Multi-step Visual Reasoning with Visual Tokens Scaling and Verification
Authors: Tianyi Bai
Zengjie Hu
Fupeng Sun
Qiu Jiantao
Yizhen Jiang
Guangxin He
Bohan Zeng
Conghui He
Binhang Yuan
Wentao Zhang
Venue: NeurIPS 2025 poster ()
Keywords: MLLMs
Primary area: deep_learning

Abstract: Multi-modal large language models (MLLMs) have achieved remarkable capabilities by integrating visual perception with language understanding, enabling applications such as image-grounded dialogue, visual question answering, and scientific analysis. However, most MLLMs adopt a static inference paradigm, encoding the entire image into fixed visual tokens upfront, which limits their ability to iteratively refine understanding or adapt to context during inference. This contrasts sharply with human perception, which is dynamic, selective, and feedback-driven.
In this work, we introduce a novel framework for inference-time visual token scaling that enables MLLMs to perform iterative, verifier-guided reasoning over visual content. We formulate the problem as a Markov Decision Process, involving a reasoner that proposes visual actions and a verifier—trained via multi-step Direct Preference Optimization (DPO)—that evaluates these actions and determines when reasoning should terminate. To support this, we present a new dataset, VTS, comprising supervised reasoning trajectories (VTS-SFT) and preference-labeled reasoning comparisons (VTS-DPO).
Our method significantly outperforms existing approaches across diverse visual reasoning benchmarks, offering not only improved accuracy but also more interpretable and grounded reasoning processes. These results demonstrate the promise of dynamic inference mechanisms for enabling fine-grained, context-aware visual reasoning in next-generation MLLMs. Code and datasets are publicly released at https://vts-v.github.io/.

Multi-Step Visual Reasoning with Visual Tokens Scaling and Verification
Tianyi B.i Zengjie Hu Fupeng Sun Jiantao Qiu Yizhen Jiang", Guangxin He', Bohan Zeng", Conghui He Binhang Yuan' Wentao Zhang?)
'The Hong Kong University of Science and Technology, PPeking University Shanghai Artificial Intelligence Laboratory. *Imperial College London heconghui@ppjab. org. en, biyuan@ust. hk, wentao. zhang@pku. edu. edu.
Abstract
Multi-modal large language models (MLLMs) have achieved remarkable capa- bilities by integrating visual perception with language understanding, enabling applications such image-grounded dialogue, visual question answering, and scientific analysis. However, most MILMs adopt static inference paradigm, en- coding the entire image into fixed visual tokens upfront, which limits their ability iteratively refine understanding or adapt to context during inference. This contrasts sharply with human perception, which is dynamic, selective, and (eedback-driven In this work, we introduce a novel framework for inference- -iteeecceeeieeeeee visual token scaling that enables MLLMs to perform iterative, verifier verifier-guided reasoning over visual content. We formulate the problem reasoner that proposes visual actions and a terifier-trainee via multi-step Di- rect Preference Optimization (DPO) that evaluates these actions and determines when reasoning should terminate. To support this, we present new dataset, VTS, comprising supervised reasoning trajectories (VTS-SFT) and preference-labelee reasoning comparisons (VTS-DPO). Our method significantly outperforms existing approaches across diverse visual reasoning benchmarks, offering not only improved accuracy but also more interpretable and grounded reasoning processes. These results demonstrate the promise of dynamic inference mechanisms for enabling line-grained context-aware visual reasoning in next- next-gennration MLLMs. Code and datasets are publicly released at https: : //vtsvvtvv github.. io/.
Markov Decision Process, involving
Introduction
Multi-modal large language models (MLLMs) that perceive and reason over visual content a foundational component modern AI systems. By extending large language models (LLMs) with visual perception capabilities, MLLMs support wide range of applications- from image- grounded dialogue and visual question answering to robotics and scientific analysis. Yet despite their impressive generalization, one fundamental challenge remains unsolved: how conduct effective inference-tine scaling for MLLMs to enable fine- grained, context-aver aware interaction with visual information?
Current MILMS typically adopt static inference static fixed set of visual tokens in single step, and conducting all reasoning based solely on this static embedding. This approach limits the model's ability to recover from ambiguity, occlusion, or missing
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Figure I: Iterative Visual Reasoning with VTS-V. Our framework equips both open-source and closed-source models with dynamic visual token scaling and step-wise verification to solve complex visual tasks. The example shows how VTS-V: (1) decomposes questions into executable steps, (2) invokes vision tools, and (3) iteratively refines answers via verifier feedback, achieving correct results. In contrast, vanilla models fail to ground detailed visual operations without token scaling, leading to incorrect answers.
detail: once the initial representation is formed, there is no mechanism to query the image again or refine visual understanding. In contrast, human perception is inherently dynamic-w iteratively inspect regions, zoom in, and seek new visual evidence as reasoning unfolds. Bridging this gap between static MILMM inference and dynamic human reasoning is the central problem addressed in this work.
Multi-step visual reasoning is critical for robust AI systems. Many tasks require identifying small objects, interpreting text in images, or reasoning about spatial relations-activities that benefit from an iterative, context-sensitive exploration of visual content. Furthermore, dynamic scaling enables more efficient reasoning by focusing computational resources on the most relevant parts of the image, rather than uniformly processing all pixels or tokens. Without this flexibility, existing models exhibit degraded performance on benchmarks such as BLINK [6], V-Star Bench [27], and MMVP [23]. which are designed to probe deeper visual understanding.
The core technical challenge lies in the absence of expressive framework for flexible, inference- time visual exploration. Existing approaches either construct improved visual reasoning datasets for fine-tuning [7, 21]. which still rely heavily on the pretrained model's image-text alignment quality, or attempt to enhance inference through text token scaling [2] and the use of external vision tools [11, 8, 22, 27]. However, these methods are limited in scope, focusing narrowly on static token expansion or employing small set of fixed visual tools in predefined pipelines. As a result, these methods fail to give the model agency in choosing what to observe next, how focus visual attention, or when to stop reasoning. What's needed is a unified framework that allows the model to take structured, interpretable visual actions-guiln by image content.
Contributions. To address this, we propose novel framework for inference-time visual token scaling, enabling MLLMs to engage in iterative, verifier-guided reasoning over images, Our contributions are threefold:

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Expressive and theoretically grounded framework. We formulate visual reasoning as a Markov Decision Process (MDP) with two key components: a reasoner that proposes visual actions, and a verifier, trained via multi-step Direct Preference Optimization (DPO), which evaluates action quality and terminates reasoning when appropriate. We prove that our reasoner and verifier cooperation system ensures alignment between reasoning actions and visual content, while guaranteeing bounded number of steps through an early stopping mechanism.
A new dataset for tool-augmented visual reasoning. We introduce two-part dataset: VIS-SFT (supervised reasoning trajectories with tool use), and VTS-DPO (preference-labeled reasoning pairs). These resources enable effective training of both the reasoner and verifier, supporting dynamic visual interaction with multi-step grounding.
Comprehensive evaluation and state-of-the-art results. Our experiments span variety of Vision-language tasks demanding multi-step reasoning. Across these scenarios, our approach significantly outperforms strong baselines, including models augmented with limited tool use and those employing ofain-of-thought prompting. We observe not only accuracy improvements but also more interpretable reasoning traces, the model's step-b process explicitly justifies each answer with visual evidence. These results underscore the effectiveness of inference-tine seeence--mmeeeee visual token scaling: by enabling an AI look deeper into images in controlled, stepwise fashion, achieve new state-of-the-an performance on tasks that previously stymied conventional MLL.ss
These contributions move us toward flexible, grounded, and interpretable visual reasoning in crucial for building AI systems that can "think with their eyes."
2
Related Work
Visual reasoning, Visual reasoning in VLMs focuses on integrating visual and textual inputs to
enable effective Docisiin-mmakngg Early approaches, such as Shikra [2), applied Chain of Thought
(26T))26) techniques to visual tasks. Meanwhile, methods like SoM[29] and Scaffolding [13] improved reasoning by leveraging visual anchors, such as segmentation maps. V [27] introduced a
two-step CoT approach for high-resolution visual search, demonstrating the potential of structured reasoning in visual contexts. More recently, efforts have been made to develop improved reasoning datasets for training visual language models (VLMs) [21, 7]. However, most of this work primarily focuses on scaling text tokens during the visual reasoning phase. Limited attention has been given to frameworks that scale visual tokens to address complex visual reasoning tasks.
Visual programming and tool-using. Recent research has focused on integrating visual tools with large language models (LLMs) and vision- sainunla models (VLMs) to address complex visual tasks. These studies aim to leverage LLMs and VLMs to generate code that utilizes external vision tools for solving complex vision problems [11, 8, 22, 31J. For instance, Visprog [8] and ViperGPT [22] prompt VLMs produce single-step Python code that interacts with external vision tools, while Visual Sketchpad [10] enhances these methods by introducing multi-step reasoning capabilities, enabling VLMs to rethink and correct execution errors. However, these approaches fail address the critical aspect of iterative visual reasoning, as their reasoning steps are typically limited to only 1-2 steps. This prevents them from performing reflective refinements akin VLMs, hindering their ability to tackle complex visual tasks that require deeper inference and multi-step adjustments.
Verifier design. Recent advancements have leveraged verifiers to enhance language model rea- soning and solution quality. Approaches include deriving reward signals for reasoning [15, 16], combining solution- and step-level verifiers for math problems [33], and using graph search or Monte Carlo rollouts for rationale generation [19, 24]. Training methods range from human annotations for RL with feedback [34] to synthetic data for RL with AI feedback [30]. Some treat verifiers as generative models, scoring solutions via control tokens [12] or likelihoods [17]. Closely related is V-STaR [9], which uses Direct Preference Optimization (DPO) for solution ranking. However, existing verifiers are typically designed for specific tasks and tailored training datasets. Our work utilizes multi-step DPO as a verification mechanism, supported by theoretical guarantees.
3 Visual Tokens Scaling with Verification
We first formally formulate the visual reasoning tasks with visual token scaling and verification.
3

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3.1 Problem Formulation
At the first step, -question-image pair $1 is sampled from some distribution D as the initial state. For each step 2 2, we conduct:
Planning: the VLM observes the current state 8h, which is the history of the previous h reasoning steps, i.e., = (sh-1: 11, 04-1, 0h-1), ). and generates planning of h-th step t by some distribution p(- 8n). in can be regarded as the text tokens and determines how to manipulate the image at the h-th step.
Action: based on planning 4, the VLM further chooses an action On E A according to policy T(- tA), where A is the finite action (module) set. This means that the VLM decides which visual module to implement for a specific instruction ty--
Observation: in response the action, the environment then returns a visual observation Oh = San, (fx) for some deterministic function f. Here the visual observation is assumed to be deterministic since it is the code execution result by some visual module, the depth map of an image, for example.
Then we transit to a new state 8h+1 and a new reasoning step begins.
Verification: after each set of planning, action and observation, verifier r* designed to decide whether to continue this iterative reasoning, or to stop and give out the final result.
We regard the final planning as the final result the initial question-image pair. Eventually, we will collect reasoning sequence
(81, a1, 01,-..,H,, - HH,, OH,, (1) sH, +1 U (fu,++) +1},
(I)
where H, (a random variable) is the length of the total reasoning steps for path т.
3.2 Visual Reasoning with Visual Token Scaling and Verification
To enhance performance in visual reasoning tasks, the reasoning process will consist of main components: a reasoner capable of generating visual reasoning steps, and verifier that guides the reasoner in visual token scaling and determines the terminal condition.
Reasoner. The reasoner is a pre-trained VLM augmented with plug-and-play modules, which are denoted by RØ where On encapsulates all the parameters. The module tools can be off- sheflf vision models (depth maps, bounding box generation, etc), table operations (add columns, select row, etc), web search engines, and Python functions (plot figures, calculation, etc). The reasoner supposed to present the reasoning steps in a sequential format as in equation (1), where p(- 8%) = Ra (- 88) and 7- | (.)= (- 4.). In practice, the reasoner can be: (i) a model such GPT-4o; (ii) an open-source model fine-tuned on self-crafted datasets. In this case, 0g can be further updated to ÔSFT by SFT.
Verifier. The verifier rd is function that maps the reasoning trajectory generated by the reasoner to a real number, At each reasoning step h, the reasoner will continue to generate one additional step the reward difference between step and step + 1 is no less than some predetermined positive threshold In this paper, we utilize a verifier derived from multi-step DPO [28]. Specifically, we begin with a base VLM Vo,, capable of generating reasoning sequences, where do is known and encompasses all the parameters. Using multi-step DPO with preference data, do is further updated to 'SDPO. Consequently, the verifier can be represented by Voo and V Vixeo jointly.
3.3 Reasoner and Verifier Training
The training stage is divided into parts: fine-tuning the reasoner with SFT and verifier training based on DPO (answer level and multi-step level). Correspondingly, the training dataset consists DSFT and DDPO, we will describe the details of Visual Tokens Scaling SFT and DPO training dataset construction in Section 4.
Fine-tune the reasoner by SFT. Suppose have base reasoning model Reg-
SFT training. Given a Visual Token Scaling SFT training dataset DSFT. the supervised finetuning process refers to the learning of reasoner Rg through minimizing the following cross-entropy loss
s == argmin,
Σ TEDSE
LSFT (Ro TT),T)
|Derr
H, H,+1
In practice, will also include system prompts.

