L\}\.

Definition 3\.2\(Reasoning Trajectory\)\. A complete reasoning trajectoryτ\\tauof lengthTTis a sequenceτ=\{s0,s1,…,sT\}\\tau=\\\{s\_\{0\},s\_\{1\},\\ldots,s\_\{T\}\\\}wheres0=\(q,∅\)s\_\{0\}=\(q,\\emptyset\)denotes the initial state andsT=\(q,ξ,a\)s\_\{T\}=\(q,\\xi,a\)includes the final answera∈𝒜a\\in\\mathcal\{A\}\. For multimodal reasoning, we extend these definitions:

Definition 3\.3\(Multimodal Chain\-of\-Thought\)\. Given a multimodal query\(q,𝐯\)\(q,\\mathbf\{v\}\)where𝐯=\{v1,…,vn\}⊂𝒱\\mathbf\{v\}=\\\{v\_\{1\},\\ldots,v\_\{n\}\\\}\\subset\\mathcal\{V\}represents visual inputs, a multimodal CoT state is:

smm=\(q,𝐯,ξmm\)s^\{\\text\{mm\}\}=\(q,\\mathbf\{v\},\\xi^\{\\text\{mm\}\}\)\(1\)whereξmm=\{ξ1mm,…,ξtmm\}\\xi^\{\\text\{mm\}\}=\\\{\\xi\_\{1\}^\{\\text\{mm\}\},\\ldots,\\xi\_\{t\}^\{\\text\{mm\}\}\\\}and eachξimm∈ℒ×𝒱\\xi\_\{i\}^\{\\text\{mm\}\}\\in\\mathcal\{L\}\\times\\mathcal\{V\}can reference or incorporate visual information\. While powerful, existing multimodal CoT process\(Hong et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib12); Yang et al\.,[2025a](https://arxiv.org/html/2607.03530#bib.bib49); Wei et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib43); Zheng et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib64)\)remains fundamentally linguistic\. The model verbalizes its interpretation of visual data rather than reasoning within a visual space\.

### 3\.2Think\-with\-SVG: A Structured Visual Reasoning Pipeline

Thethink\-with\-SVGpipeline reframes the reasoning process by replacing or augmenting purely linguistic thought steps with a structured, visual\-symbolic representation\. We now formalize this paradigm, establishing SVG as a structured bridge between symbolic and visual reasoning\.

Definition 3\.4\(Structured Visual Language\)\. We define SVG code space𝒮\\mathcal\{S\}as a structured visual language with the following properties:

𝒮=\{σ:σ=⟨E,A,H⟩\}\\mathcal\{S\}=\\\{\\sigma:\\sigma=\\langle E,A,H\\rangle\\\}\(2\)whereE=\{e1,e2,…,en\}E=\\\{e\_\{1\},e\_\{2\},\\ldots,e\_\{n\}\\\}is a set of primitive elements \(e\.g\.,<rect\>,<circle\>,<path\>\)\.A=\{ai​j\}A=\\\{a\_\{ij\}\\\}represents attributes for each elementeie\_\{i\}\(e\.g\., position\(x,y\)\(x,y\), dimensions\(w,h\)\(w,h\), style properties\)\.HHdenotes the hierarchical structure through grouping \(<g\>\) and transformations\. Unlike natural language descriptions, SVG enforcessyntactic structureandsemantic precision:

σvalid∈𝒮⇔Grammar​\(σ\)=True∧Renderable​\(σ\)=True\\sigma\_\{\\text\{valid\}\}\\in\\mathcal\{S\}\\iff\\text\{Grammar\}\(\\sigma\)=\\text\{True\}\\land\\text\{Renderable\}\(\\sigma\)=\\text\{True\}\(3\)
This structured nature provides three key advantages: \(i\)Deterministic mappingfrom code to visual output, \(ii\)Compositional semanticswhere complex scenes are built from primitive elements, and \(iii\)Parametric controlover visual properties through explicit attributes\.

Definition 3\.5\(SVG\-Augmented Reasoning State\)\. An SVG\-augmented reasoning state extends multimodal CoT as:

ssvg=\(q,𝐯,ξsvg\)s^\{\\text\{svg\}\}=\(q,\\mathbf\{v\},\\xi^\{\\text\{svg\}\}\)\(4\)whereξsvg=\{\(ℓ1,σ1\),\(ℓ2,σ2\),…,\(ℓT,σT\)\}\\xi^\{\\text\{svg\}\}=\\\{\(\\ell\_\{1\},\\sigma\_\{1\}\),\(\\ell\_\{2\},\\sigma\_\{2\}\),\\ldots,\(\\ell\_\{T\},\\sigma\_\{T\}\)\\\}withℓi∈ℒ\\ell\_\{i\}\\in\\mathcal\{L\}representing linguistic reasoning andσi∈𝒮∪\{∅\}\\sigma\_\{i\}\\in\\mathcal\{S\}\\cup\\\{\\emptyset\\\}representing optional SVG code\. Through SVG\-augmented reasoning, the model learns to adaptively generate SVG code when it needs to applymental imageryduring thinking\.

Definition 3\.6\(SVG Rendering Environment\)\. The rendering process from SVG code to raster image involves a deterministic transformation:

ℛ:𝒮→𝒱,ℛ​\(σ\)=𝐈σ∈ℝH×W×C\\mathcal\{R\}:\\mathcal\{S\}\\rightarrow\\mathcal\{V\},\\quad\\mathcal\{R\}\(\\sigma\)=\\mathbf\{I\}\_\{\\sigma\}\\in\\mathbb\{R\}^\{H\\times W\\times C\}\(5\)
The rendering pipelineℛ\\mathcal\{R\}consists of three sequential transformations:

σ→Parse𝒯DOM→Layout𝒢=\{g1,…,gm\}→Rasterize𝐈σ\\sigma\\xrightarrow\{\\text\{Parse\}\}\\mathcal\{T\}\_\{\\text\{DOM\}\}\\xrightarrow\{\\text\{Layout\}\}\\mathcal\{G\}=\\\{g\_\{1\},\\ldots,g\_\{m\}\\\}\\xrightarrow\{\\text\{Rasterize\}\}\\mathbf\{I\}\_\{\\sigma\}\(6\)where𝒯DOM\\mathcal\{T\}\_\{\\text\{DOM\}\}is the document object model tree, and𝒢\\mathcal\{G\}represents geometric primitives in the coordinate space and graphic scene\. Through this SVG environment, the model can iteratively generate, render, and reason about visual representations, creating a feedback loop between symbolic manipulation and visual interpretation\. Figure[2](https://arxiv.org/html/2607.03530#S2.F2)gives a detailed example showing thatMentalThinkfirstestablishes the absolute spatial layout, thendefines the egocentric reference frame, followed byevaluating the target positionto get the final answer\.

This structured visual language enables MLLMs to perform “mental rendering” – constructing and manipulating visual representations through code generation, thereby achieving native visual reasoning without external tools or specialized visual encoders\.

### 3\.3MentalThink Training Recipe

Overview\.We formulate theMentalThinkprocess as optimizing a multimodal policyπθ\\pi\_\{\\theta\}to generate optimal reasoning trajectoriesτ\\tau\. Unlike standard linguistic policies,πθ\\pi\_\{\\theta\}operates over the augmented state space defined in Definition 3\.5, where the model must learn to interleave symbolic reasoningℓ\\ellwith structured visual codesσ∈𝒮\\sigma\\in\\mathcal\{S\}\. We optimizeπθ\\pi\_\{\\theta\}through a progressive two\-stage framework\.

Stage 1: Syntactic Alignment via Cold Start\.To initialize the policyπθ\\pi\_\{\\theta\}with the capability to generate valid statesssvgs^\{\\text\{svg\}\}, we perform supervised fine\-tuning \(SFT\)\. Given a dataset of expert trajectories𝒟SFT=\{τ∗\}\\mathcal\{D\}\_\{\\text\{SFT\}\}=\\\{\\tau^\{\*\}\\\}, where each step fits the definitionξi=\(ℓi,σi\)\\xi\_\{i\}=\(\\ell\_\{i\},\\sigma\_\{i\}\), we minimize the negative log\-likelihood:

ℒSFT​\(θ\)=−𝔼τ∼𝒟SFT​∑t=0Tlog⁡πθ​\(ξtsvg∣stsvg\)\\mathcal\{L\}\_\{\\text\{SFT\}\}\(\\theta\)=\-\\mathbb\{E\}\_\{\\tau\\sim\\mathcal\{D\}\_\{\\text\{SFT\}\}\}\\sum\_\{t=0\}^\{T\}\\log\\pi\_\{\\theta\}\(\\xi\_\{t\}^\{\\text\{svg\}\}\\mid s\_\{t\}^\{\\text\{svg\}\}\)\(7\)This stage ensures the model aligns with the structural constraints of𝒮\\mathcal\{S\}\(Definition 3\.4\), learning to generate syntactically valid SVG codes before engaging in complex reasoning\. In addition, we also synthesize a small amount ofthink\-with\-SVGcold\-start data for thinking pattern warm\-up\. More details are shown in Appendix[A\.1](https://arxiv.org/html/2607.03530#A1.SS1)\.