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where -)Fr(.,)) is defined as
H. +1
H. log R (ah (t))
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Σ
log Rş (t%
sh))
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h=1
h=
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0 0 a
1
E
1
VLSFT (Ro (7).T).
(3)
(DSTT
H, +++1
TED
where is the learning rate and the initial parameter is 0g-
Verifier training by DPO, We use multi-step DPO to derive the desired verifier that aligns with human preferences, building upon base VLM Voy. such as LLaVA-v1.5-7B. Suppose we are given preference pairs (81, 75, "0 -²), where 7 is preferred trajectory over unpreferred trajectory r'.
The key idea of multi-step DPO is assume that belongs a family of one-parameter functions (ra(-)) i.e., r-)) = Tisuro (-) for some unknown ground truth parameter ΦSDPO. Specifically, if (-))) is defined
H.
Vo (th shh) Vo (th. 5h)
H log
Vá
(as
th. (h)
(T(
log
+ Q(s1),
h=1 Voo
(an
where is a positive constant and Q(-) is fixed function that depends only on 81, then the preference model V éumo will align with the verifier Tésono while remaining close the original Vop automatically, as shown by Equation 8 and Proposition A.1.
Furthermore, OSDPO be determined by maximizing the expected likelihood under the Bradley- Terry model
E (( ,t) [IP (7" > =r)]]
(4)
where
(T - -4) (r" (T
(T'))
(5)
Once dsDPP is obtained, the verifier Téssoo can be used to guide the reasoner in generating the reasoning procedure. The detailed training procedure is as follows.
Multi-step DPO. Define the empirical multi-step DPO loss LSPPO (ø, do) by equation (11). Let
ŌSDrO = argmin CsDro (ø, Φo),
then dspro can be obtained by the iteration of gradient descent
Φu+1 = 02 a'
Σ
VLSDPO (Ø, do),
(6)
where a' is the learning rate and the initial parameter is do. The verifier r" operates some reasoning trajectory т could be approximated by "innro (T).
3.4 Inference Algorithm with Practical Efficiency and Theoretical Guarantees
In this subsection, we show our algorithm during inference time and the theoritical guarantees.
Given new test pair 81 D. use the verifier V V to instruct reasoner whether to continue generating the reasoning sequence. Assume a reasoning sequence 5h is generated by the reasoner Regh" We determine whether Rāgz need to generate one additional reasoning step
the reasoner Rigr for scaling the inference sequence, and
ty Rost (- 1t), az RoSer tw), On fap (tw),
81+1 = (sh, la ah, on),
by checking whether |rasvo (SK+1) "aseo (sn) 6, where e is some predetermined positive threshold. We repeat such procedure unless | T'soo (9h+1) Téxnoo (sx) < e. The following lemma gives equivalent explicit termination condition.
5

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Lemma 3.1. The reasoner Ro, stops at the reasoning step h if
V Senro (fn. 1 1%2)
log V Vanno (an 1/h
Traaro (sn+1) "ésoro (8n) <<
log
<.
Vao (4p s9)))
Voo (4 1
Algorithm characterizes the full training and test procedure of our method.
Given ~ D, denote by H (ŌSDPO, Φo; (SFT the total reasoning step given by Algorithm 1, the next theorem shows that H, (ōSTPO, Φo: SSFT is finite almost surely (a.s.).
Theorem 3.2 (Reasoning steps characterization). The total reasoning step satisfies that
1. H, (ōspro, ou: BSrT) is a stopping time.
2. (Informal). Under some mild condition, H, (ōsoro, do; 0srr) is finite with probability
Theorem 3.2 shows that our algorithm is not only flexible-allownng variational reasoning steps that improve upon the results of Xiong et al. [28]-but also guarantees a bounded number of reasoning steps. This ensures that our method avoids scenarios in which the reasoner would otherwise produce looping or repetitive outputs. The detailed proof can be found in Appendix A.4. The superiority of our algorithm can be shown the following experiments.
4 Visual Tokens Scaling Dataset Construction
As discussed in Section 3, our goal is to train a reasoner capable of performing visual token scaling-namely, -namely, learning to invoke visual understanding tools throughout the reasoning process to generate intermediate images rich in detailed visual token information. At the same time, we aim to train a verifier that can distinguish between two reasoning trajectories of similar structure for the same task, identifying the one that more effectively scales visual information. This collaborative setup enables the verifier to guide and refine the reasoner's 's visual reasoning process.
However, a major challenge lies in the absence of existing datasets that contain long-chain, tool- grounded reasoning traces with rich intermediate visual states. In particular, no existing datasets provide both detailed visual CoT--ttyle supervision and curated accepted-rejected trajectory pairs required for DPO training. To address this, we construct a dedicated dataset by building upon the tongleiimage dataset of the LLaVA-One Vision dataset (LLaVA-OV [14], which contains 3.2M lsiiunlangguae examples covering a broad range of tasks.
In this section, we describe our dataset construction pipeline in detail. Section 4.1 introduces how we collect and preprocess visual reasoning examples from VLLVVAOVV produce structured tool-based trajectories. Section 4.2 then explains how we derive both the SFT and DPO datasets from these verified trajectories.
4.1 Visual Token Scaling Dataset Collection and Preprocessing
We begin our dataset construction by sampling maage-question pairs from the single-image portion of the LLaVA-ON OV dataset, which covers wide range of languanl tasks such as grounding, chart understanding. OCR, and mathematica reasoning. To ensure sufficient task diversity, we uniformly sample across all 83 task types included in the dataset.
For each sampled example, we employ Qwen-2.5 2.5en-2.5VLL-- 5-VL-72B in a few-shot prompting setting to gener- visual token scaling trajectory. This trajectory is composed of sequence of tool-based operations drawn from our predefined action space A (as described in Section 3.1). In line with prior work [8, 1 I]], the action space comprises ten visual tools: GroundingAction, DepthAction, ZoomInAction. srualSearchAction Crop, OCR, ImageSegment, ImageCaptioner: Similarite AimilarityComputt ing. and Overlay. These tools allow the model iteratively perceive, transform, and enrich the visual content throughout the multi-step reasoning process.
Generated trajectories may include errors, invalid tool use, or inconsistent reasoning. We apply preprocessing pipeline to flatten nested structures, merge related turns, remove malformed examples, and ensure metadata consistency. We also filter out trivial cases with tool use and those exceeding 20,000 tokens due to memory limits. To guarantee the correctness of each trajectory, we employ
$ For notation simplicity, here omit the dependence 81.

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Figure 2: Pipeline for Synthetic Data Generation and Curation in VTS-V. Our data construction process consists of three stages: (1) generating multi-step reasoning trajectories with visual tool calls, (2) filtering out incorrect trajectories using an LLM-as-aa-udde framework, and (3) creating contrastive (correct vs. incorrect) trajectory pairs for multi-step DPO training.
the same 5-VL-7BB model an LLM-based verifier (11m_ j_jueee) to filter out those whose final answers are deemed incorrect. Starting from over 650K generated trajectories, this process results in curated set of 315K high-quality visual token scaling examples, which serve as the basis for supervised fine-tuning and preference training.
4.2 VTS-SFT and VTS-DPO Dataset Construction
Starting from the 315K verified visual token scaling trajectorics described above, we construct two datasets: one for supervised fine-tuning (VTS-SFT) and one for direct preference optimization (VTS-DPO).
VTS-SFT Dataset Construction. To construct the VTS-SFT dataset, we transform each verified trajectory into supervised training instance. Each trajectory follows the reasoning path format defined in Equation 1, consisting of a sequence of textual states, tool actions, and visual observations, concluding with a final answer. We retain trajectories where the final answer satisfies [ = (", where 1" is the ground-truth label associated with the input 81. The resulting supervised dataset is defined as:
DSPT = ((117) 1H,+1= =t", ll___a_a_______eeaeaeea_aaaa____ _____jjudee(7 correct).
Each trajectory in DsEr is tool- and preserves all intermediate reasoning states, providing rich supervision for training. After processing, the dataset contains approximately 315K high-quality examples.
VTS-DPO Dataset Construction. To construct the preference dataset DDPO, we generate suboptimal reasoning trajectories as contrastive pairs. For each (81, r") > E DSFT, where 7 is a correct trajectory, we design prompts that instruct the model to begin from an intermediate point and then proceed with incorrect reasoning steps, yielding wrong final answer, which is also the Error Induction step in Figure 4. The resulting suboptimal trajectory 7' paired with 7 to form a preference tuple "5,,"",7)
We format these pairs into the standard DPO training structure and remove any example where either 7 or r' contains empty or missing image inputs. After filtering, the final dataset Drro comprises 301K preference pairs for training the verifier to assess and guide visual token scaling quality.
5 Experiments
We conduct comprehensive experiments to evaluate the effectiveness of our proposed Visual Token Scaling with Verification (VTS-V) framework across range of visual reasoning tasks. This section is organized as follows: In Section 1. we describe the experimental setup, including model variants, training configurations, and evaluation benchmarks. Section 5.2 presents our end-to-end experiments, comparing VTS-V to several strong baselines in both closed-source and open- ooun-source settings. Finally, in Section 5.3, we conduct ablation studies to analyze the individual contributions of visual token scaling and verifier integration.
7