Stage 2: Strategic Reasoning via Multi\-Turn RL\.SFT provides the form, but not the reasoning dynamics\. To enable self\-correction, we optimizeπθ\\pi\_\{\\theta\}using Group Relative Policy Optimization \(GRPO\)\(Shao et al\.,[2024](https://arxiv.org/html/2607.03530#bib.bib35); Yu et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib56)\)on a reasoning corpus𝒟RL\\mathcal\{D\}\_\{\\text\{RL\}\}\. The optimization objective is to maximize the expected returnJ​\(θ\)=𝔼τ∼πθ​\[R​\(τ\)\]J\(\\theta\)=\\mathbb\{E\}\_\{\\tau\\sim\\pi\_\{\\theta\}\}\[R\(\\tau\)\], where the generation process is treated as an interaction with the SVG Rendering Environment \(Definition 3\.6\)\.

Interactive Reasoning Loop\.We model the multi\-turn reasoning as a state transition processst→st\+1s\_\{t\}\\to s\_\{t\+1\}within the SVG rendering environment \(Definition 3\.6\):

- •Hypothesis Generation \(Policy Rollout\):At steptt, conditioned on the current historysts\_\{t\}, the policy samples an actionat=\(ℓt,σt\)∼πθ\(⋅\|st\)a\_\{t\}=\(\\ell\_\{t\},\\sigma\_\{t\}\)\\sim\\pi\_\{\\theta\}\(\\cdot\|s\_\{t\}\)\.
- •Deterministic Visual Feedback \(SVG Rendering\):If the action includes non\-empty SVG code \(σt≠∅\\sigma\_\{t\}\\neq\\emptyset\), the environment triggers the rendering function defined in Eq\.[6](https://arxiv.org/html/2607.03530#S3.E6): 𝐈t=ℛ​\(σt\)\\mathbf\{I\}\_\{t\}=\\mathcal\{R\}\(\\sigma\_\{t\}\)\(8\)This step effectively converts the model’s symbolic hypothesisσt\\sigma\_\{t\}into pixel\-space observation𝐈t\\mathbf\{I\}\_\{t\}\.
- •State Transition \(Context Update\):The rendered image is appended to the visual context, updating the state: st\+1=st⊕\(ℓt,σt,𝐈t\)s\_\{t\+1\}=s\_\{t\}\\oplus\(\\ell\_\{t\},\\sigma\_\{t\},\\mathbf\{I\}\_\{t\}\)\(9\)This explicitly closes the loop, allowingπθ\\pi\_\{\\theta\}to condition its next reasoning stepξt\+1\\xi\_\{t\+1\}on the visual verification of its previous thought\.
- •Termination:The trajectory terminates when the model outputs a stop token, reachesTmaxT\_\{\\max\}, or triggers a hard syntax failure \(σt∉𝒮\\sigma\_\{t\}\\notin\\mathcal\{S\}\)\.

Reward Formulation\.The rewardR​\(τ\)R\(\\tau\)is designed to enforce the structural integrity defined in Definition 3\.4 and the final correctness:

rt=λfmt​rformat​\(σt\)\+λans​ranswer​\(aT\)⋅𝕀​\(t=T\)r\_\{t\}=\\lambda\_\{\\mathrm\{fmt\}\}\\,r\_\{\\mathrm\{format\}\}\(\\sigma\_\{t\}\)\+\\lambda\_\{\\mathrm\{ans\}\}\\,r\_\{\\mathrm\{answer\}\}\(a\_\{T\}\)\\cdot\\mathbb\{I\}\(t=T\)\(10\)
- •Format Reward \(rformatr\_\{\\mathrm\{format\}\}\):A dense reward that validates ifσt\\sigma\_\{t\}satisfies the grammar of𝒮\\mathcal\{S\}\. Specifically,rformat=1r\_\{\\mathrm\{format\}\}=1iffRenderable​\(σt\)=True\\text\{Renderable\}\(\\sigma\_\{t\}\)=\\text\{True\}, ensuring the “mental image” is valid\.
- •Answer Reward \(ranswerr\_\{\\mathrm\{answer\}\}\):A sparse reward awarded only at the final stepTT, measuring if the predicted answer matches the ground truth\.

## 4Experiments

Table 1:Evaluation on spatial understanding and reasoning benchmarks\.MindCube\*denotes MindCube\-Tiny\.Improveindicates gains over the Qwen2\.5\-VL\-7B backbone\. Dark/light purple highlights the best/second\-best results in Proprietary and Open\-source categories, respectively\.ModelsVSIBenchMMSIOmniSpatialMindCube∗SpatialVizViewSpatialProprietary ModelsSeed\-1\.6\-2025\-06\-1549\.938\.354\.548\.734\.943\.8Gemini\-2\.5\-pro\-2025\-0653\.538\.043\.057\.615\.946\.0GPT\-5\-nano\-2025\-08\-0738\.922\.542\.319\.04\.538\.5GPT\-5\-mini\-2025\-08\-0748\.234\.352\.050\.022\.542\.4GPT\-5\-2025\-08\-0755\.041\.849\.556\.37\.245\.5Open\-source ModelsQwen2\.5\-VL\-3B27\.028\.640\.334\.730\.231\.9Qwen2\.5\-VL\-7B31\.027\.839\.236\.026\.836\.8Qwen2\.5\-VL\-72B34\.730\.747\.937\.035\.038\.9LLaVA\-Next\-Video\-7B35\.6\-28\.5\-20\.930\.6LLaVA\-Next\-Video\-72B40\.9\-\-\-\-\-LLaVA\-OneVision\-7B32\.424\.535\.7\-24\.727\.5LLaVA\-OneVision\-72B40\.228\.445\.7\-\-\-InternVL3\-8B42\.128\.041\.641\.530\.338\.6InternVL3\-78B\-28\.549\.3\-32\.3\-Spatial\-Specific ModelsMindCube\-3B\-RawQA\-SFT17\.21\.724\.551\.726\.524\.1SpatialLadder\-3B45\.727\.441\.943\.428\.444\.2Spatial\-MLLM\-4B47\.326\.138\.033\.4\-34\.6SpaceR\-SFT\-7B41\.627\.441\.038\.029\.235\.8VILASR\-7B44\.630\.219\.235\.131\.335\.7MentalThink\-SFT53\.924\.544\.974\.234\.262\.3MentalThink\-RL55\.128\.043\.476\.038\.762\.5Improve↑\\uparrow\+24\.1\+0\.2\+4\.2\+40\.0\+11\.9\+25\.7

### 4\.1Experimental Setup

Implementation Setup and Baselines\.We implementMentalThinkatop theQwen2\.5\-VL\-7Bbackbone\(Bai et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib1)\)\. This choice allows us to strictlyisolatethe empirical gains attributable to thethink\-with\-SVGparadigm from those potentially stemming from mere model scaling\. We comprehensively compareMentalThinkagainst three categories of competitive baselines:

- •Proprietary Models:Seed\-1\.6\(Guo et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib10)\), Gemini\-2\.5\-pro\(Team et al\.,[2023](https://arxiv.org/html/2607.03530#bib.bib40)\), and the GPT\-5 series \(nano, mini, full\)\(Singh et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib37)\)\.
- •Open\-source General MLLMs:Qwen2\.5\-VL\(Bai et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib1)\)\(3B/7B/72B\), LLaVA\-Next\-Video\(Zhang et al\.,[2024](https://arxiv.org/html/2607.03530#bib.bib60)\)\(7B/72B\), LLaVA\-OneVision\(Li et al\.,[2024](https://arxiv.org/html/2607.03530#bib.bib18)\)\(7B/72B\), and InternVL3\(Zhu et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib65)\)\(8B/78B\)\.
- •Spatial\-Specific Models:MindCube\-3B\-RawQA\-SFT, SpatialLadder\-3B\(Li et al\.,[2025c](https://arxiv.org/html/2607.03530#bib.bib22)\), Spatial\-MLLM\-4B\(Wu et al\.,[2025a](https://arxiv.org/html/2607.03530#bib.bib44)\), SpaceR\-SFT\-7B\(Ouyang et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib30)\), and VILASR\-7B\(Wu et al\.,[2025b](https://arxiv.org/html/2607.03530#bib.bib45)\)\.

Data Synthesis and Composition\.We utilize the multimodal dataset curated in Section[3\.3](https://arxiv.org/html/2607.03530#S3.SS3), specifically tailored for our two\-stage training strategy\. The supervised fine\-tuning \(SFT\) corpus consists of approximately200ksamples, categorized into three functional pillars: \(1\)Visual\-Syntactic Alignment \(50k\)to bridge pixel\-level perception with vector\-based descriptions; \(2\)Visual Thought Externalization \(50k\)featuring explicit SVG\-mediated reasoning chains; \(3\)Fundamental Spatial Perception \(100k\)sampled from Euclid\(Lian et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib23)\), DrivingVQA\(Corbière et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib4)\), SAT\(Ray et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib32)\), SpaceVista\(Sun et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib38)\), VLM\-3R\(Fan et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib7)\), and Spatial\-SSRL\(Liu et al\.,[2025c](https://arxiv.org/html/2607.03530#bib.bib26)\)\.

Our SVG reasoning and reconstruction data are constructed through a teacher\-student pipeline and filtered with SVG structural validity and basic visual integrity checks\. Detailed prompts, filtering rules, and dataset construction procedures are provided in Appendix[A\.1](https://arxiv.org/html/2607.03530#A1.SS1)\. For the subsequent RL stage, we use prompts from the*training*splits ofVSIBenchandMindCube\.