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Modil
Depth
Spaiial
liyew
ViCCer
SenDen
AnStyle
Count
FunCeer
Lecal
MaliVV
Fon
Veen2.5-VL.7B--llo Variants
Qwen2.5VL 7B
65.32
83.22
56.67
40.12
24,46
58,97
55.00
19.23
41.90
43.61
25.37
34.85
79.26
49.07
Qwen2.5V 7B VTS
66.13
37.76
53.33
59.72
36,88
58,97
41.18
23,85
45.05
42.86
25.12
38.64
64.42
45.07
Ours VTS-V
70997
86.01
08.07
54.46
33,81
07.52
55.85
30,00
49.15
15.64
35,06
36.36
50,00
$6.65
Owend -n-tttttttt Vartants
Qu
79:72
34.00
51.28
73.35
18.46
45.11
38.64
48.01
Qwen2VL-7BB VTS.V
67.83
17.56
43.35
12.00
40.99
30.83
29:55
Our VTS-V
60.48
60448
58.00
37.21
40.58
63.35
25.35
31.64
47.37
34.09
$4.21
52.19
LLLMM-33.2-1BB
1--.--------o----eee Variants
63,1
07.13
55.31
50.98
99,57
41.88
55 00
$3.3
62.90
48.1
51,34
25. 06
46.67
47.96
1R VIS-V
Oun VTS-V
68.55
69.23
$7.31 31
18.60
47, AB
$5.95
56 67
$5.43
16.30
52
$7.58
23. 48
$7.46
50.32
GPT-4e Variants
GPT-4
69:23
55.90
53.96
70 55
GPT-4 Skoispudd
$3.00
81:10
70.70
66:70
45:40
70.00
$4:20
GPI-40 Col
73.39
82.52
02.00 00
82.56
57.55
92.05
00:00
57.09
00006
53.38
41.04
02.88
03.70
64.99
GPI-40 S0M
88.35
76. 22
49:31
85.72
52.52
63.35
67.00
19.84
16.40
033700
GPI-4o MMfoactryy
80:30
81
90
58. 10
83.00
61.70
55.40
59.00
00:30
75.30
GPT-4 VTS-VV (Dhin)
79.34
83
75.55 81
56.83
80.34
67.50
$3.08
68.85
52.63
71.21
85.19
69:18
Table 1: Model performance on BLINK subtasks. Each column corresponds to different visual reasoning task in the BLINK benchmark. Highlighted cells show whether using the proposed VTS-V method improves or degrades the performance compared to the base model.
5.1 Experimental Setup
Models and Baselines. Our experiments are divided into two main parts: closed- models and open-souree models. For the closed-souree setting, we follow prior work and evaluate the effectiveness of VTS-V V using GPT-4o, comparing it with four strong baselines: (i) Zero-shot reasoning on GPT-4o: (ii) Chain-of-Thowne Thought (CoT) reasoning on GPT-4o: (iii) Visual prompting framework: Set-of-Mark (SoM), and Visual Sketchpad; and (iv): Tool-using framework: MMFactory.
For the open-source setting, we fine-tune three vision-language model: Qwen2-VL- VL---B--ssttt [25]. and LLaMA3.24 1....--viiion-Instruee
IB on our VTS-SFT dataset. We evaluate the performance of VTS-V both before and after fine-tuning to assess its impact. Our verifier model is trained on Qwen2. G-VL-7B-Instruct using our VTS-DPO dataset. All SFT experiments are conducted using LLaMA Factory under unified settings, and DPO training carried out with TRL. Detailed training configurations are provided in Appendix B.
Bwven..--VL-7B-Insee
Evaluation Tasks. We evaluate four representative vision-langusee reasoning benchmarks: BLINK [6]. Bench [27], MMStar [3]. and Math Vista [18]. These benchmarks span a diverse set of capabilities, including multi-image perception and reasoning (BLINK), fine- fine-grained understanding of small visual objects (VBench), broad general knowledge QA (MMStar), and visual mathematical reasoning (Math Vista). Following [11] and [5], we conduct our main experiments 13 tasks from BLINK, a challenging and diverse benchmark designed to evaluate fine-grained visual reasoning. These tasks span visual and semantic correspondence, spatial understanding, multi-view reasoning, depth and reflectance estimation, counting, object localization, pattern alignment (e.g.. jigsaw,,, art style comparison, functional and semantic matching, visual similarity, and forensic image detection. Further evaluation details are provided in the Appendix.
5.2 End-to-End Experiments
VTS-V improves performance of closed-source models. As shown Table 1, our VTS-V V framework brings robust and consistent improvements to GPT-4o the BLINK benchmark. The significant performance gain, achieved without fine-tuning, demonstrates the inherent effectiveness of our verifier- verifier-guided guided visual token scaling method for enhancing visual reasoning. Specifically, the average performance increases from 62.25% to 69.15% 15% (+6.90), outperforming all other prompting- based and tool-augmented variants. Compared with GPT-4o + MMFactory, VTS-V yields slight but meaningful gain of +0.25. It shows larger improvements over GPT-40 + CoT (+3.30), GPT-4o + SoM (49.02), and GPT-4o Sketchpad (+2.37). The largest gains are observed on complex compositional (+12.91). and risually-Correlater (+7.56),
tasks, such as Counting (+18.33), Lunetionally-Correlle indicating that VTS-V strengthens reasoning over fine-grained and structured visual information.
VTS-V enhances open-source models fine-tuned on our dataset. Open-source models also benefit significantly from our framework. When these models are first fine-tuned on our VTS-SFT dataset and then evaluated using VTS-V, consistent gains are observed. For example, Qwen2V1.-7B improves from 48.01% % to 52, 19% (+4.18), showing gains in Multi-view (+3.44), Local (+2.48), and
8

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Jigsaw (+4.08), Similarly. Qwen2.5VL-7B improves from 49.07% to 56.65% (+7.58), with boosts in Depth (+5.65). Spatial (+2.79), and Visual Correlation (+14.32). LLaMA3.2-113 despite being larger model, shows an improvement from 47.98% to 50.32% (+2.34), especially on tasks like Semantic Correlation (+8.89) and Functional Correlation (+3.12). These results demonstrate that VTS-V generalizes well to open-source architectures and consistently improves performance across vision reasoning categories.
Fine-tuning on VTS-SFT datasets enhances models' tool-using abilities. We find that apply- ing VTS-V directly to open-source models without supervised fine-tuning can harm performance. For instance, applying VTS-V to Qwen2VL-7B drops performance from 48.01 % to 38.54%, and LLaMA3.2-1 1B fails to output any valid tool-use actions. This behavior contrasts with GPT-4o, which can reliably follow verifier guidance even without additional training. These results suggest that base open-source models do not possess the necessary behavior patterns to interact properly with verifier signals external tools. However, after supervised fine-tuning on our VTS-SFT dataset, these models not only recover but surpass their original performance. Post-finett sosstiinttunng, Qwen2VL-7B improves 52%, Qwen2.5VL-77 rises to 56.65%, and LLaMA3.2- 1B reaches 50.32%. More importantly, they now produce valid tool-use actions, indicating successful alignment with verifier guidance. This confirms that the VTS-SFT dataset is critical for enabling reliable tool interaction in open-source VLMs.
VTS-V generalizes to diverse bench- marks. To assess generalization, we eval-
uate models V*Bench(27], MMStarr3), and Math Vista[18] (Table 2). Without fine-
Trained Model
V-Bench
MMStar
Math Vista
Qwen2.5VL-7B Qwen2.5VL-7B VIS-V
73.30
55.00
67.50
tuning, applying VTS-V degrade per- formance- for instance, Owen2.5VL-777 drops from 73.30 67.54 VBench. After full training (VTS-SFT + VTS-V), performance improves across all models: Qwen2.5VL-7B reaches 75.13, Qwen2VL- 7B recovers 66.67, and LLaMA3.2-1ID rises to 60.21. The results for GPT-4o on these benchmarks can be found in Table 5.
67.54
55.93
52.60
Owen2.5VL--7B (Ouns) +
Qwen2V1.-7R
66.49
53.93
58.20
Qwen2VL--BB VTS-V
50,80
44.29
37.50
Qwen2VL-7B (Ours) + VIS-V
66.67
55.26
60,30
LLaMA-3,2-1JB
54.45
50.57
32.20
LLaMA-3.2.11 3.2-1--.--11-- VTS-V
L1aMA-3.2-1 (Ours)) VTS-V
60.21
50.71
48.10
Table 2: Model performance on general bench-
5.3 Ablation Study and Discussion
marks. Evaluation on V*Bench, MMStar, and Math- Vista. Dashes indicate missing results.
We compare GPT-4o + VTS-V with text-only chain-of-thought base- line (GPT-40 + CoT). VTS-V achieves 69.15% average accuracy, surpassing CoT's 64.96% by +4.19 points. The gains especially strong on tasks needing structured visual reasoning, such as Counting (+10.90), Functionally Correlated (+1.76). These results highlight that scaling visual reasoning via verifie- guided tool use is more effective than relying solely on extended textual reasoning.
(+10.98). and Visually-
Verifier improves reasoning quality. Ablation results in Table 3 clearly demon- strate the effectiveness of the verifier mod- ule. When the verifier is removed ("w/o verifier"),, accuracy consistently drops across all models- Qwen2.5VL sees de- cline from 54.44 to 47.09, Qwen2VL from 37.21 to 33,14, and 1lama3.2visio from 38.60 to 36.63. This indicates that the ver- ifier plays a crucial role improving rea- soning by filtering out suboptimal answer paths and enhancing decision quality. These improvements are even more pronounced compared to removing the whole VTS and verifier, which leads to further substantial accuracy drops.
Qwen2.5VL
Qwen2VL
Llama3.2vision
Full
54.44
37.21
38.60
w/o verifier w/o VTS-V
47.09
33.14
36.63
40.70
19.77
31.98
Table 3: Ablation results: accuracy drops when remov-
ing verifier or VTS-V.
Conclusions and Limitations
This paper presents a new framework, Visual Token Scaling with Verification (VTS-V), to enhance multi-step visual reasoning by iteratively selecting visual actions and verifying their utility at each

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step. By framing the process as Markov Decision Process and integrating verifier trained via step-wise Direct Preference Optimization, the approach enables models to progressively refine their understanding of complex visual inputs. VTS-V achieves strong performance across range of challenging visual reasoning benchmarks, outperforming existing baselines.
Limitations. The framework can be adapted to support a broader set of visual tools and more diverse reasoning formats. Enhancing the verifier's adaptability across tasks and integrating it more tightly with downstream applications may further improve robustness. We believe VTS-V offers a flexible foundation for future research in compositional and aa-gumeeeeedd visual reasoning.
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18

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Appendices
Proofs
20
A.I Verifier Obtaining
20
A.2 Proof of Lemma 3.1
22
A.3 Practical Algorithm for VTS
22
A.4 Proof of Theorem 3.2
22
B Experimental Details
24
Examples
25
C.I VTS-DPO Dataset Examples
25
C.2 VTS-SFT Dataset Examples
28
C,3 Benchmark Examples
D Broader Impact
33
Inference-Timee Time Overhead Analysis
33
F Extended Evaluation Broader Benchmarks
35
F.1 Experimental Setup
35
F.2 Results and Analysis
35
Analysis of Performance Differences Between GPT-4o and Open-Source Models
35
H Visual Token Scaling Analysis with Optimal-Stopping Verifier
36
I Robustness and Generalization Analysis of the Verifier
36
J Separate Reasoner and Verifier
37
K Interpretability of Reasoning Traces
37
L Ablation Study on the Reasoner Module
38
M Comparison with Dynamic Visual Attention Methods
38
Novelty Analysis and Comparison with Prior Work
39
19

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A Proofs
In this section, we provide the detailed proof that omitted in the main paper.
A.1 Verifier Obtaining
Given the base model Vog and preference pairs (81, ("; ,'), "..),,the the key idea of multi-step DPO (Rafailov al. [20]; Xiong et al. [28]) is to assume that r" has a specific structure under which the new prefer- ence model Vosuro and verifier r" can be obtained by jointly solving the following KL-regularized planning problem and the maximum likelihood estimation of the Bradley-Terry model.
@SDPO E argmin E s1 D. (o (-le))) M {ox (1 (4n) - (T)+
E
H.+1
H. Σ h=1
n
Σ
DEL (Vo (- (s) 11 (- (())
DEL (Vo llVo (-1ta)
(8)
ØSDPO argming - E (()
[IP ( > x1)] argmin
(e lor (r")))- -r (r'))]
Firstly, the next proposition shows that problem (8) can be solved directly when y* lies in a specific family of one-parameter functions,.
Proposition A.1. (f) = (T = =
H.+1 log [,,(),
+ Exe log [,(a,,)) + (881)
Yeu (3,1=,)
Yog (4,11,))
for some 6', where Q(-) is some fixed function that only depends on $1, then the optimal solution of problem (8) is d'
Hence if r" takes the form rer, by Proposition A.1 and equation (8), have r" Tézeo- Then to further obtain @SDrO, we can plug rer (T) in equation (9) and optimize over 6', i.e.,
OSDRO Eargming y
E (es, [o (rav (1")-ra (+)))]
arggmin ((,,,
log a ("
HH,w+1
Σ
log
Vor (th"
8h
H
log
Vor (a
th
V (5%
18h
Veoo (a7,
11h""
h=1
H11+1
Var 1/ 1//"
H_1
Val a/ 1thh"
log
log
V. Vo
(17 187
V (a (17
h=1
(10)
Here we use superscript to indicate which trajectory path the reasoning steps lie in. Now we can use the following empirical multi-step DPO loss
LSDPO (g. =
Σ
log
"
H1 Σ
log
Vor
Voo (t."
(th""
s
18h
Hyw
log
Var (a 1th
V do
(a)
H H11+1
V 11/ 18%
H
V
4 o 11h
log
log
V (1% sT
Voo (aj (
h=1
and obtain the optimal êSPPo E argmin ESPPO (Ø,, Φn) by gradient descent. Finally, we use Tó to approximate the verifier r* Tosseo
20

---

Proof of Proposition A.I. The key idea is, given any and H,, using backward induction to check the optimality of ø' for 1 S H, + For any given Sn2 define the value function Qn (3/, + as
H++1
Ver (tw spr))
Qn (8/= Φ) -E Ww (1e Wi (- (ww)
log
Vi (l 8px))
k'=h
H,+1
DKL (V (- (888)))) 11 8xx))
M/=
H+
Ver (ax (w) + DKL (Vo (.1tt)) ||Voo C ( (1wll)))
+n { $ H }
log
V (ax twe)
h/=h
(h- - Q (si).
Then our goal is show that
Φ E a E. Eirn 0).
(12)
Observe that by the construction, Qa(: satisfies the following recurrence formula
Qn (5), o)
= =B, ~v vo (,)s))), ~o -Vo J (t,.) (t.) Qu+1 ($a+1:
1 = 11
Vor (1/ 1 8/)) + DEL (Vo (. 8n) 1| (- (s,))
+ nB, -Vo ~ sonss (3w)
log Vol (tn sp))
(13)
Var (ap 1 1p) + DKL (Vo (: (x) ||Voo (: (1,)))
+ 11 (h H4 (1 - ((a)
-log
log
Veto (a,, (%))
(14)
We now use backward induction to show that for any fixed 8n 1 S S Hy + 1, o E argmin (sp, 6).
(a). For h = Hr +1,
Var (tu,+1 181++1) DDL (Vo (: (8, \| 6 sH (x,,
Qu,+1 (SH, Φ) F., B....-1- - (1 lnlog
Vau (1 (81+1))
By directly using Lemma A.2, we can conclude that QH,+1 (5H, +1H Φ)) 2 O, where the equality
holds when V (-1 (H,+1) V (-1 (HH+1). Hence &' argmin Samning@HH+- QH,-1 (sH++1:0). (b). Assume for h h1 2 < M < H, d' argmin QN ($w Φ). Then for h h - 1,
o' E argmin, E W- ~o (-15 ) No ( (+w-1) QN ($w,
To show o' E argmin O (sH= 11 Φ) by the definition of Q (s @), one only needs to show that both term (13) and term (14) obtain the minimum at ø' when substituting h to h 1. This can be checked by using conditional expectation and Lemma A.2.
Hence by combining (a) and (b), we have ø' E argmmnn,Qui (81, Φ). which implies equation (12), as desired.
Lemma A.2 (Proposition 7.16 and Theorem 15.3 of Zhang [32]). Let U() be given function and po(.) be a given density function. Then the solution of argmin p()) Exmp()) (-U(x) + Dx (p(-))lo(())))
given by
U(x)
p" (x) = (x)()))
"
where C log E Rroppot)) exp
U(x) p² (-) is known as the Gibbs distribution.
21

---

A.2
Proof of Lemma 3.1
Proof of Lemma 3.1. This is directly obtained from the definition of "surra
A.3 Practical Algorithm for VTS
Algorithm Visual Reasoning with Visual Token Scaling and Verification
Require Training dataset Dunin initial reasoner Re, and base model Vo Input: new test question-image pair 8 D.
Output:
Reasoning trajectory
1: Reasoning Sequence Generation: Initialize reasoning trajectory T + {81}.
2: Set step counter h
3: while True do
4: Planning: Generate step planning in RossT (- [s))-
5: Action: Select action d₁ Rager (-1()) (b).
6: Observation: Return O₁ = fan (tx.)-
7: Update State: 8/+1 - (Sh, f aj: 0h)-
8: Append (t,, ag. 0% ) to reasoning trajectory т.
9: Verification: Compute reward difference Ar Tésoro (sh+1) Tosopo (sh).
10: if Ar < then
11:
Break loop. end if
13:
1
end while
Generate the final result & (dsnro) Roser (-) S (dsnno) (d where H, (ŌSDPo- Φo: 0SFT is the total reasoning step.
Return final trajectory - = H. (san U { {lee, (ex(0uu0)+11
16:
A.4 Proof of Theorem 3.2
Before we proceed with the main proof, we provide some relevant definitions and conclusions at the beginning.
Definition A.3 (Martingale, supermartingale, and submartingale), Let Fn be filtration, i.e., an increasing sequence of o-fillds. A sequence X,, is said to be adapted to F, if X,, E Fr for all n. If X, is a sequence with
1. E xn| < C0,
2. X,, is adapted to Fr.
3. E [Xa+1 Ful = X,, for all n,
then X, is said to be martingale (with respect to F.). If in the last definition, = is replaced by S or 2. then X,, is said be a supermartingale or submartingale, respectively.
Definition A.4 (Stopping time). A random variable N is said to be a stopping time if (N = = Fr for all n < co, i.e., the decision to stop at time must measurable with respect the information known at that time.
Theorem A.5 (Martingale convergence theorem, Theorem 4.2.11 of Durrett [4]). X,, is sub- martingale with sup EX* < co, then as - co, Xn converges a.s. to limit X with EE < co.
Theorem A.6 (Formal version of Theorem 3.2).
1. Hy (ŌSDPo, do; SSFT) is stopping time.
2. Assume the following two conditions hold.
(i) sup E,, En,M(s))~a
r Oero
(Tn) < oo for any given $1 D.
22

---

(ii) for any Sp+1 Böge Veu and Venno satisfy that
DxL. Risen (: 18h) Voo (: (8p)) 2 DKc. (Rower (. (188)) 33000 (. (18))))
and
DEL Riss (- 1l (- (1tt))) 2 DEL [Bours (ha) exwo (- th.)
Then H, (ŌSDPO: do: @SPT) is finite with probability 1.
Remark A.7 (Discussion of the conditions in Theorem A.6). Condition (i) assumes that the verifier is finite for paths generated by reasoner Röght expectation. This can easily achieved when the verifier finite.
Condition (ii) can be interpreted as assuming that the distance between RoST and Vo. is greater than the distance between Reger and V V This assumption reasonable, as both Rōgez and oseeo align with human preferences and therefore tend be closer to each other.
Proof of Theorem A.6. 1. Let Fn be the smallest a-field generated by *A+1- i.e., Fn ($8+1). Observe that by the definition of the stopping rule shown in equation (8), H, @SDPO Oo: ÖSFT) = h is determined by 4/+1 Hence { Hr (ŌSDPO- do: B h E F which implies that H, @SDPO Φo; ( is a stopping time.
2. By the definition of "anns we have
E T'éeeo (sh+1) 8h
Vesoro (12, 188)
V Vossero (an 1,,) Vol (an (
-raswo (sh) + 18,, Rase (-19 (oll)))an )a, (l,l))),nnBa Bostr ( (ll))o==fo, (4x)
log
+ log
Vou (th, 88)
Observe that condition (ii) implies that
V Vesooo (tp, 52.) B Rown (11ma) log Vœo (1p, (8%)
=DKL (Rossr (-1 sh) llVoo (-
snn) (-1s))) DKL (Roor (.1sw) asnmo ( 1
(nn)
20,
and
V Vasno (ap (n))
ag Mirn (-1(a)
log
Vou (an tpp)
V Visuro (an (t,))
Boar (an (tx)
logg
E Base (-1(n)
log
+ E BB Begr (.10g)
Rāge (ap, 1.4))
Vat (ah (x)
DKL (Bésrr (- thh lIV tn)) DKL (Rggr (- th) 1/V piscro (- (tt)))
20,
hence E resuro (Sh+1) sh 2 Temmn (st), which indicates that Touoro (sa) is submartingale.
Then combining condition (i) and Martingale convergence theorem A.5, Tosoro (sn) converges a.s. to limit F(s1) as h + Hence for > 0, with probability 1, there exists H.(s1) such that Ir "' (8h+1) T'sseo (sh) < when h > H81))). Therefore, H, (ŌSDPO, Φo; 0SFT) < H, (s1) with probability 1, as desired.
23

---

B Experimental Details
Table 4: Hyperparameters for training Qwen2-VL-7B-Instruue & Qween25--L--7--nnstruet ALaMA-33--IB-Tiionnnnstuuu models
Hyperparameter
Value
LoRA Rank
LoRA
LoRA Dropout
LoRA Target
all
GPU
8 x NVIDIA A800
Per Device Train Batch Size
Gradient Accumulation Steps
Warmup Ratio
0.03
Learning Rate
3e-5
Learning Rate Scheduler
Cosine
Unfreeze Vision Tower
False
Number Train Epoch
Max Gradient Norm
1.0
bf16
True
Cut Off Length
65536
24

---

C Examples
C.1 VTS-DPO Dataset Examples
EXAMPLES
Chosen
Rejected
Q: What team hat is he wearing?
Q: What team hat is he wearing?
Reasoner
To determine the team hat, I will first use the grounding action to locate the on the hal to gel a cleater view any lagas text that might indicate the
Reasoner
image.
hat, Identify the logo on the cap using the grounding ng action. This will help me recognize the associated logo.
determine
grounding action ("image index"ddexx "text" ("hat]]
Action grounding action
('image index': "ext": ("logo"))
The has been located, and there szems he Iogo visible it. will now use the zoomin_action actionn to focus logo for better clarity.
Reasoner
D.
Wrong
will thebisuul search action thoroughlly scan image any logos or text that cou indicate the team, This will ensure don't miss details
Action :
zoomin action(""mage index"" 'bounding box": min': Y_max' 260),, "padding" a.s)
K
Action visuaf search action ('image index": "'objects"; I'logo" "text"]
max": 272,
Reasoner
Reasoner
The visual search artion highlighted some areas but didn't clearly identify the will the OCR action extract any text reveals the team name.
zoomed-in image
view the logo
hat. The logo appeaars to be 'NY,, which commanly associated with the New York Yankees baseball tea confirm will the action to extract the text from
the highlighted regions see
Action: ocr action ('imago index': 2, "engine": "easyocr")
Action : ocr action" actlon"immage index:: "onginn"" "easyacr") )
Reasoner
Reasoner
The OCR did not detect any text, likely due to the stylized nature of the logo. However, the visual appearance of the logo strongly resembles the 'NY' lage the New York observation, hat is New York Yankees hat.
did Civen the lack of clear identification, will conclude that the team cannot be dettermined from the image-
team.
Yankees. Based
Final Result
Final Result
The hat is a New York Yankees hat.
Unknown
Figure 3: We present an example of the generated DPO data.
25

---

DPO EXAMPLES
Chosen
Rejected
Q: Which country is highlighted?
Which country highlighted?
Choices:
Choices:
Solomon Islands
A. Solomon Islands
Tonga the Marshall Islands
B. Tonga
C. the Marshall Islands
D. Samoa
Samoa
Answer with the option's 's letter from given choices directly.
Answer with the option's 's letter from the given choices directly.
Reasoner
Reasoner
The image shows map highlighiing region Pacific:
To deterri which country is highlightte. I'll first try to identify the geugraphical features and then use the provided options down the possibilines
highlighted area seems to correspund to a group of is islands. To determine ne which country highlighted, will use ground ing action to identify the general location and then use the visual seurch action to find sprciliic
Action grounding action ('image index": "text" ('Solomon Islands", 'Tonge", 'Marshall Islands", "Samoe'
Action: groundingg_ntion action indees__idexx" 0, "lext": ["sland"") "
Reasoner
Reasoner
The highlighted area seems to correspond to Solomon Islands based on its However, confidence score for Samoa also relatively high, suggesting some ambiguity. To clarify,
To get clearer view and confirm the detalls, will use the the highlighted
location north
Action:
wanz:
depth actior analize spatial relationship highlighted ed area with nearby landiaasees.
zoomin poomin_actionn" actiann""nnnnn ('image_innee indext": 1, l'boundiig hox"s f'x "y min" 26 'x "umx" 450, "y_mar"" 176), "padding": 0.05)
Wrong action
Action depth action! 'Image
Reasoner
Reasoner
The depth map shows that the highlightee ited relatively
compared to ot her islands. This supports the possibility that could be Samoa, as it geographicall
To determine the country, will use the compare this image
image. texts similarity the provided options.
Australia than Solomon slands,
image to similarity ('inage 12, "texts" :: ('Solamon Islands", "Tonge", " Marshall Isfands +, "Samoa") 'I)
overlay the depth map with the original lmngge tu beiler visualize the spatial relationships..
To further confirm.
index" Action: overlay _ationn ("background jongg index::
Similaariy scores: 187 0:1771, 0220, 0.1682) Best matching the Marshall Islands
"overlay image index": "overlay proportion ("x min 50,
7-0, max":), max):))
Reasoner
1
Reasoner
Based similarity the highlighted region the image most likely the Marshall blands. Therefore, the correct answer is C.
The overlay confirms that the highlighted httd area indeed cluser to Australia, supporting the conclusion that il Samou, Thereiore, the highlighted country Samna.
Final Result
Final Result
Figure 4: We present additional examples of the generated DPO data.
26