Training Protocols\.All experiments are conducted on a cluster of 32 NVIDIA H800 GPUs\. We employ Group Relative Policy Optimization \(GRPO\) driven by the hybrid reward function defined in Eq\.[10](https://arxiv.org/html/2607.03530#S3.E10)\(with coefficientsλf​m​t=0\.25\\lambda\_\{fmt\}=0\.25andλa​n​s=0\.75\\lambda\_\{ans\}=0\.75\)\. The maximum reasoning horizon for iterative refinement is capped atTm​a​x=5T\_\{max\}=5\. To balance convergence and stability, we adopt a progressive training schedule:

- •SFT Stage:The model is trained with a learning rate of5×10−55\\times 10^\{\-5\}and a global batch size of256256\.
- •RL Stage:To ensure policy stability, we transition to a more conservative learning rate of2×10−62\\times 10^\{\-6\}and a global batch size of6464\.

### 4\.2Main Results

We evaluateMentalThinkacross a comprehensive suite of spatial understanding and reasoning benchmarks, includingVSIBench,MMSI\-Bench\(Yang et al\.,[2025c](https://arxiv.org/html/2607.03530#bib.bib51)\),OmniSpatial\(Jia et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib15)\),MindCube,SpatialViz\(Wang et al\.,[2025](https://arxiv.org/html/2607.03530#bib.bib41)\), andViewSpatial\(Li et al\.,[2025b](https://arxiv.org/html/2607.03530#bib.bib20)\)\. Table[1](https://arxiv.org/html/2607.03530#S4.T1)summarizes the performance trajectory from the baseline to the SFT intermediate, and finally to the RL\-optimized model\.

Superior Spatial Performance\.As evidenced in Table[1](https://arxiv.org/html/2607.03530#S4.T1),MentalThinkdemonstratessubstantial improvementson geometry\-intensive tasks\. Most notably, onMindCubethat demands complex 3D mental rotation and spatial manipulation, our method improves accuracy from 36\.0% to76\.0%\. This remarkable gain of40 pointsvalidatesour core hypothesis: explicitly externalizing thought processes into SVG code enables the model to resolve spatial relationships thatremain intractablefor purely linguistic reasoning\. Consistent gains are also observed onVSIBench\(\+24\.1%\) andViewSpatial\(\+25\.7%\), demonstratingMentalThink’s powerful spatial perception and reasoning abilities\.

Synergy of SFT and RL\.The performance comparison in Table[1](https://arxiv.org/html/2607.03530#S4.T1)between SFT and RL stages highlights the necessity of the two\-stage pipeline\. While SFT establishes the capability to generate valid SVG \(“drawing mental image”\), the RL stage is crucial formastering complex reasoning logic\(“thinking in mental image”\)\. We observe that RL boosts performance on the most challenging logical tasks \(e\.g\., MindCube\+1\.8%\+1\.8\\%, SpatialViz\+4\.5%\+4\.5\\%\)\.

### 4\.3Ablation Studies

In this section, we aim to conduct comprehensive ablation studies on the proposedMentalThinkframework, covering data design and training paradigms\. From the results shown in Table[2](https://arxiv.org/html/2607.03530#S4.T2), we can observe:

SVG data enhances spatial perception\.Comparing rows \#1 and \#2 in Table[2](https://arxiv.org/html/2607.03530#S4.T2), incorporating SVG\-Reasoning data yields a foundational performance gain of 13\.4% in average score, rising from 31\.0% to 44\.4%\. By framing spatial reasoning as structured SVG reconstruction, the model develops a more granular perception of layouts\. This effect is most prominent in theAppearance Ordermetric, which nearly doubles from 28\.2 to 56\.0, andObject Size, which surges from 37\.2 to 55\.9\. These results indicate that the SVG modality effectively serves as a structured inductive bias, bridging the gap between raw visual inputs and precise spatial grounding\.

Table 2:Ablation study of our proposed components on VSIBench\.The results demonstrate that SVG\-reasoning data, general spatial perception data, and RL training each provide complementary performance gains \(✓/✗ denote whether each component is enabled\)\. The integrated model \(last row\) achieves the best performance across all metrics\.SVG\-Reas\.DataGen\-Perc\.DataRLTaskAvg\.Numerical QuestionMultiple\-Choice QuestionObj\. SizeRoom\. SizeRel\. Dir\.Rel\. Dist\.Appr\. Order\.✗✗✗31\.037\.243\.236\.337\.328\.2✓✗✗44\.455\.931\.941\.947\.656\.0✓✓✗53\.964\.258\.447\.155\.563\.8✓✓✓55\.164\.858\.951\.456\.566\.7

General data yields the complementary gains\.The addition of General Spatial Perception Data results in a substantial further improvement, raising the average performance from 44\.4 to 53\.9\. This module provides broad spatial priors necessary to master scene\-level attributes that specialized SFT might overlook\. Notably, theRoom Sizemetric experiences a massive recovery and gain, increasing by 26\.5 points \(from 31\.9 to 58\.4\)\. This highlights that extensive and diverse spatial exposure is essential for robust environment modeling and overcoming the limitations of domain\-specific data\.

RL optimizes complex reasoning\.The multi\-turn RL stage acts as the catalyst for overcoming reasoning bottlenecks observed in SFT\-only variants\. While SFT models \(row \#3\) achieve strong results in perception, RL training further incentivizes the model to iteratively refine its internal hypotheses, pushing the average score to a peak of 55\.1%\. This improvement is consistent across challenging logical tasks, withRelative Directionincreasing from 47\.1 to 51\.4 andAppearance Orderreaching 66\.7\. This framework provides the ”System 2” slow thinking capability, allowing the model to convert additional inference\-time computation into higher reasoning precision through verified visual simulation\.

Ultimately, the full configuration ofMentalThinkachieves peak performance across all metrics\. This integrated pipeline successfully bridges the gap between abstract reasoning and concrete grounding by synthesizing high\-quality spatial data with iterative reinforcement learning\.

## 5Analysis and Discussion

### 5\.1Empirical Analysis of Think\-with\-SVG

![Refer to caption](https://arxiv.org/html/2607.03530v1/x3.png)Figure 3:Examples of Spatial Reasoning Patterns\.MentalThinkdemonstrates dynamic perspective taking, reflective visual refinement, and compositional scene construction\.Analysis of different thinking paradigms\.We evaluate three thinking paradigms—Think\-with\-Text, Think\-with\-BBox, and Think\-with\-SVG—under a controlled setting where the same teacher model, task inputs, and supervision signals are used, differing only in the form of intermediate reasoning representation\.

Table 3:Performance comparison between different thinking paradigms on MindCube and VSIBench\.Thinking ParadigmMindCubeVSIBenchThink\-with\-Text42\.524\.5Think\-with\-BBox41\.117\.4Think\-with\-SVG\(ours\)57\.839\.4As reported in Table[3](https://arxiv.org/html/2607.03530#S5.T3), SVG\-based reasoning consistently outperforms text\-based and box\-based reasoning on both MindCube and VSIBench, with the largest relative gains observed on VSIBench\.

These results suggest that structured and executable spatial representations provide a more effective inductive bias for complex multi\-step visual reasoning\.

System 1 vs\. System 2 Behavior via Adaptive Reasoning\.As shown in Table[4](https://arxiv.org/html/2607.03530#S5.T4), we observe a systematic shift in inference behavior across task types\. We quantify this computational cost via three metrics: Avg\. Turns, representing the total execution cycles where a baseline LLM response counts as one turn; SVG Invoc\., the rate of externalizing thought into vector code; and Avg\. Tokens/Ex\., the total information density per response\. For perception\-dominant tasks, the model exhibits System 1\-style intuition, providing direct answers with only 1\.19 average turns and a low 18\.5% SVG invocation rate\.

Table 4:System 1 vs\. System 2 style behavior across task types\.We report the average reasoning turns, SVG invocation rate, average token length per example, and final task accuracy\. Notably, the model adapts its reasoning effort \(reasoning turns, SVG invocation, and token usage\) to task complexity while maintaining comparable final accuracy across both regimes\.Task TypeAvg\. TurnsSVG Invoc\.Avg\. Tokens/Ex\.AccuracyIntuitive Visual Perception1\.1918\.5%109\.255\.11Compositional Visual Reasoning1\.6463\.7%544\.555\.10

In contrast, complex visual reasoning tasks trigger a deliberate System 2 process, characterized by a surge in SVG invocation \(63\.7%\) and token length \(544\.5 vs\. 109\.2\)\. The increase to 1\.64 average turns for reasoning tasks validates an adaptive allocation of effort\. This test\-time scaling demonstrates thatMentalThinkautonomously invokes iterative mental imagery to transform additional inference\-time compute into rigorous visual grounding when faced with intricate spatial logic\.

### 5\.2Case Analysis: Emergent Spatial Reasoning via Think\-with\-SVG

Figure[3](https://arxiv.org/html/2607.03530#S5.F3)shows howthink\-with\-SVGoperationalizes mental imagery as an explicit and revisable spatial workspace, enabling structured manipulation of reference frames and object relations beyond surface\-level visual description\.

Dynamic Perspective Taking\.In the top case, the model anchors an egocentric coordinate frame on the man in green and projects the man in white into this frame, converting camera\-centric observations into agent\-centric spatial relations\. Our model explicitly encodes forward and left–right axes through SVG generation during thinking, enabling reliable perspective transformation\.

Reflective Visual Refinement\.In the middle case, the model constructs an initial room layout around the TV and table, then revises left–right relations after detecting a mismatch between assumed orientation and the user’s facing direction\. This correction is realized through iterative updates to the SVG, which serves as a visual scratchpad for hypothesis validation\.

Compositional Scene Construction\.In the bottom case, the model integrates multiple views by fixing the door as a reference point and aligning the table and backpack into a shared spatial layout\. The composed SVG supports inferring the backpack’s front\-left relation, which depends on global scene consistency rather than any single view\.

Overall, these cases indicate thatthink\-with\-SVGinduces a structured form of visual reasoning in which spatial hypotheses are explicitly instantiated, inspected, and revised within a mental image, enabling consistent perspective alignment and global spatial coherence beyond language\-only reasoning\.

## 6Limitation and Conclusion

Representing the physical world effectively is a fundamental challenge for multimodal intelligence\. We present evidence that Scalable Vector Graphics \(SVG\) serve as a structured, visual\-symbolic representation bridging symbolic reasoning and visual perception\. By treating SVG as an executable “mental scratchpad,” ourthink\-with\-SVGpipeline enables models to ground their thoughts in precise geometric structures, and withinMentalThinkachieves state\-of\-the\-art performance across multiple spatial reasoning benchmarks\.

However, empowering the model to spontaneously activate and explore this ability remains a non\-trivial challenge\. High\-quality chain\-of\-thought data interwoven with valid, meaningful SVG code is scarce in standard pre\-training corpora\. Consequently, relying on naturally occurring data is insufficient; sophisticated data synthesis and reinforcement strategies are required to bridge this gap\. We hope this work can serve as a foundational step toward neuro\-symbolic multimodal systems, inspiring future exploration into how explicit visual imagery can drive more robust and interpretable machine reasoning\.

## Impact Statements

This paper presents work whose goal is to advance the field of machine learning\. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here\.