---

DPO EXAMPLES
Chosen
does player catchingthe baseball play for?
Q: What team does the player catching baseball play for?
Reasoner
Wrong action
Reasoner
To determinc which team the player catching the baseball plays will try use dheth actior any spatial clues that could help dentify the team. This might directly give team name rould provide additional context.
player catching the baseball p plays for, I'll first identily ly the player and then look for visible logas
determine which
there
uniform.
use the grounding action toal to locate the player catching the ball.
Action : depth_ ("Image_index'e index" 9-
Action:
grounding action L'imag_innex''0 Index" "text": (player catching haseball")
Reasoner
The depth map doesn't provide clear information about the Now,
the OCK action cottact the text from these highlighted rogions identify team
Reasoner
The player catching the baseball is highlighted. Now,
Action ouz action 'Inaage index": J, "engine": 'easyocr"?
Extracted text: No text detected
player's uniform to clearly see the team name. will use the zoomin, action tool to facus the player's jensey.
Image Index.
Reasoner
The action not cletect any text, possibly clue to the angle or clarity of the image. As final attermtt I will use the to texts similarity description identtryy the team.
Action action ('image index's "bounding box': ("x : "y_mir": 55, "X_max" 129, 'y_max": 216), "padding 0.05)
find the image, which might help
imuge 0, "texts :: ('New York Yankees", "Boston Red Sox", 'Chicago Cabs "Los Angeles Dodgers'I
similarity pacaaccconninaan "image iinex";
Reasoner
The zoamed in image clearly shows the word TEXAS' the player's s uniform. Therefore, the player catching baseball plays for the lexas team, will now terminate the process with the final response.
Similaniyy scores (0.260 2683, 0,2695, 0,255, 0,2573)
matching text:
Reasoner
Based the similarity the most similar description, image
therefore, player catching the baseball kikeyy plays for the Boston Red Sox.
The player catching the baseball plays for Texas team
Final Result
Boston Red Sox
Figure 5: We present additional examples of the generated DPO data.
27

---

C.2 VTS-SFT Dataset Examples
SFT EXAMPLES
Q: Given an image of an animal, identify the kind animal the image.
The picture could be more popular animals that are visible around zoos sometimes domesticated home. They could also sometimes be found in wild.
Q: What the lugo the image?
Reasoner
Reasoner
ideetiffy the logo, will first the OCR tool to extract logo image. help
if
To identify kind animal in the image, I will first use the grounding action tool locate any animals mentloned in elephants, the image
visible.
Action acr_actioon ('image_inden e "'nginn": eeeasoorr)
by searching for elophant"
Extracted text: YBS,, Ks55, 8 KNiFF
Image Index:
Action : grounding
acttionng.ction action l'image. index": 0, "text: ("eeephann")
Reasoner
extracted
include
Reasoner
recognizable logo
use the grouncing action to locate any graphical elements that could represent logo in the image.
cucressiully image. Now. use the depth. action tool undersfand the sputial relationship these elephants with respect to the camera and other objects the scene.
grounding. action
identified elephants
Action: grounding ("image_index"
0, "teet" ('logo '))
depth ("image. index":
grounding use the crop action focus on the logo region for better clarity and further analysis.
potential logo
crop_ actionn ("image_idexx? 2. L'bounding__on box': ('x min"; 30, "y_min": 239, "x_xax" 253, "y_marr: 562), "padding": 9.05)
depth map shows that elephants are relatively close to the camera compared to the distant mountains. Now. will use the overlay, action cambine death map with original spatial arrangement the elophants and their surroundings.
Reasoner
The crapped image visually suggests a logu resembling "Baskin Kobbins'. To coniirm, will use the similarityy artion image with descriptions brands.
the popular ice
Action: overlay action ("hackground index': 2 "overloy indez": "overlyy propurtion 0 "_mxx" "y_mx":
Action: image, to texts similarity action! 'imagy index:: 3 "uxtaa: y (Baskin Ruisbina", , "Ben & Jurry's st, "Haggnn Dasz'))
Similarity scores: 0.3345, 0,2606, 0,2011
Reasoner
Best matching text: Blakkin Robbins
The overlayed image confirms the presence elephants Based the evidence successful identi fication of elephanis in previous sleps, the currect answer clear.
Reasoner
Based the similarity the loga the image is must likely with
Final
Final Result
The logo in the image Baskin Robbins.
elephant
Figure 6: We present examples of the SFT data.
28

---

compared the couc couch SFT EXAMPLES
Q: In this task, you will be provided with an image and two captions. Your to identify which the two captions correctly describes the image. Options: (a) a circular sign above a rectangular sign (b) a rectangular sign above circular sign
Q: the given caption "The couch is adjacent pizza. fitting the image? Answer the question with Yes or
70
Reasoner
Reasoner
determine if caption fitting. need to spatial relationship between the couch and the pizza. I will first the grounding action locate the couch and the pizza
detennine the currect caption, need signs
azalyzee arrangement
image: The signs appear to be stacked vertically. I'll stari identilying the shapes the signs their
70
Action aatioon "image index":
Action
: grounding action f'iaage iodex": "text": l'cimular sign", 'rectangular sign")
"text" "ext":/'couchh "pizza") 'I
Reasoner
Reasoner
The bounding boxes indicate that there is rectang rectangular sign positioned above circular sign. However, there also triangular sign above the rectangular sign. confirm the relationship belween the rectangular and circular signs, should focus their positions relative each other.
The boundinn boxes show that the couch each
the pizza indeud other. However, better understand the spatial arrangement. I will use the depth action to estimate the relative distances between the couch and the pizza.
Action: actioni actainn""maaee index::
"bounding box": ("x_nio" "y_ min"; "x mmxx: 11399 "y_mxx"; 754), "padding": 0.05)
T2900 m 1
Action: depth action ("Image_indxx': Index": 0)
Reasoner
Reasoner
The depth map indicates that the pizza is closer to the
The cropped image confirms the presence of rectangular sign 2900 written
need verify the
This confirms
position of the circular sign relative to this rectangulat lr sign. will proceed tu crop the circula sign next.
adjacent to the pizza. Now, will overlay th depth map with the original image the spatial relationship more
Action: crop, actionn pac.annniiaageee..... index":
d'bounding box": ('x ('x_min", 734, 'Y "_min" 743,
70
clearly.
max": 1142, Y maxx 1762), "padding" 0.05)
Action: overlay actionn"backyrronnn image_index":: index": "overlay image index": "overlay proportion". ("x 'y_min': 0, "x_mxx' "y_max" 13}
Reasoner
The cropped image confirms the presence of circular sign with the number 70. Based the previous observat ions, rectangular sign indeed Therefore, option (b) reciangular sign is above a circular sign' correct description.
Reasoner
circular sign.
The overlayed image clearly shows that the couch adjacent to the pizza. The depth map and visual contirmation support given caption.
Final Result
Final Result
Option (b) rectangular sign is above circular sign'
Figure 7: We present examples of the SFT data.
29

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SFT EXAMPLES
Q: Give short and clear explanation subsequent image.
QF: Subtract all purple cylinders. many purple blucks left?
Reasoner
explain image, identify objects present using the grounding ng. action tool.
question purple cylinders there are no purple objocts in the image. will first use the grounding action confi the absence of purple objects.
Action: grounding action""mage,_, index""
"lext""" ('book" "tespot,, 'cup"l
Action
grounding action! 'image index" "tete"": Deet":/'purplee cylinder', "purple
Reasoner
block
use baok cover to provide more details about its content.
Reasoner
Action ('image
"engine": "easyocr")
The grounding action did not correctly identify any purple objects. will there
Extracted text: BEST Of, Edward, THE,, Abbey Image Index:
the visual search action or hidden purple objects in the image.
Action visual_search search, cecoo__eerch__ttee action ('image index 0, "objects" I'purple cylinder', "puppe block"1)
Reasoner
To further analyze the spatial arrangement of the objectt,, will depth. action estimate the relative distances teapot, cup, book from
1B
Reasoner
Action:
The visual search action also failed to find any purple objocts. will now use the depth action check if there any purple objects hidden behind others.
depch wwwpocniioannen.n...ooa "imoge_innexx":22
Reasoner
Based the depth map, teapot, cup, and book appear be similar distances from the camera, lying flat on the Now, I will overlay the segmentation mask on the original
Action depthhactonn actiont 'image
hitpinggeeedddeeeeeeeee index" 0)
better visualize the objects' boundaries.
Reasoner
Action: overlay action
The depth map shows no purple objects either. now use the segment action to see if there are any purple objects that missed due to blending with the background.
("background Image
image Index":
d'overlay_jmme jmage index":
1/ d'overlay_prope proportionn" ("x_min" 0, "y_min' " "mmx": 1, y__mx": max": 13)
Action acgmmnttaaction" actianniinageee........ Indox"
o'bounding boxes' Il'x min": 158,
"y mumin: "_max'' 236, "y_max" 181), (xK min 345, ". min' 168, "x. max": 385,
Reasoner
The overlayed image clearly shows segmentation masks teapot, cup, and book. All objects are well-defined and positioned on a wooden table. With all necessary information gathered, explanation image.
"y_max" 232), m"x "y_min": "__max"
provide concise
Reasoner
segmentation
not any purple
Final Result
objerts. Since all attempts to find purple objects have been unsuccessful, I can cunclude that there are purple objects the Thereiore, subtracting purple cylinders would result in zero purple blocks remaining.
The image shows white teapot, cup of tea with spoon, and book titled The Best of Edward Abbey placed on wooden table. The objects are neatly arranged, suggesting a cozy setting reading and enjoyingtes tea
Final Result
There purple blocks left.
Figure 8: We present examples of the SFT data.
30

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C.3 Benchmark Examples
BENCHMARK CASES
Vstar
Vstar
Q: Is the vehicle on or right side of the blue umbrella?
Q: What is the color of the handbag?
(A) Brown (B) black (C) white Answer with the option's letter from the given choices
Right left Answer with the option's letter from the given choices directly.
Reasoner
Reasoner
position the vehicle relative umbrella, need to identify both objects the image. start by grounding the objects vehicle and blue umbrella'.
determine the color of handbag, to identify the handbag the image first.
Action grounding action ("inage index 50, "texi" "exii"vehicce"" "blue umbrellla '
Action
grounding actionf"imag iimage inde x"50, "text"s" ("bandbagg ")
Verifier
Continue
Verifier
Continue
Reasoner
The blue umbrella identified the image. Now; I need to locate the vehicle and determine ne position relative umbrella. perform
Reasoner
Now have the bounding coordinates for handbag, will zoom in to determine its color.
vehicle.
Action:
visuaf search, action("image
Action
Index'sd "objects v/"vehidfe "I)
action) "image index bounding. box's (1'x "i""__min :1772 "y_ min":963, "x. max": (1795, "y. max "9
Verifier
Verifier
Reasoner
Reasoner
vehicle located image, see its position relative to the blue umbrella. The vehicle is on the leit side of the blue umbrella.
The zoomed-in image clearly shows the color of the handbag,
Final
Final Result
D
Figure We demonstrate examples of reasoning on benchmark data using VTS-V. V.
31