## References

- Bai et al\. \(2025\)Bai, S\., Chen, K\., Liu, X\., Wang, J\., Ge, W\., Song, S\., Dang, K\., Wang, P\., Wang, S\., Tang, J\., et al\.Qwen2\. 5\-vl technical report\.*arXiv preprint arXiv:2502\.13923*, 2025\.
- Chen et al\. \(2025\)Chen, Q\., Qin, L\., Liu, J\., Peng, D\., Guan, J\., Wang, P\., Hu, M\., Zhou, Y\., Gao, T\., and Che, W\.Towards reasoning era: A survey of long chain\-of\-thought for reasoning large language models\.*arXiv preprint arXiv:2503\.09567*, 2025\.
- Chern et al\. \(2025\)Chern, E\., Hu, Z\., Chern, S\., Kou, S\., Su, J\., Ma, Y\., Deng, Z\., and Liu, P\.Thinking with generated images\.*arXiv preprint arXiv:2505\.22525*, 2025\.
- Corbière et al\. \(2025\)Corbière, C\., Roburin, S\., Montariol, S\., Bosselut, A\., and Alahi, A\.Retrieval\-based interleaved visual chain\-of\-thought in real\-world driving scenarios, 2025\.URL[https://arxiv\.org/abs/2501\.04671](https://arxiv.org/abs/2501.04671)\.
- DeepSeek\-AI et al\. \(2025\)DeepSeek\-AI, Guo, D\., Yang, D\., Zhang, H\., Song, J\., Zhang, R\., Xu, R\., Zhu, Q\., Ma, S\., Wang, P\., Bi, X\., Zhang, X\., Yu, X\., Wu, Y\., Wu, Z\. F\., Gou, Z\., Shao, Z\., Li, Z\., Gao, Z\., Liu, A\., Xue, B\., Wang, B\., Wu, B\., Feng, B\., Lu, C\., Zhao, C\., Deng, C\., Zhang, C\., Ruan, C\., Dai, D\., Chen, D\., Ji, D\., Li, E\., Lin, F\., Dai, F\., Luo, F\., Hao, G\., Chen, G\., Li, G\., Zhang, H\., Bao, H\., Xu, H\., Wang, H\., Ding, H\., Xin, H\., Gao, H\., Qu, H\., Li, H\., Guo, J\., Li, J\., Wang, J\., Chen, J\., Yuan, J\., Qiu, J\., Li, J\., Cai, J\. L\., Ni, J\., Liang, J\., Chen, J\., Dong, K\., Hu, K\., Gao, K\., Guan, K\., Huang, K\., Yu, K\., Wang, L\., Zhang, L\., Zhao, L\., Wang, L\., Zhang, L\., Xu, L\., Xia, L\., Zhang, M\., Zhang, M\., Tang, M\., Li, M\., Wang, M\., Li, M\., Tian, N\., Huang, P\., Zhang, P\., Wang, Q\., Chen, Q\., Du, Q\., Ge, R\., Zhang, R\., Pan, R\., Wang, R\., Chen, R\. J\., Jin, R\. L\., Chen, R\., Lu, S\., Zhou, S\., Chen, S\., Ye, S\., Wang, S\., Yu, S\., Zhou, S\., Pan, S\., Li, S\. S\., Zhou, S\., Wu, S\., Ye, S\., Yun, T\., Pei, T\., Sun, T\., Wang, T\., Zeng, W\., Zhao, W\., Liu, W\., Liang, W\., Gao, W\., Yu, W\., Zhang, W\., Xiao, W\. L\., An, W\., Liu, X\., Wang, X\., Chen, X\., Nie, X\., Cheng, X\., Liu, X\., Xie, X\., Liu, X\., Yang, X\., Li, X\., Su, X\., Lin, X\., Li, X\. Q\., Jin, X\., Shen, X\., Chen, X\., Sun, X\., Wang, X\., Song, X\., Zhou, X\., Wang, X\., Shan, X\., Li, Y\. K\., Wang, Y\. Q\., Wei, Y\. X\., Zhang, Y\., Xu, Y\., Li, Y\., Zhao, Y\., Sun, Y\., Wang, Y\., Yu, Y\., Zhang, Y\., Shi, Y\., Xiong, Y\., He, Y\., Piao, Y\., Wang, Y\., Tan, Y\., Ma, Y\., Liu, Y\., Guo, Y\., Ou, Y\., Wang, Y\., Gong, Y\., Zou, Y\., He, Y\., Xiong, Y\., Luo, Y\., You, Y\., Liu, Y\., Zhou, Y\., Zhu, Y\. X\., Xu, Y\., Huang, Y\., Li, Y\., Zheng, Y\., Zhu, Y\., Ma, Y\., Tang, Y\., Zha, Y\., Yan, Y\., Ren, Z\. Z\., Ren, Z\., Sha, Z\., Fu, Z\., Xu, Z\., Xie, Z\., Zhang, Z\., Hao, Z\., Ma, Z\., Yan, Z\., Wu, Z\., Gu, Z\., Zhu, Z\., Liu, Z\., Li, Z\., Xie, Z\., Song, Z\., Pan, Z\., Huang, Z\., Xu, Z\., Zhang, Z\., and Zhang, Z\.Deepseek\-r1: Incentivizing reasoning capability in llms via reinforcement learning, 2025\.URL[https://arxiv\.org/abs/2501\.12948](https://arxiv.org/abs/2501.12948)\.
- Dinneen \(1995\)Dinneen, F\. P\.*General linguistics*\.Georgetown University Press, 1995\.
- Fan et al\. \(2025\)Fan, Z\., Zhang, J\., Li, R\., Zhang, J\., Chen, R\., Hu, H\., Wang, K\., Qu, H\., Wang, D\., Yan, Z\., Xu, H\., Theiss, J\., Chen, T\., Li, J\., Tu, Z\., Wang, Z\., and Ranjan, R\.Vlm\-3r: Vision\-language models augmented with instruction\-aligned 3d reconstruction, 2025\.URL[https://arxiv\.org/abs/2505\.20279](https://arxiv.org/abs/2505.20279)\.
- Gan et al\. \(2025\)Gan, Z\., Yi, H\., and Liu, Y\.Cot\-space: A theoretical framework for internal slow\-thinking via reinforcement learning\.*arXiv preprint arXiv:2509\.04027*, 2025\.
- Gandhi et al\. \(2025\)Gandhi, K\., Chakravarthy, A\., Singh, A\., Lile, N\., and Goodman, N\. D\.Cognitive behaviors that enable self\-improving reasoners, or, four habits of highly effective stars, 2025\.URL[https://arxiv\.org/abs/2503\.01307](https://arxiv.org/abs/2503.01307)\.
- Guo et al\. \(2025\)Guo, D\., Wu, F\., Zhu, F\., Leng, F\., Shi, G\., Chen, H\., Fan, H\., Wang, J\., Jiang, J\., Wang, J\., et al\.Seed1\. 5\-vl technical report\.*arXiv preprint arXiv:2505\.07062*, 2025\.
- Han et al\. \(2025\)Han, J\., Tong, S\., Fan, D\., Ren, Y\., Sinha, K\., Torr, P\., and Kokkinos, F\.Learning to see before seeing: Demystifying llm visual priors from language pre\-training, 2025\.URL[https://arxiv\.org/abs/2509\.26625](https://arxiv.org/abs/2509.26625)\.
- Hong et al\. \(2025\)Hong, W\., Yu, W\., Gu, X\., Wang, G\., Gan, G\., Tang, H\., Cheng, J\., Qi, J\., Ji, J\., Pan, L\., et al\.Glm\-4\.1 v\-thinking: Towards versatile multimodal reasoning with scalable reinforcement learning\.*arXiv preprint arXiv:2507\.01006*, 2025\.
- Hu et al\. \(2024\)Hu, Y\., Shi, W\., Fu, X\., Roth, D\., Ostendorf, M\., Zettlemoyer, L\., Smith, N\. A\., and Krishna, R\.Visual sketchpad: Sketching as a visual chain of thought for multimodal language models\.*Advances in Neural Information Processing Systems*, 37:139348–139379, 2024\.
- Huang et al\. \(2026\)Huang, A\., Yao, C\., Han, C\., Wan, F\., Guo, H\., Lv, H\., Zhou, H\., Wang, J\., Zhou, J\., Sun, J\., et al\.Step3\-vl\-10b technical report\.*arXiv preprint arXiv:2601\.09668*, 2026\.
- Jia et al\. \(2025\)Jia, M\., Qi, Z\., Zhang, S\., Zhang, W\., Yu, X\., He, J\., Wang, H\., and Yi, L\.Omnispatial: Towards comprehensive spatial reasoning benchmark for vision language models\.*arXiv preprint arXiv:2506\.03135*, 2025\.
- Johnson\-Laird \(1983\)Johnson\-Laird, P\. N\.*Mental models: Towards a cognitive science of language, inference, and consciousness*\.Harvard University Press, 1983\.
- Kosslyn \(1980\)Kosslyn, S\. M\.*Image and mind*\.Harvard University Press, 1980\.
- Li et al\. \(2024\)Li, B\., Zhang, Y\., Guo, D\., Zhang, R\., Li, F\., Zhang, H\., Zhang, K\., Zhang, P\., Li, Y\., Liu, Z\., and Li, C\.Llava\-onevision: Easy visual task transfer, 2024\.URL[https://arxiv\.org/abs/2408\.03326](https://arxiv.org/abs/2408.03326)\.
- Li et al\. \(2025a\)Li, C\., Wu, W\., Zhang, H\., Xia, Y\., Mao, S\., Dong, L\., Vulić, I\., and Wei, F\.Imagine while reasoning in space: Multimodal visualization\-of\-thought\.*arXiv preprint arXiv:2501\.07542*, 2025a\.
- Li et al\. \(2025b\)Li, D\., Li, H\., Wang, Z\., Yan, Y\., Zhang, H\., Chen, S\., Hou, G\., Jiang, S\., Zhang, W\., Shen, Y\., Lu, W\., and Zhuang, Y\.Viewspatial\-bench: Evaluating multi\-perspective spatial localization in vision\-language models, 2025b\.URL[https://arxiv\.org/abs/2505\.21500](https://arxiv.org/abs/2505.21500)\.
- Li et al\. \(2026\)Li, D\., Zhao, Y\., Cheng, X\., Lin, K\., Peng, H\., Li, H\., Wang, Z\., Dai, Y\., Li, H\., Wang, J\., et al\.Spatialevo: Self\-evolving spatial intelligence via deterministic geometric environments\.*arXiv preprint arXiv:2604\.14144*, 2026\.
- Li et al\. \(2025c\)Li, H\., Li, D\., Wang, Z\., Yan, Y\., Wu, H\., Zhang, W\., Shen, Y\., Lu, W\., Xiao, J\., and Zhuang, Y\.Spatialladder: Progressive training for spatial reasoning in vision\-language models, 2025c\.URL[https://arxiv\.org/abs/2510\.08531](https://arxiv.org/abs/2510.08531)\.
- Lian et al\. \(2025\)Lian, S\., Wu, C\., Yang, L\. T\., Yuan, H\., Yu, B\., Zhang, L\., and Chen, K\.Euclid’s gift: Enhancing spatial perception and reasoning in vision\-language models via geometric surrogate tasks, 2025\.URL[https://arxiv\.org/abs/2509\.24473](https://arxiv.org/abs/2509.24473)\.
- Liu et al\. \(2025a\)Liu, C\., Xu, Z\., Wei, Q\., Wu, J\., Zou, J\., Wang, X\. E\., Zhou, Y\., and Liu, S\.More thinking, less seeing? assessing amplified hallucination in multimodal reasoning models\.*arXiv preprint arXiv:2505\.21523*, 2025a\.
- Liu et al\. \(2025b\)Liu, M\., Diao, S\., Lu, X\., Hu, J\., Dong, X\., Choi, Y\., Kautz, J\., and Dong, Y\.Prorl: Prolonged reinforcement learning expands reasoning boundaries in large language models, 2025b\.URL[https://arxiv\.org/abs/2505\.24864](https://arxiv.org/abs/2505.24864)\.
- Liu et al\. \(2025c\)Liu, Y\., Zhang, B\., Zang, Y\., Cao, Y\., Xing, L\., Dong, X\., Duan, H\., Lin, D\., and Wang, J\.Spatial\-ssrl: Enhancing spatial understanding via self\-supervised reinforcement learning, 2025c\.URL[https://arxiv\.org/abs/2510\.27606](https://arxiv.org/abs/2510.27606)\.
- Meng et al\. \(2025\)Meng, F\., Du, L\., Liu, Z\., Zhou, Z\., Lu, Q\., Fu, D\., Shi, B\., Wang, W\., He, J\., Zhang, K\., et al\.Mm\-eureka: Exploring visual aha moment with rule\-based large\-scale reinforcement learning\.*arXiv preprint arXiv:2503\.07365*, 2025\.
- OpenAI \(2024\)OpenAI\.Learning to reason with llms, September 2024\.URL[https://openai\.com/index/learning\-to\-reason\-with\-llms/](https://openai.com/index/learning-to-reason-with-llms/)\.
- OpenAI \(2025\)OpenAI\.Openai o3\-mini system card, 2025\.URL[https://cdn\.openai\.com/o3\-mini\-system\-cardfeb10\.pdf](https://cdn.openai.com/o3-mini-system-cardfeb10.pdf)\.
- Ouyang et al\. \(2025\)Ouyang, K\., Liu, Y\., Wu, H\., Liu, Y\., Zhou, H\., Zhou, J\., Meng, F\., and Sun, X\.Spacer: Reinforcing mllms in video spatial reasoning, 2025\.URL[https://arxiv\.org/abs/2504\.01805](https://arxiv.org/abs/2504.01805)\.
- Qin et al\. \(2025\)Qin, L\., Gong, J\., Sun, Y\., Li, T\., Yang, M\., Yang, X\., Qu, C\., Tan, Z\., and Li, H\.Uni\-cot: Towards unified chain\-of\-thought reasoning across text and vision\.*arXiv preprint arXiv:2508\.05606*, 2025\.
- Ray et al\. \(2025\)Ray, A\., Duan, J\., Brown, E\., Tan, R\., Bashkirova, D\., Hendrix, R\., Ehsani, K\., Kembhavi, A\., Plummer, B\. A\., Krishna, R\., Zeng, K\.\-H\., and Saenko, K\.Sat: Dynamic spatial aptitude training for multimodal language models, 2025\.URL[https://arxiv\.org/abs/2412\.07755](https://arxiv.org/abs/2412.07755)\.
- Rodriguez et al\. \(2025\)Rodriguez, J\. A\., Puri, A\., Agarwal, S\., Laradji, I\. H\., Rodríguez, P\., Rajeswar, S\., Vázquez, D\., Pal, C\., and Pedersoli, M\.Starvector: Generating scalable vector graphics code from images and text\.In*Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\)*, pp\. 16175–16186, 2025\.
- Sarch et al\. \(2025\)Sarch, G\., Saha, S\., Khandelwal, N\., Jain, A\., Tarr, M\. J\., Kumar, A\., and Fragkiadaki, K\.Grounded reinforcement learning for visual reasoning\.*arXiv preprint arXiv:2505\.23678*, 2025\.
- Shao et al\. \(2024\)Shao, Z\., Wang, P\., Zhu, Q\., Xu, R\., Song, J\., Bi, X\., Zhang, H\., Zhang, M\., Li, Y\., Wu, Y\., et al\.Deepseekmath: Pushing the limits of mathematical reasoning in open language models\.*arXiv preprint arXiv:2402\.03300*, 2024\.
- Shepard & Metzler \(1971\)Shepard, R\. N\. and Metzler, J\.Mental rotation of three\-dimensional objects\.*Science*, 171\(3972\):701–703, 1971\.
- Singh et al\. \(2025\)Singh, A\., Fry, A\., Perelman, A\., Tart, A\., Ganesh, A\., El\-Kishky, A\., McLaughlin, A\., Low, A\., Ostrow, A\., Ananthram, A\., Nathan, A\., Luo, A\., Helyar, A\., Madry, A\., Efremov, A\., Spyra, A\., Baker\-Whitcomb, A\., Beutel, A\., Karpenko, A\., Makelov, A\., Neitz, A\., Wei, A\., Barr, A\., Kirchmeyer, A\., Ivanov, A\., Christakis, A\., Gillespie, A\., Tam, A\., Bennett, A\., Wan, A\., Huang, A\., Sandjideh, A\. M\., Yang, A\., Kumar, A\., Saraiva, A\., Vallone, A\., Gheorghe, A\., Garcia, A\. G\., Braunstein, A\., Liu, A\., Schmidt, A\., Mereskin, A\., Mishchenko, A\., Applebaum, A\., Rogerson, A\., Rajan, A\., Wei, A\., Kotha, A\., Srivastava, A\., Agrawal, A\., Vijayvergiya, A\., Tyra, A\., Nair, A\., Nayak, A\., Eggers, B\., Ji, B\., Hoover, B\., Chen, B\., Chen, B\., Barak, B\., Minaiev, B\., Hao, B\., Baker, B\., Lightcap, B\., McKinzie, B\., Wang, B\., Quinn, B\., Fioca, B\., Hsu, B\., Yang, B\., Yu, B\., Zhang, B\., Brenner, B\., Zetino, C\. R\., Raymond, C\., Lugaresi, C\., Paz, C\., Hudson, C\., Whitney, C\., Li, C\., Chen, C\., Cole, C\., Voss, C\., Ding, C\., Shen, C\., Huang, C\., Colby, C\., Hallacy, C\., Koch, C\., Lu, C\., Kaplan, C\., Kim, C\., Minott\-Henriques, C\., Frey, C\., Yu, C\., Czarnecki, C\., Reid, C\., Wei, C\., Decareaux, C\., Scheau, C\., Zhang, C\., Forbes, C\., Tang, D\., Goldberg, D\., Roberts, D\., Palmie, D\., Kappler, D\., Levine, D\., Wright, D\., Leo, D\., Lin, D\., Robinson, D\., Grabb, D\., Chen, D\., Lim, D\., Salama, D\., Bhattacharjee, D\., Tsipras, D\., Li, D\., Yu, D\., Strouse, D\., Williams, D\., Hunn, D\., Bayes, E\., Arbus, E\., Akyurek, E\., Le, E\. Y\., Widmann, E\., Yani, E\., Proehl, E\., Sert, E\., Cheung, E\., Schwartz, E\., Han, E\., Jiang, E\., Mitchell, E\., Sigler, E\., Wallace, E\., Ritter, E\., Kavanaugh, E\., Mays, E\., Nikishin, E\., Li, F\., Such, F\. P\., de Avila Belbute Peres, F\., Raso, F\., Bekerman, F\., Tsimpourlas, F\., Chantzis, F\., Song, F\., Zhang, F\., Raila, G\., McGrath, G\., Briggs, G\., Yang, G\., Parascandolo, G\., Chabot, G\., Kim, G\., Zhao, G\., Valiant, G\., Leclerc, G\., Salman, H\., Wang, H\., Sheng, H\., Jiang, H\., Wang, H\., Jin, H\., Sikchi, H\., Schmidt, H\., Aspegren, H\., Chen, H\., Qiu, H\., Lightman, H\., Covert, I\., Kivlichan, I\., Silber, I\., Sohl, I\., Hammoud, I\., Clavera, I\., Lan, I\., Akkaya, I\., Kostrikov, I\., Kofman, I\., Etinger, I\., Singal, I\., Hehir, J\., Huh, J\., Pan, J\., Wilczynski, J\., Pachocki, J\., Lee, J\., Quinn, J\., Kiros, J\., Kalra, J\., Samaroo, J\., Wang, J\., Wolfe, J\., Chen, J\., Wang, J\., Harb, J\., Han, J\., Wang, J\., Zhao, J\., Chen, J\., Yang, J\., Tworek, J\., Chand, J\., Landon, J\., Liang, J\., Lin, J\., Liu, J\., Wang, J\., Tang, J\., Yin, J\., Jang, J\., Morris, J\., Flynn, J\., Ferstad, J\., Heidecke, J\., Fishbein, J\., Hallman, J\., Grant, J\., Chien, J\., Gordon, J\., Park, J\., Liss, J\., Kraaijeveld, J\., Guay, J\., Mo, J\., Lawson, J\., McGrath, J\., Vendrow, J\., Jiao, J\., Lee, J\., Steele, J\., Wang, J\., Mao, J\., Chen, K\., Hayashi, K\., Xiao, K\., Salahi, K\., Wu, K\., Sekhri, K\., Sharma, K\., Singhal, K\., Li, K\., Nguyen, K\., Gu\-Lemberg, K\., King, K\., Liu, K\., Stone, K\., Yu, K\., Ying, K\., Georgiev, K\., Lim, K\., Tirumala, K\., Miller, K\., Ahmad, L\., Lv, L\., Clare, L\., Fauconnet, L\., Itow, L\., Yang, L\., Romaniuk, L\., Anise, L\., Byron, L\., Pathak, L\., Maksin, L\., Lo, L\., Ho, L\., Jing, L\., Wu, L\., Xiong, L\., Mamitsuka, L\., Yang, L\., McCallum, L\., Held, L\., Bourgeois, L\., Engstrom, L\., Kuhn, L\., Feuvrier, L\., Zhang, L\., Switzer, L\., Kondraciuk, L\., Kaiser, L\., Joglekar, M\., Singh, M\., Shah, M\., Stratta, M\., Williams, M\., Chen, M\., Sun, M\., Cayton, M\., Li, M\., Zhang, M\., Aljubeh, M\., Nichols, M\., Haines, M\., Schwarzer, M\., Gupta, M\., Shah, M\., Huang, M\., Dong, M\., Wang, M\., Glaese, M\., Carroll, M\., Lampe, M\., Malek, M\., Sharman, M\., Zhang, M\., Wang, M\., Pokrass, M\., Florian, M\., Pavlov, M\., Wang, M\., Chen, M\., Wang, M\., Feng, M\., Bavarian, M\., Lin, M\., Abdool, M\., Rohaninejad, M\., Soto, N\., Staudacher, N\., LaFontaine, N\., Marwell, N\., Liu, N\., Preston, N\., Turley, N\., Ansman, N\., Blades, N\., Pancha, N\., Mikhaylin, N\., Felix, N\., Handa, N\., Rai, N\., Keskar, N\., Brown, N\., Nachum, O\., Boiko, O\., Murk, O\., Watkins, O\., Gleeson, O\., Mishkin, P\., Lesiewicz, P\., Baltescu, P\., Belov, P\., Zhokhov, P\., Pronin, P\., Guo, P\., Thacker, P\., Liu, Q\., Yuan, Q\., Liu, Q\., Dias, R\., Puckett, R\., Arora, R\., Mullapudi, R\. T\., Gaon, R\., Miyara, R\., Song, R\., Aggarwal, R\., Marsan, R\., Yemiru, R\., Xiong, R\., Kshirsagar, R\., Nuttall, R\., Tsiupa, R\., Eldan, R\., Wang, R\., James, R\., Ziv, R\., Shu, R\., Nigmatullin, R\., Jain, S\., Talaie, S\., Altman, S\., Arnesen, S\., Toizer, S\., Toyer, S\., Miserendino, S\., Agarwal, S\., Yoo, S\., Heon, S\., Ethersmith, S\., Grove, S\., Taylor, S\., Bubeck, S\., Banesiu, S\., Amdo, S\., Zhao, S\., Wu, S\., Santurkar, S\., Zhao, S\., Chaudhuri, S\. R\., Krishnaswamy, S\., Shuaiqi, Xia, Cheng, S\., Anadkat, S\., Fishman, S\. P\., Tobin, S\., Fu, S\., Jain, S\., Mei, S\., Egoian, S\., Kim, S\., Golden, S\., Mah, S\., Lin, S\., Imm, S\., Sharpe, S\., Yadlowsky, S\., Choudhry, S\., Eum, S\., Sanjeev, S\., Khan, T\., Stramer, T\., Wang, T\., Xin, T\., Gogineni, T\., Christianson, T\., Sanders, T\., Patwardhan, T\., Degry, T\., Shadwell, T\., Fu, T\., Gao, T\., Garipov, T\., Sriskandarajah, T\., Sherbakov, T\., Kaftan, T\., Hiratsuka, T\., Wang, T\., Song, T\., Zhao, T\., Peterson, T\., Kharitonov, V\., Chernova, V\., Kosaraju, V\., Kuo, V\., Pong, V\., Verma, V\., Petrov, V\., Jiang, W\., Zhang, W\., Zhou, W\., Xie, W\., Zhan, W\., McCabe, W\., DePue, W\., Ellsworth, W\., Bain, W\., Thompson, W\., Chen, X\., Qi, X\., Xiang, X\., Shi, X\., Dubois, Y\., Yu, Y\., Khakbaz, Y\., Wu, Y\., Qian, Y\., Lee, Y\. T\., Chen, Y\., Zhang, Y\., Xiong, Y\., Tian, Y\., Cha, Y\., Bai, Y\., Yang, Y\., Yuan, Y\., Li, Y\., Zhang, Y\., Yang, Y\., Jin, Y\., Jiang, Y\., Wang, Y\., Wang, Y\., Liu, Y\., Stubenvoll, Z\., Dou, Z\., Wu, Z\., and Wang, Z\.Openai gpt\-5 system card, 2025\.URL[https://arxiv\.org/abs/2601\.03267](https://arxiv.org/abs/2601.03267)\.