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BENCHMARK CASES
MMVet
MMVet
What the color hat worn by the person in the front left?
Q: What the price for tomatoes?
Reasoner
Reasoner
person
To find the price of tomatoes, I will grounding identify location that specific area.
front left, will the grounding aclion identily
person and then analyze the color of the hat.
grounding
Action grounding action 'Image Indext:0, "text" "tott'""ommtoss" "))
('image index" O0, "texti 'vehicle / "person")) 'I)
Verifier
Continue
Verifier
Continue
LB
Reasoner
bounding 252, 22, 2851. will zoom into this area to determine the color of the hat.
person
Reasoner
w crop around the tomalces perform on the specific region containing the price.
Action zroomin action("imag image index"s0, "bo unding box':l'x min";0, '0, 1252, x2:2, Y_Jmax :2833)
Action xrop
"image. index"s) "boun
ding box "f " min 1:26, yy y_mnir 225,, mum *566,, "y maxi "A46),, "padding": (0.05)
Verifier
Continue
Verifier
Continue
Reasoner
The zoomedkin image does not show the correct area, will try different bounding box locus the the
Reasoner
OCR cropped image price the tomatoes..
Action zoomin acctinntiiinnn lriianaa_ Jndex": '0, "bounding 1112 "__nio 2211, muxx 1232, 2232 y.m
Actionaecr "image index 13 "engine""" "eassocrr)
ax :600)
Extracted text Pluin, 8.00 Image Index:
Verifier
OK
Verifier
OK
Reasoner
The zoomedinn Image clearly shows the person in the frant left.
Reasoner
The hat blue with white stripe and a red emblem.
The price for
Final Result
Blue with white stripe and emblem
8.00
Figure 10: We demonstrate examples of reasoning benchmark data using VTS-V.
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BENCHMARK CASES
MMStar
BLINK (Counting)
Q: What color is the microphone in the image!
Q: How many people are drinking water? Select from the following choices. (A) (B) (B) (D)
Options:
A: Silver, B: White, C: Black,
D: Red
Reasoner
Reasoner
To determine how many people drinking water, first use grounding action to identify people the image.
determine the microphone, use
grounding action to identily and segment the microphone the imugee.
Action grounding action! aitionniimagee index"; ""person'" "B
Action grounding action ('image index 10, "text" m'micropho ne"lj
Verifier
Continue
Verifier
Continue
Reasoner
Reasoner
There are three people detected in the image. will any them drinking water.
The microphone identified in the image. will zoom in the bounding determine its color.
Action:
search. aaction "inage *,,, 'objects" of d'drinking water'll
zoomin action "inage index -0, "boundingg box":('x min "164, "'_min :25," "_.xa":9992 y m36]
driking
Verifier
Verifier
OK
Reasoner
Reasoner
The visual search did not find any people drinking water. The detected objects were incorrect. heerefore, the answer drinking
The zoomed-in image shows the microphone, and appears be black color.
Final Result
Final Result
C: Black
Figure 11: We demonstrate examples of reasoning benchmark data using VTS-V.
D
Broader Impact
Our work presents a foundational framework for enhancing visual reasoning via Visual Token Scaling with Verification (VTS-V). While not tied to specific deployment, the technology could pose risks misused. For instance, improved fine-grained image understanding may be applied in surveillance disinformation pipelines, raising concerns about privacy, fairness, and potential for malicious To mitigate such risks, we recommend responsible release practices (e.g., usage restrictions, auditing tools, or gated access) and encourage further research bias and misuse detection. Though the societal impact is limited at this stage, we acknowledge its importance as the technology evolves.
Inference-Time Overhead Analysis
This section provides a detailed quantitative analysis of the inference- overhead introduced by VTS-V framework, including latency, memory usage, and the number of intermediate tokens generated during dynamic reasoning.
Our method employs iterative reasoning steps composed of two main components:
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Verifier calls: Require only prefill computation (forward pass over the input context to
generate stop/continue decisions)
Reasoner calls: Involve autoregressive decoding to produce tool instructions
The iterative interaction follows this structured process:
context
Q (image, text_ _ext_qquestoon)
while verifier (context) == 'continue':
current_outpur reasoner(contee
physical_feedbare tool_ sool_using API licuureet_ouuputtt
We define the total inference latency as:
1
C
0g
Latency
Σ
+
(15)
Pr
Dz
Where:
H: Total number of reasoning steps
C Number of input tokens at step (verifier prefill)
O Number of generated tokens at step (reasoner decode)
P:: Model's prefill throughput (tokens/sec)
Dy: Model's decode throughput (tokens/sec)
For Qwen2.5-VL-7B-Be with VTS-V, V, we observe the following characteristics:
Average steps (H): 3.1
Average verifier prefill tokens: ~ 10058.0 O per step
Average reasoner decode tokens: ~95.3 per step
Throughput on 80GB A800 GPUs (float16):
- Pr R 18493.6 tokens/s
D, 231.8 tokens/s
The total latency is calculated as:
10058.0
95.3
Total Latency 3.1
2.96 seconds
18493.6
231.8
Memory requirements for our framework include:
With max_ fex__model_lee le__een=665555 and ftype=float16, models can be deployed within 32GB through vLLM or SGLang on 80GB A800 GPUs
All tool models (including GroundingIDINO, Depth-Anything etc.) collectively require approximately 23 GB of additional memory during inference
We observe a clear tradeoff between reasoning depth and computational cost, which justified by significant accuracy gains (c.g., +7.58% average improvement on BLINK for Qwen2.5-VL-7B. Instruct). To mitigate latency for practical deployment, our framework supports several optimization strategies, such parallel verifier batching, early stopping, and adaptive step truncation via threshold.
This analysis demonstrates that while our framework introduces additional computational overhead, the resulting accuracy improvements justify this cost, and practical deployment is feasible with appropriate optimizations.
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Extended Evaluation on Broader Benchmarks
This section presents extended evaluation results of our VTS-V framework additional benchmarks, providing a more comprehensive assessment of its generalization capabilities across diverse visual reasoning tasks.
F.1 Experimental Setup
We conducted additional experiments evaluating GPT-4o augmented with our VTS-V framework on three challenging benchmarks: V*Bench [27], MMStar [3], and Math Vista [18]. For comparison, we included the following baseline methods:
GPT-4o: The base model without additional reasoning mechanisms
GPT-40 CoT: GPT-4o with Chain-of- Thhouh prompting [26]
GPT-4o Sketchpad: GPT-4o with Visual Sketchpad framework [11]
F.2
Results and Analysis
Table 5 summarizes the performance comparison across different benchmarks:
Table 5: Performance comparison of GPT-4o variants on broader benchmarks. Best results are in bold.
Method
V*Bench
MMStar
Math Vista
GPT-4o
60.73
58.40
63.80
GPT-4o + CoT
60.73
56.47
66.50
GPT-4o + Sketchpad
71.20
60.33
59.40
GPT-4o + VTS-V (Ours)
73.82
65.80
65.90
Key observations from these extended evaluations:
Our VTS-V V framework achieves state-of-the-art performance on both V*Bench and MMStar benchmarks, with absolute improvements of 13.09% % and 7.40 % over the baseline GPT-4o, respectively. These results demonstrate the effectiveness of our verifier-guided visual token scaling approach for complex visual reasoning tasks.
On the Math Vista benchmark, our method outperforms the base GPT-4o by 2.10% and achieves competitive performance compared to GPT-40 CoT, with only 0.60% difference from the oop-erforming method. This demonstrates the versatility of our approach across mathematical reasoning in visual contexts.
The consistent improvements across diverse benchmarks highlight the generalization capa- bility of our framework, which effectively enhances visual reasoning without task tasc-fpec adaptations.
G Analysis of Performance Differences Between GPT-4o and Open-Source Models
This section analyzes the performance differences observed when applying VTS-V to GPT-4o versus open-source models without fine-tuning. While GPT-4o shows consistent improvements with VTS-V without additional training, open-source models like Qwen2-VL WL and LLaMA-33 2- Vision initially experience performance degradation. This discrepancy stems from several key factors:
Tool-Using Priors: GPT-4o has extensive exposure to tool-augmented workflows during pretraining, enabling it to handle structured reasoning formats (e.g., Plan - Action - Tool call) naturally. Open-source source models lack this prior and struggle to generate valid tool-use commands without fine-tuning.
Instruction Following Robustness: GPT-4o's alignment tuning (e.g., RLHF) allows it to interpret multi-turn instructions and verifier signals effectively. Open-source models require fine-tuning to learn how to respond to verifier guidance correctly.
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Empirical Recovery via Fine-Tuning After supervised fine-tuning on our VTS-SFT dataset, open-source models not only recover but exceed baseline performance (e.g.. Qwen2VI.-7B improves from 48.01 % to $2. 19%), demonstrating the dataset's role in enabling tool-use behaviors.
This analysis highlights the importance of our VTS-SFT dataset for adapting open-source models to verifier-guided reasoning, while confirming the framework's ' generality with state-of-the-ar models like GPT-4o.
H
Visual Token Scaling Analysis with Optimal-Stopping Verifier
This section presents experimental results demonstrating the relationship between multi-step reasoning performance and visual token scaling, highlighting framework's dynamic behavior and the effectiveness of the optimal-stopping verifier.
Table 6: Visual token scaling performance for GPT-4o on BLINK Counting task
Visual & Text Tokens Per Sample GPT-4o BLINK Counting Accuracy
550
49.17%
1 1100
58.33%
1650
67.50 %
2200
64. 16%
2750
65.83%
Table 7: Visual token scaling performance for open-source models on BLINK subtasks
Visual & Text Tokens
Qwen2.5-VL Fun.Corr.
Qwen2-VL Depth LLaMA-3.2 Spatial
600
19.23%
56.45%
62.94%
1200
23.85%
60.48 % *
65.03%
1800
25.38%
58.87%
69.23 %
2400
30.00 % *
57.26%
67.83%
3000
26.15%
58.06%
67.13%
The tables illustrate the scaling relationship between reasoning accuracy and token usage across different models. On average, GPT-4o generates approximately 50 text tokens per reasoning step, while our trained open-source models generate around 100 text tokens per step, with both processing approximately 100 visual tokens through dynamic image operations per step.
Key observations from the scaling analysis:
Accuracy improves with increased visual tokens initially, but may decline with excessive reasoning steps, indicating diminishing returns.
Non-monotonic scaling:
Verifier-guided optimal stopping: Our VTS-V verifier consistently identifies the best stopping points (marked by *), balancing reasoning depth and computational efficiency.
Robust performance: Accuracy remains substantially higher than under-reasoning base- lines even beyond optimal steps, demonstrating the benefits of sufficient visual grounding.
These results validate our verifier's ability to dynamically scale visual tokens while maintaining optimal reasoning performance across different model architectures and task types.
I Robustness and Generalization Analysis of the Verifier
This section provides additional analysis of the verifier's robustness and generalization capabilities, addressing its performance unseen domains and tasks beyond the training distribution.
The VTS-DPO dataset is constructed from the comprehensive LLaVA-Onel dataset, which spans over 80 distinct vasion-language task types. Our curated DPO dataset comprises 002.028 preference pairs that cover a diverse range of visual reasoning domains, ensuring broad coverage and representation.
(LLaVA-OV)
36

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Table 8: VTS-DPO dataset composition across different domains
Domain Category
Tasks
Examples
General VQA
25
135,804
Sroument/Chart/Seree
18
100,681
Math/LLogice Reasoning
15
52,049
OCR/Text-grounded Tasks
6
12,494
The dataset encompasses diverse visual reasoning capabilities including document understanding, scientific diagram interpretation, mathematical problem solving, chart question answering, optical character recognition, and general commonsense visual question answering.
Importantly, all evaluation benchmarks used in our experiments (BLINK, V*Bench, MMStar, and Math Vista) are held-out from the training data, ensuring that the verifier is tested on completely unseen reasoning tasks and domains. The consistent performance improvements observed across these diverse benchmarks demonstrate the verifier's strong generalization capabilities beyond its training distribution.
The comprehensive coverage of VTS-DPO, combined with the held-out evaluation protocol, validates the robustness of our verifier training approach and its applicability to novel visual reasoning scenarios.
Separate Reasoner and Verifier
This section explains our design decision to maintain separate reasoner and verifier components rather than employing a single unified model. While unified approach offers potential efficiency benefits, our analysis demonstrates that a decoupled architecture provides superior performance for multi-modal, aug-eeteeete reasoning tasks.
Reasoning and verification represent fundamentally distinct capabilities: the reasoner must generate executable tool-using action plans conditioned on complex multi-modal contexts, while the verifier must evaluate the overall quality and utility of reasoning steps. Empirical observations show that when both responsibilities assigned to single model, performance typically deteriorates the model struggles to maintain both generative planning and discriminative evaluation capabilities.
Experimental results provide strong validation for the separated architecture. As shown in Table 9, adding a standalone verifier module to GPT-4o yields substantial performance gains:
Table 9: Performance comparison of GPT-4o with and without separate verifier BLINK benchmark
Model
Avg Accuracy (BLINK)
GPT-4o
62.25%
GPT-40 Verifier
69.15% % (+6.90%)
These improvements are particularly pronounced tasks requiring structured multi-step reasoning, with gains of +18.33% on Counting and +12.91% % on Functionally-Correlae tasks. Beyond per- formance benefits, the separated architecture offers practical advantages including model-agnostic verifier deployment across architectures (GPT-40, Qwen, LLaMA), reduced fine-tuning costs, and enhanced extensibility for tasks and domains. This analysis confirms that the separated reasoner- verifier design provides both performance benefits and practical advantages for complex visual reasoning tasks.
K Interpretability of Reasoning Traces
This section clarifies our claim regarding improved interpretability reasoning traces generated by our VTS-V framework. We define interpretability in this context as the explicit, grounded, and stepwise nature of the reasoning process that makes the model's s decision decision-making transparent and verifiable.
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Traditional vision-language models perform latent, one-shot image encoding and generate answers based on static visual token embeddings, offering limited insight into their reasoning process. In contrast, our framework produces multi-turn reasoning traces composed of explicit tool-use steps, where each turn includes:
A verbalized subgoal planning statement
A specific tool invocation with parameters
Visual feedback or observation from tool exccution
These intermediate outputs grounded in actual visual content through operations such as region cropping, OCR text extraction, depth map generation, and spatial analysis. This structured output format provides transparent reasoning trajectory that allows both human users and automated systems to inspect the decision process at each step.
Empirical evidence supports this improved interpretability. Across multiple benchmarks, our models generate longer and more structured reasoning trajectories compared to vanilla baselines. For instance, the average reasoning steps increase from approximately 1.5 (GPT-4o baseline) to 3.2 (our VTS-V framework), with diverse tool usage patterns including grounding actions, depth analysis, OCR operations, and region cropping.
Examples of these interpretable reasoning traces are visible in Figure 1 and Appendix C.3 of the main paper, demonstrating how models produce dynamic reasoning involving tool selection and verification-guu guidedd iteration. While future work could include manual evaluations of reasoning quality, our current framework already provides verifiable, human-readable sub-decisions that represent significant advancement beyond traditional black-box VLM inference.
L Ablation Study on the Reasoner Module
This section presents an ablation study evaluating the specific contribution of the reasoner module within our VTS-V framework. We compare two configurations: models using verifier guidance without the trained reasoner (tool actions generated directly by the base model) versus our full VTSSV framework with both trained reasoner and verifier components.
Table 10: Performance comparison with and without the reasoner module
Model Variant
V*Bench
MMStar
Math Vista
Twen2.5VVL-P2 + Verifier (w/o Reasoner)
67.54
55.93
7.80
DWe-2.5VL--BB- VTS-V (w/ Reasoner)
75.13
57.93
23.52
Qwen2VL-7B + Verifier (w/o Reasoner) Qwen2VL-7B + VTS-V (w/ Reasoner)
50.80
44.29
20.24
66.67
55.26
23.80
The results demonstrate that incorporating the trained reasoner significantly improves performance across all benchmarks. Without the reasoner module, models struggle to perform reliable multi-step reasoning, particularly on complex tasks like Math Vista where performance degrades substantially.
The addition of the reasoner consistently produces large performance gains, with improvements of up +15.72 points on MathVista for Qwen2.5V1L-7B and +15.87 points on V*Bench for Qwen2V1.-7B, These findings highlight the critical importance of the reasoner module in executing valid tool-use actions and effectively following verifier guidance during multi-step reasoning processes.
M Comparison with Dynamic Visual Attention Methods
This section provides comparative analysis between our VTS-V framework and prior work on dynamic visual attention, highlighting key distinctions in methodology and capabilities.
Our framework introduces a general, verifier-guided inference-time reasoning process based on Markov Decision Process (MDP) formulation, enabling multi-step refinement of visual understanding through a flexible set of visual tools. This approach differs fundamentally from existing methods in several important aspects:
38

---

While LMEye allows large language models to request new visual evidence, it lacks structured action space and formal termination control. Our approach models perception MDP-driven tool selection with a multi-step DPO-trained verifier that dynamically determines when to terminate reasoning.
LMEye:
InstructBLIP. This method enhances initial visual encoding through instruction tuning but performs single-pass perception. In contrast, our framework supports iterative, adaptive reasoning during inference, allowing models to invoke diverse tools (OCR, zoom, grounding) based on evolving contextual understanding.
V*: Primarily designed for recursive visual search to locate objects in high-resolution images, V operates with a binary search objective. Our framework addresses a broader range of tasks including mathematical reasoning. OCR, and chart understanding, with termination based on verifier-guided reasoning quality rather than search completion.
Our core innovations distinguish VTS-V V from these approaches:
1. Inference-time visual token scaling:
Dynamically adjusts which image regions receive detailed processing through tool invocation, rather than using fixed input-time processing.
2. MDP-based multi-step reasoning: Formally defines each state-action step to support structured perception and tool-based decision-making with theoretical guarantees.
3. Verifier-guided termination: Employs a learned verifier trained via multi-step DPO to provide step-wise feedback and enforce bounded reasoning (Lemma 3.2), improving both efficiency and robustness.
These innovations position VTS-V as a more comprehensive and theoretically grounded approach to dynamic visual reasoning compared to existing methods.
N Novelty Analysis and Comparison with Prior Work
In this section, provide detailed analysis of the novelty of our VTS-V framework and its distinctions from related works. While our method shares some conceptual similarities with prior research in iterative reasoning, reasiner-verifier separation, and tool use, it introduces several key innovations that advance the state of the art in multi-step visual reasoning:
MDP-based Reasoning Framework for Dynamic Visual Token Scaling: Unlike V* [27] which primarily focuses on task-specific visual cropping, we formulate multi-step visual reasoning as a Markov Decision Process over diverse and extensible set of visual tools (e.g., OCR, grounding, depth, segmentation). This formulation enables dynamic visual token scaling-allowingg the model to adaptively focus different regions modalities each reasoning step across a wide range of tasks and model architectures.
Step-wise Veritier with Theoretical Guarantees: While V-STaR [9] employs verifier to rank final answers, our verifier operates at each reasoning step, providing real-time guidance and enabling early termination with theoretically bounded steps (Theorem 3.2). This ensures both interpretability and computational efficiency, a feature not present in prior verifier-based methods.
First Dataset for Multi-Step Visual Tool Reasoning: Existing tool-use datasets (e.g.. from Visual Program Distillation [1]]) do not support multi-turn visual reasoning with rich intermediate states. We introduce VTS-SFT and VTS-DPO, the first datasets designed for fine-grained tool selection and verifier training over more than 80 diverse vision- language tasks, enabling robust generalization and grounding.
Generalization Without Fine-Tuning Our framework generalizes effectively even to closed-source models like GPT-4o without additional fine-tuning, improving performance by +6.9% on the BLINK benchmark. This demonstrates the flexibility and model aggostic nature of approach.
In summary, while our work builds upon prior art, it integrates these ideas into a unified, theoretically sound, and empirically validated framework that supports multi-step. tool-augmented, verifier-guided visual reasoning. We believe this represents a meaningful step forward enabling fine-grained and interpretable reasoning in multimodal systems.
39