- Sun et al\. \(2025\)Sun, P\., Lang, S\., Wu, D\., Ding, Y\., Feng, K\., Liu, H\., Ye, Z\., Liu, R\., Liu, Y\.\-H\., Wang, J\., and Yue, X\.Spacevista: All\-scale visual spatial reasoning from mm to km, 2025\.URL[https://arxiv\.org/abs/2510\.09606](https://arxiv.org/abs/2510.09606)\.
- Team \(2025\)Team, G\.Gemini 3 pro: the frontier of vision ai, 2025\.URL[https://blog\.google/innovation\-and\-ai/technology/developers\-tools/gemini\-3\-pro\-vision//](https://blog.google/innovation-and-ai/technology/developers-tools/gemini-3-pro-vision//)\.
- Team et al\. \(2023\)Team, G\., Anil, R\., Borgeaud, S\., Alayrac, J\.\-B\., Yu, J\., Soricut, R\., Schalkwyk, J\., Dai, A\. M\., Hauth, A\., Millican, K\., et al\.Gemini: a family of highly capable multimodal models\.*arXiv preprint arXiv:2312\.11805*, 2023\.
- Wang et al\. \(2025\)Wang, S\., Pei, M\., Sun, L\., Deng, C\., Shao, K\., Tian, Z\., Zhang, H\., and Wang, J\.Spatialviz\-bench: An mllm benchmark for spatial visualization, 2025\.URL[https://arxiv\.org/abs/2507\.07610](https://arxiv.org/abs/2507.07610)\.
- Wei et al\. \(2022\)Wei, J\., Wang, X\., Schuurmans, D\., Bosma, M\., Xia, F\., Chi, E\., Le, Q\. V\., Zhou, D\., et al\.Chain\-of\-thought prompting elicits reasoning in large language models\.*Advances in neural information processing systems*, 35:24824–24837, 2022\.
- Wei et al\. \(2025\)Wei, Y\., Zhao, L\., Sun, J\., Lin, K\., Yin, J\., Hu, J\., Zhang, Y\., Yu, E\., Lv, H\., Weng, Z\., et al\.Open vision reasoner: Transferring linguistic cognitive behavior for visual reasoning\.*arXiv preprint arXiv:2507\.05255*, 2025\.
- Wu et al\. \(2025a\)Wu, D\., Liu, F\., Hung, Y\.\-H\., and Duan, Y\.Spatial\-mllm: Boosting mllm capabilities in visual\-based spatial intelligence, 2025a\.URL[https://arxiv\.org/abs/2505\.23747](https://arxiv.org/abs/2505.23747)\.
- Wu et al\. \(2025b\)Wu, J\., Guan, J\., Feng, K\., Liu, Q\., Wu, S\., Wang, L\., Wu, W\., and Tan, T\.Reinforcing spatial reasoning in vision\-language models with interwoven thinking and visual drawing, 2025b\.URL[https://arxiv\.org/abs/2506\.09965](https://arxiv.org/abs/2506.09965)\.
- Wu & Xie \(2024\)Wu, P\. and Xie, S\.V\*: Guided visual search as a core mechanism in multimodal llms\.In*Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*, pp\. 13084–13094, 2024\.
- Xiaomi & Team \(2025\)Xiaomi, L\. and Team, C\.Mimo\-vl technical report\.*arXiv preprint arXiv:2506\.03569*, 2025\.
- Xing et al\. \(2024\)Xing, X\., Zhou, H\., Wang, C\., Zhang, J\., Xu, D\., and Yu, Q\.Svgdreamer: Text guided svg generation with diffusion model\.In*Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition \(CVPR\)*, pp\. 4546–4555, 2024\.
- Yang et al\. \(2025a\)Yang, B\., Wen, B\., Ding, B\., Liu, C\., Chu, C\., Song, C\., Rao, C\., Yi, C\., Li, D\., Zang, D\., et al\.Kwai keye\-vl 1\.5 technical report\.*arXiv preprint arXiv:2509\.01563*, 2025a\.
- Yang et al\. \(2025b\)Yang, J\., Yang, S\., Gupta, A\. W\., Han, R\., Fei\-Fei, L\., and Xie, S\.Thinking in space: How multimodal large language models see, remember, and recall spaces, 2025b\.URL[https://arxiv\.org/abs/2412\.14171](https://arxiv.org/abs/2412.14171)\.
- Yang et al\. \(2025c\)Yang, S\., Xu, R\., Xie, Y\., Yang, S\., Li, M\., Lin, J\., Zhu, C\., Chen, X\., Duan, H\., Yue, X\., et al\.Mmsi\-bench: A benchmark for multi\-image spatial intelligence\.*arXiv preprint arXiv:2505\.23764*, 2025c\.
- Yang et al\. \(2025d\)Yang, Y\., Cheng, W\., Chen, S\., Zeng, X\., Yin, F\., Zhang, J\., Wang, L\., Yu, G\., Ma, X\., and Jiang, Y\.\-G\.Omnisvg: A unified scalable vector graphics generation model\.*arXiv preprint arXiv:2504\.06263*, 2025d\.
- Yang et al\. \(2025e\)Yang, Z\., Yu, X\., Chen, D\., Shen, M\., and Gan, C\.Machine mental imagery: Empower multimodal reasoning with latent visual tokens\.*arXiv preprint arXiv:2506\.17218*, 2025e\.
- Yin et al\. \(2025\)Yin, B\., Wang, Q\., Zhang, P\., Zhang, J\., Wang, K\., Wang, Z\., Zhang, J\., Chandrasegaran, K\., Liu, H\., Krishna, R\., Xie, S\., Li, M\., Wu, J\., and Fei\-Fei, L\.Spatial mental modeling from limited views\.*arXiv preprint arXiv:2506\.21458*, 2025\.
- Yu et al\. \(2023a\)Yu, E\., Zhao, L\., Wei, Y\., Yang, J\., Wu, D\., Kong, L\., Wei, H\., Wang, T\., Ge, Z\., Zhang, X\., et al\.Merlin: Empowering multimodal llms with foresight minds\.*arXiv preprint arXiv:2312\.00589*, 2023a\.
- Yu et al\. \(2025\)Yu, E\., Lin, K\., Zhao, L\., Yin, J\., Wei, Y\., Peng, Y\., Wei, H\., Sun, J\., Han, C\., Ge, Z\., Zhang, X\., Jiang, D\., Wang, J\., and Tao, W\.Perception\-r1: Pioneering perception policy with reinforcement learning, 2025\.URL[https://arxiv\.org/abs/2504\.07954](https://arxiv.org/abs/2504.07954)\.
- Yu et al\. \(2023b\)Yu, L\., Jiang, W\., Shi, H\., Yu, J\., Liu, Z\., Zhang, Y\., Kwok, J\. T\., Li, Z\., Weller, A\., and Liu, W\.Metamath: Bootstrap your own mathematical questions for large language models\.*arXiv preprint arXiv:2309\.12284*, 2023b\.
- Yue et al\. \(2023\)Yue, X\., Qu, X\., Zhang, G\., Fu, Y\., Huang, W\., Sun, H\., Su, Y\., and Chen, W\.Mammoth: Building math generalist models through hybrid instruction tuning\.*arXiv preprint arXiv:2309\.05653*, 2023\.
- Zhang et al\. \(2025a\)Zhang, X\., Cao, J\., Wei, J\., You, C\., and Ding, D\.Why does your cot prompt \(not\) work? theoretical analysis of prompt space complexity, its interaction with answer space during cot reasoning with llms: A recurrent perspective\.*arXiv e\-prints*, pp\. arXiv–2503, 2025a\.
- Zhang et al\. \(2024\)Zhang, Y\., Li, B\., Liu, h\., Lee, Y\. j\., Gui, L\., Fu, D\., Feng, J\., Liu, Z\., and Li, C\.Llava\-next: A strong zero\-shot video understanding model, April 2024\.URL[https://llava\-vl\.github\.io/blog/2024\-04\-30\-llava\-next\-video/](https://llava-vl.github.io/blog/2024-04-30-llava-next-video/)\.
- Zhang et al\. \(2025b\)Zhang, Y\.\-F\., Lu, X\., Yin, S\., Fu, C\., Chen, W\., Hu, X\., Wen, B\., Jiang, K\., Liu, C\., Zhang, T\., Fan, H\., Chen, K\., Chen, J\., Ding, H\., Tang, K\., Zhang, Z\., Wang, L\., Yang, F\., Gao, T\., and Zhou, G\.Thyme: Think beyond images, 2025b\.URL[https://arxiv\.org/abs/2508\.11630](https://arxiv.org/abs/2508.11630)\.
- Zhang et al\. \(2023\)Zhang, Z\., Zhang, A\., Li, M\., Zhao, H\., Karypis, G\., and Smola, A\.Multimodal chain\-of\-thought reasoning in language models\.*arXiv preprint arXiv:2302\.00923*, 2023\.
- Zhao et al\. \(2023\)Zhao, L\., Yu, E\., Ge, Z\., Yang, J\., Wei, H\., Zhou, H\., Sun, J\., Peng, Y\., Dong, R\., Han, C\., et al\.Chatspot: Bootstrapping multimodal llms via precise referring instruction tuning\.*arXiv preprint arXiv:2307\.09474*, 2023\.
- Zheng et al\. \(2025\)Zheng, Z\., Yang, M\., Hong, J\., Zhao, C\., Xu, G\., Yang, L\., Shen, C\., and Yu, X\.Deepeyes: Incentivizing” thinking with images” via reinforcement learning\.*arXiv preprint arXiv:2505\.14362*, 2025\.
- Zhu et al\. \(2025\)Zhu, J\., Wang, W\., Chen, Z\., Liu, Z\., Ye, S\., Gu, L\., Tian, H\., Duan, Y\., Su, W\., Shao, J\., et al\.Internvl3: Exploring advanced training and test\-time recipes for open\-source multimodal models\.*arXiv preprint arXiv:2504\.10479*, 2025\.

## Appendix AAppendix

### A\.1Data Pipeline

#### Overview\.

We construct training data via a teacher\-student pipeline, usingGemini 3\(Team,[2025](https://arxiv.org/html/2607.03530#bib.bib39)\)as the teacher model to generate SVG\-based reasoning traces\. The data underpin the two\-stage training recipe by providing both structured SVG reasoning demonstrations and reconstruction targets\.

#### Data Sources\.

The 50kVisual Thought Externalizationdata is drawn from the training splits ofMindCube\(10k\) andVSIBench\(40k\); from VSIBench we keep items that require strong visual reasoning\.

#### Prompt Templates\.

We use two prompt templates to generate the SVG reasoning and reconstruction data\.

Prompt A: SVG Reasoning[⬇](data:text/plain;base64,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)Youareanexpertinvisualthinkingwhocansolveproblemsthroughvisualization\.Whetherfacingmathematical,logical,spatial,systemdesign,orprocessanalysischallenges,youleverageSVGgraphicsasthinkingtools\.\#\#CorePrinciples\-SVGisnotdecoration,butathinkinginstrument\-Graphiccomplexityshouldmatchproblemneeds\(simplegraphicsforsimpleproblems\)\-Eachmodificationshouldbringnewunderstanding\#\#Problem\-SolvingSteps\#\#\#1\.\[ProblemModeling\]VisualizecoreelementswithSVG:\-Whatshapesrepresententities/concepts?\-Howtoshowrelationships/connections?\-Howtoannotateconstraints/conditions?\#\#\#2\.\[ExploratoryAnalysis\]DeepenunderstandingthroughSVGmanipulation:\-Transformation:Canrotation,scaling,ormovementrevealnewperspectives?\-Decomposition:Cancomplexproblemsbebrokenintosimpleparts?\-Composition:Docombinationsofelementscreatenewpatterns?\#\#\#3\.\[PatternRecognition\]AnnotatediscoveredpatternsinSVG:\-Symmetry,periodicity,recursivestructures\-Bottlenecks,criticalpaths,equilibriumpoints\-Hiddencorrelations,unexpectedsimplifications\#\#\#4\.\[SolutionConstruction\]ShowsolutionpathswithSVG:\-Forsequentialprocesses,showthesequence\-Forstructuralproblems,showthearchitecture\-Fordynamicproblems,showthetransformation\#\#ApplicationScenarios\*\*Math/Geometry\*\*:Shapetransformations,spatialrelationships,functionvisualization\*\*SystemDesign\*\*:Architecturediagrams,dataflows,statemachines\*\*LogicalReasoning\*\*:Venndiagrams,decisiontrees,causalchains\*\*ProcessAnalysis\*\*:Flowcharts,timelines,dependencies\*\*DataUnderstanding\*\*:Distributionplots,relationshipnetworks,hierarchies\#\#ResponseRequirementsForeachSVGthinkingstep,explain:1\.\[DesignIntent\]Whychoosethisvisualizationapproach?2\.\[Observations\]Whatdoesthisgraphicreveal?3\.\[ThinkingProgress\]Howdoesthischangeyourunderstanding?Remember:Goodvisualizationmakescomplexitysimple,implicitexplicit,andabstractconcrete\.

Prompt B: SVG Reconstruction[⬇](data:text/plain;base64,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)YouareanexpertSVGcodegenerator\.YourtaskistoanalyzetheprovidedimageandgeneratepreciseSVGcodethataccuratelyreconstructsthevisualelementsintheimage\.Guidelines:Carefullyobserveallvisualelementsincludingshapes,colors,text,gradients,patterns,andspatialrelationshipsGenerateclean,validSVGcodethatcanbedirectlyrenderedinanybrowserUseappropriateSVGelements\(path,rect,circle,ellipse,polygon,text,etc\.\)basedontheshapesintheimagePreserveaccurateproportions,positions,andcolorvalues\(usehexcodesorrgbvalues\)OptimizethecodeforreadabilitywhilemaintainingaccuracyIncludeproperSVGheaderwithviewBoxanddimensionsUsegroups\(<g\>\)andsemanticIDswhenappropriatefororganizationForcomplexshapes,usepathelementswithprecisecoordinatesIftheimagecontainstext,recreateitusingSVGtextelementswithappropriatefontsAddcommentstoexplaincomplexsectionsifneededOutputformat:Providecomplete,standaloneSVGcodewrappedin‘‘‘svgcodeblocksEnsurethecodeisproperlyformattedandindentedTheSVGshouldbescalableandmaintainaspectratioTestthatallpathsareclosedproperlyandcolorsareaccurateYourgoalistocreateSVGcodethat,whenrendered,producesafaithfulreproductionoftheoriginalimage\.AnsweronlytheSVGcode,noothertext\.

#### Sources and Licensing\.

We use the publicMindCubeandVSIBenchdatasets under their original licenses and usage terms\. We do not redistribute raw data; instead, we report results on their official evaluation splits\. We exclude samples that are corrupted or fail basic visual integrity checks\. From the590kVSIBench training set, we retain a40ksubset that requires strong visual reasoning\.

### A\.2Thinking with Different Patterns

To study how different intermediate reasoning representations affect learning and generalization, we construct three controlled variants of system prompts that induce distinct*thinking patterns*from the same teacher model\. All variants share identical task inputs, output requirements, and supervision signals, differing only in the form of intermediate reasoning representation\.

#### Thinking Pattern Abstraction\.

A thinking pattern is the structured intermediate representation the teacher model uses to externalize its reasoning\. We explore three: \(i\)Text\-based thinking, expressed in natural language; \(ii\)Box\-based thinking, grounded in spatial bounding boxes; \(iii\)SVG\-based thinking, expressed through executable vector graphics\. The Text\- and Box\-based variants usePrompt CandPrompt Dbelow, respectively, while the SVG\-based variant uses theSVG Reasoningprompt \(Prompt A\) from the Data Pipeline above\.

Prompt C: Text\-based Reasoning[⬇](data:text/plain;base64,WW91IG11c3QgcmVhc29uIHVzaW5nIE9OTFkgbmF0dXJhbCBsYW5ndWFnZS4KCkluc2lkZSA8dGhpbms+OgotIERlc2NyaWJlIG9iamVjdHMsIHNwYXRpYWwgcmVsYXRpb25zLCBhbmQgcmVhc29uaW5nIHN0ZXBzIHVzaW5nIHRleHQgb25seS4KLSBEbyBOT1QgdXNlIGNvb3JkaW5hdGVzLCBib3VuZGluZyBib3hlcywgU1ZHLCBkaWFncmFtcywgb3Igc3ltYm9saWMgbGF5b3V0cy4KLSBEbyBOT1QgaW52ZW50IHByZWNpc2UgbWVhc3VyZW1lbnRzLgotIEV4cHJlc3MgdW5jZXJ0YWludHkgZXhwbGljaXRseSB3aGVuIG5lZWRlZC4KClRoZSA8dGhpbms+IHNlY3Rpb24gc2hvdWxkIHJlYWQgbGlrZSBhIGNhcmVmdWwgaHVtYW4gcmVhc29uaW5nIHByb2Nlc3MKdGhhdCBpbnRlcnByZXRzIHRoZSB2aXN1YWwgc2NlbmUgdmVyYmFsbHkuCgpBZnRlciA8dGhpbms+LCBvdXRwdXQgdGhlIGZpbmFsIGFuc3dlciBpbiBcXGJveGVke30u)YoumustreasonusingONLYnaturallanguage\.Inside<think\>:\-Describeobjects,spatialrelations,andreasoningstepsusingtextonly\.\-DoNOTusecoordinates,boundingboxes,SVG,diagrams,orsymboliclayouts\.\-DoNOTinventprecisemeasurements\.\-Expressuncertaintyexplicitlywhenneeded\.The<think\>sectionshouldreadlikeacarefulhumanreasoningprocessthatinterpretsthevisualsceneverbally\.After<think\>,outputthefinalanswerin\\\\boxed\{\}\.

Prompt D: Bounding\-box Reasoning[⬇](data:text/plain;base64,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)Youmustreasonusingstructuredboundingboxrepresentations\.Inside<think\>:\-Representeachrelevantobjectusinganaxis\-alignedboundingbox\.\-Usenormalizedcoordinatesin\[0,1000\]\.\-Formateachobjectas:ObjectName:bbox\(x\_min,y\_min,x\_max,y\_max\)\-Useboundingboxestoinferspatialrelationships\.\-DoNOTuseSVG,curves,paths,orfree\-formdrawings\.\-DoNOTdescribeshapesbeyondwhatboundingboxescanrepresent\.Afterlistingboundingboxes,explicitlyreasonaboutspatialrelations\(left/right/front/behind/overlapping\)basedontheboxes\.After<think\>,outputthefinalanswerin\*\*\\\\boxed\{\}\*\*\.

### A\.3More Case Studies

We present more case studies to illustrate the SVG reconstruction capability \(Figure[4](https://arxiv.org/html/2607.03530#A1.F4)\) and thethink\-with\-SVGcapability \(Figures[5](https://arxiv.org/html/2607.03530#A1.F5)and[6](https://arxiv.org/html/2607.03530#A1.F6)\) ofMentalThink\.

![Refer to caption](https://arxiv.org/html/2607.03530v1/x4.png)Figure 4:Additional case studiesfor the SVG reconstruction capability ofMentalThink\.![Refer to caption](https://arxiv.org/html/2607.03530v1/x5.png)Figure 5:Additional case studiesforthink\-with\-SVGreasoning ofMentalThink\(1/2\)\.![Refer to caption](https://arxiv.org/html/2607.03530v1/x6.png)Figure 6:Additional case studiesforthink\-with\-SVGreasoning ofMentalThink\(2/2\)\.