Reviews:
[{"review_id": "gRmZrgiWch", "reviewer": "Reviewer_MBvX", "summary": "This paper presents VTS-V, a novel framework for inference-time visual token scaling in multi-modal large language models (MLLMs). Inspired by the dynamic, feedback-driven nature of human visual perception, the authors model visual reasoning as a Markov Decision Process. The framework consists of a reasoner that plans visual actions and a verifier trained via multi-step Direct Preference Optimization (DPO) to guide the reasoning steps and determine termination. To support this framework, the authors introduce VTS, a new dataset including supervised reasoning trajectories (VTS-SFT) and preference-labeled trajectory pairs (VTS-DPO). They demonstrate consistent improvements over several benchmarks, showing enhanced performance and interpretability.", "questions": "Please address the weaknesses above.", "limitations": "yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The iterative inference-time scaling of visual tokens using verifier-guided reasoning presents a new perspective in the field.\n- The iterative nature of VTS-V provides clear, interpretable reasoning paths, enhancing the transparency of model decisions.\n- The new dataset (VTS) provides valuable resources for further research.\n\nWeaknesses:\n- The complexity of implementation and computation inherent in training and inference procedures may limit widespread adoption. I encourage the authors to include a more detailed analysis of inference-time overhead, such as latency, and memory usage across models and datasets. \n- While the authors present comprehensive results for GPT-4o variants on the BLINK benchmark, the evaluation on other datasets such as V*Bench, MMStar, and MathVista is only conducted for open-source models. As GPT-4o represents a strong closed-source baseline, its exclusion from these additional benchmarks limits the understanding of how the proposed VTS-V framework generalizes across diverse reasoning tasks for top-tier models. Including these comparisons would strengthen the empirical claims.\n- The paper observes that integrating VTS-V with GPT-4o yields consistent improvements, even without additional fine-tuning, whereas applying the same method to open-source models (e.g., Qwen2-VL, LLaMA3.2) without fine-tuning leads to significant performance drops. However, this discrepancy is not thoroughly analyzed. The authors are encouraged to investigate and discuss potential reasons behind this behavior—for example, differences in instruction-following ability, pretraining data coverage, or inherent robustness to tool-augmented workflows.", "was_revised": true, "final_justification": "The well-designed iterative pipeline seems to be practical for visual token scaling, and the proposed dataset is useful for fine-tuning open-sourced models. I believe this work is deserved to be accepted.", "rebuttal": "**Overall Response**\n\nThanks for the detailed and thoughtful feedback. In response, we provided a quantitative analysis of inference-time latency and memory overhead, demonstrating the efficiency–accuracy tradeoffs of our verifier-guided framework. We also expanded GPT-4o evaluations across V*Bench, MMStar, and MathVista, showing strong gains over both baselines and alternative prompting methods. Finally, we clarified why our framework improves GPT-4o without fine-tuning but requires VTS-SFT to enable open-source models to follow structured, tool-based reasoning. All clarifications and new results will be incorporated into the revised version if the paper is accepted.\n\n> **Response to Weakness 1: Inference-time Overhead (Latency & Memory Usage)**\n> \n\nWe appreciate the reviewer’s thoughtful concern regarding inference complexity. To address this, we now provide a detailed quantitative analysis of inference-time overhead, including latency, memory usage, and the number of intermediate tokens generated during dynamic reasoning.\n\nOur method introduces iterative steps composed of:\n\n- Verifier calls, which require only prefill computation (i.e., forward pass over the input context to generate a stop/continue decision),\n- Reasoner calls, which involve autoregressive decoding to produce tool instructions.\n\nEach interaction is structured as:\n\n```jsx\ncontext = input_prompt: Q (image, text_question)\nwhile verifier(context) == 'continue':\n\tcurrent_output = reasoner(context)\n\tphysical_feedback = tool_using_API(current_output)\n```\n\nWe define the total inference latency as:\n\n$$\\text{Latency} = \\sum\\_{i=1}^{H} \\left( \\frac{C\\_i}{P\\_t} + \\frac{O\\_i}{D\\_t} \\right)$$\n\nWhere:\n\n- $H$: total number of reasoning steps;\n- $C\\_i$: number of input tokens at step i (verifier prefill);\n- $O\\_i$: number of generated tokens at step i (reasoner decode);\n- $P\\_t$: model’s prefill throughput (tokens/sec);\n- $D\\_t$: model’s decode throughput (tokens/sec).\n\n**Example Overhead (Qwen2.5-VL-7B-Instruct with VTS-V):**\n\n- Average steps (H): 3.1\n- Average verifier prefill tokens: ~10058.0 per step\n- Average reasoner decode tokens: ~95.3 per step\n- Throughput on 80GB A800 GPUs (float16):\n    - $P\\_t \\approx$ 18493.6 tokens/s\n    - $D\\_t \\approx$ 231.8 tokens/s\n\n**Total latency ≈ 3.1 × (10058.0 / 18493.6 + 95.3 / 231.8) ≈ 2.96 seconds**\n\n**Memory Usage:**\n\n- With max_model_len=65536 and dtype=float16, our models can be deployed within 32GB through vLLM or SGLang on 80GB A800 GPUs.\n- All tool models (including GroundingDINO, Depth-Anything, etc.) collectively require approximately 23 GB of additional memory during inference.\n\n**Tradeoffs and Mitigations:**\n\n- We find a clear tradeoff between reasoning depth and computational cost, which is justified by significant accuracy gains (e.g., +7.58% avg. on BLINK for Qwen2.5-VL-7B-Instruct).\n- To mitigate latency for deployment, our framework allows *parallel verifier batching*, *early stopping*, and *adaptive step truncation* (via ε-threshold).\n\nWe will include this analysis, along with latency and memory tables across models, in the revised Appendix B. Thank you again for the helpful suggestion.\n\n> **Response to W2: GPT-4o Evaluation on Broader Benchmarks**\n> \n\nWe sincerely appreciate the reviewer’s insightful feedback regarding the evaluation of our VTS-V framework on additional benchmarks for GPT-4o. We agree that including GPT-4o results on V*Bench, MMStar, and MathVista would better demonstrate the framework’s generalization across diverse reasoning tasks.\n\nTo address this, we conducted additional evaluation experiments, including GPT-4o, GPT-4o + CoT[1] and GPT-4o + Visual Sketchpad [2] as baselines. Our results are summarized below:\n\n|  |  V*Bench | MMStar | MathVista |\n| --- | --- | --- | --- |\n| GPT-4o | 60.73 |  58.40 | 63.80 |\n| GPT-4o + CoT | 60.73 | 56.47 | **66.50** |\n| GPT-4o + Sketchpad | 71.20 | 60.33 | 59.40 |\n| GPT-4o + VTS-V | **73.82** | **65.80** | 65.90 |\n\nKey observations:\n\n- Our VTS-V achieved state-of-the-art performance on both V*Bench and MMStar, with absolute improvements of **13.09%** and **7.4%** over the baseline GPT-4o, respectively,  demonstrating the efficiency of our approach.\n- Our method outperformed GPT-4o by 2.1% on MathVista. And it achieved nearly equivalent performance to the top-performing GPT-4o+CoT (a mere 0.6% difference), further demonstrating the competitiveness of our approach.\n\n[1] Wei J, Wang X, Schuurmans D, et al. Chain-of-thought prompting elicits reasoning in large language models[J]. Advances in neural information processing systems, 2022, 35: 24824-24837.\n\n[2] Hu Y, Shi W, Fu X, et al. Visual sketchpad: Sketching as a visual chain of thought for multimodal language models[J]. Advances in Neural Information Processing Systems, 2024, 37: 139348-139379.\n\n> **Response to W3: Performance Gap Between GPT-4o and Open-Source Models Without Fine-Tuning when integrating VTS-V**\n> \n\nWe thank the reviewer for raising this important point. While Section 5.2 (lines 306–317) of the main paper briefly mentions this observation, we now provide a more thorough explanation of why VTS-V improves performance in GPT-4o even without fine-tuning, but degrades performance in open-source models like Qwen2-VL and LLaMA-3.2-Vision.\n\nApplying VTS-V directly to GPT-4o yields consistent improvements across benchmarks without any additional training. In contrast, applying the same framework to open-source models *without fine-tuning* leads to degraded performance.\n\nWe hypothesize that this performance discrepancy stems from the following factors:\n\n1. **Lack of Tool-Using Priors in Open-Source Models.**\n    Unlike GPT-4o, open-source models are not pretrained or aligned with tool-augmented workflows. They have no exposure to structured reasoning formats like: Plan → Action → Tool call → Observation → Continue/Stop. As a result, when presented with verifier signals and expected to issue tool-use commands, these models either ignore the prompt or generate malformed instructions.\n    \n2. **Robust Instruction Following in GPT-4o.**\n    GPT-4o has undergone extensive alignment tuning (e.g., RLHF, tool-use demonstrations) which enables it to robustly interpret multi-turn instructions and unfamiliar prompting formats. This generalization allows it to cooperate with our verifier module out of the box, without dedicated SFT.\n    \n3. **Verifier Signal Interpretation.**\n    Verifier guidance in our framework (e.g., continue vs. stop) depends on implicit task understanding and adaptive response. GPT-4o can interpret these signals semantically, while open-source models require fine-tuning to learn how to react to verifier outputs correctly.\n    \n4. **Empirical Confirmation via SFT.**\n    After supervised fine-tuning on our VTS-SFT dataset, open-source models *learn valid tool-use behaviors* and align well with verifier guidance. Their performance not only recovers but exceeds the original baseline (e.g., Qwen2VL-7B-Instruct improves from 48.01% to 52.19%).\n    \n\nWe will clarify this distinction and analysis in the revision. This behavior gap also underscores the importance of our VTS-SFT dataset in enabling open-source models to benefit from verifier-guided multi-step reasoning workflows."}, {"review_id": "sQCvBUUJh4", "reviewer": "Reviewer_weSb", "summary": "This paper addresses the limitation of conventional multimodal large language models (MLLMs) with fixed and static visual tokens input, hindering iterative refinement of visual understanding. To bridge this gap, the authors propose a framework named Visual Token Scaling with Verification (VTS-V), which enables MLLMs to perform iterative, verifier-guided reasoning over visual content.\n\nVTS-V formulates visual reasoning as a Markov Decision Process (MDP) consisting of two core components: a reasoner that generates visual reasoning steps (planning, action selection, and observation) and a verifier trained via multi-step Direct Preference Optimization (DPO) to evaluate action quality and determine termination. To support training, the authors introduce the VTS dataset, comprising VTS-SFT (315K supervised reasoning trajectories with tool use) and VTS-DPO (301K preference-labeled trajectory pairs).\n\nExperimental results across diverse benchmarks (BLINK, V*Bench, MMStar, MathVista) demonstrate that VTS-V significantly outperforms baselines. For closed-source models like GPT-4o, it improves average accuracy on BLINK from 62.25% to 69.15%. For open-source models (e.g., Qwen2-VL-7B, LLaMA3.2-11B), fine-tuning on VTS-SFT followed by VTS-V yields gains of 4.18% to 7.58%. Ablation studies confirm the verifier’s critical role in filtering suboptimal paths.", "questions": "See the Weaknesses section for major concerns. Besides, I would like to ask the following questions:\n\n1. Since the pipeline is modeled as Markov Decision Process, why not train the models use RL algorithms (e.g., GRPO)?\n2. What if we train a single model to perform reasoning actions and verification both, instead of two separate models? Would it be more efficient?\n3. Can we use the trained VTS-V pipeline to construct a new iteration of VTS dataset, and iteratively boosting the framework in a self-teaching manner?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths:**\n- VTS-V effectively addresses the static inference limitation of MLLMs by introducing dynamic visual token scaling and verifier-guided iteration, aligning more closely with human-like dynamic perception.\n- The VTS dataset (VTS-SFT and VTS-DPO) fills a critical gap in tool-augmented visual reasoning data, providing high-quality supervised and preference-labeled trajectories to train both the reasoner and verifier.\n- Experiments span diverse benchmarks and model types (closed-source and open-source), showing consistent improvements in accuracy and interpretability.\n\n**Weaknesses:**  \n- Although the work is solid, the method is more like a combination of previous works [1] (for iterative observation and reasoning), [2] (for reasoner and verifier separation) and [3] (for tool-use), thus its novelty is limited.\n- The paper highlights \"visual token scaling\" as a key innovation, but it fails to clearly exhibit the scaling mechanism, e.g., a curve demonstrating the scaling law for visual tokens.\n- The verifier’s performance depends heavily on the VTS-DPO dataset, and its ability to adapt to unseen tasks or domains is not thoroughly explored. This raises questions about its robustness in real-world, diverse environments.\n\n[1] Penghao Wu and Saining Xie. $V^*$: 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.\n\n[2] ArianHosseini,XingdiYuan,NikolayMalkin,AaronCourville,AlessandroSordoni,and RishabhAgarwal. V-star: Training verifiers for self-taught reasoners. arXiv preprint arXiv:2402.06457, 2024.\n\n[3 ]Yushi Hu, Otilia Stretcu, Chun-Ta Lu, Krishnamurthy Viswanathan, Kenji Hata, Enming Luo, Ranjay Krishna, and Ariel Fuxman. Visual program distillation: Distilling tools and programmatic reasoning into vision-language models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 9590–9601, 2024.", "was_revised": true, "final_justification": "Thank you to the Authors for your patient rebuttal; my concerns have now largely been addressed. Based on this work's contributions to dataset construction and the use of verifiers, I believe it deserves to be accepted.​", "rebuttal": "**Overall Response**\n\nWe appreciate the thoughtful and constructive feedback! In response, we clarified the novelty of our verifier-guided MDP framework beyond prior work, provided visual token scaling analyses, and demonstrated strong generalization of the verifier across unseen domains. We also addressed design choices such as reasoner-verifier separation, the use of SFT over RL, and potential future directions like self-bootstrapping. These clarifications and results will be incorporated into the final version if the paper is accepted.\n\n> **Response to W1: Novelty Beyond Combining Prior Work**\n> \n\nWe appreciate this thoughtful feedback. While our work draws inspiration from prior efforts in iterative reasoning [1], reasoner-verifier separation [2], and tool use [3], we believe our contributions go beyond a simple combination. Specifically, we introduce a principled, theoretically-grounded framework tailored for multi-step visual reasoning with tool use, supported by both new methodology and new data.\n\nKey distinctions:\n\n- **MDP-based Reasoning Framework:**  Unlike V*[1], which focuses on task-specific cropping, we formulate reasoning as a Markov Decision Process over a diverse toolset (OCR, grounding, depth, etc.). This allows for flexible, dynamic visual token scaling across tasks and models.\n    \n- **Verifier for Guided Inference with Theoretical Guarantees:**  Compared to V-STaR [2], which ranks final answers, our verifier operates at each step, providing real-time guidance and bounded termination (Theorem 3.2), enabling interpretable and efficient inference.\n    \n- **New Dataset for Multi-Step Visual Tool Use:**  Prior tool-use works [3] do not support multi-turn visual reasoning. We contribute the VTS-SFT and VTS-DPO datasets, the first to support fine-grained tool selection and verifier training over >80 diverse tasks.\n    \n\nTogether, our framework enables strong generalization (e.g., +6.9% on GPT-4o without fine-tuning) and interpretability, establishing a solid foundation for future multi-modal reasoning systems. We will revise the manuscript to more clearly highlight these distinctions.\n\n> **Response to W2:  Visual Token Scaling Mechanism with Optimal-Stopping Verifier**\n> \n\nWe sincerely appreciate the reviewer’s insightful feedback regarding the need to clarify the visual token scaling mechanism. Below, we present selected experimental results demonstrating the scaling relationship between multi-step reasoning performance and output visual tokens, which reflects our framework’s dynamic behavior.\n\n- Results based on closed-source model APIs:\n\n| **Visual & Text Tokens Per Sample** | **GPT-4o BLINK Counting Accuracy** |\n| --- | --- |\n| 550 | 49.17% |\n| 1100 | 58.33% |\n| 1650 | **67.50%*** |\n| 2200 | 64.16% |\n| 2750 | 65.83% |\n\n- Results for the trained open-source models:\n\n| **Visual & Text Tokens Per Sample** | **Qwen2.5-VL BLINK Fun.Corr.** | **Qwen2-VL BLINK Depth** | **LLaMA-3.2-Vision BLINK Spatial** |\n| --- | --- | --- | --- |\n| 600 | 19.23% | 56.45% | 62.94% |\n| 1200 | 23.85% | **60.48%*** | 65.03% |\n| 1800 | 25.38% | 58.87% | **69.23%*** |\n| 2400 | **30.00%*** | 57.26% | 67.83% |\n| 3000 | 26.15% | 58.06% | 67.13% |\n\nThe tables above illustrate the relationship between reasoning accuracy and visual token usage for both GPT-4o and our trained models. On average, GPT-4o and our trained models generate approximately 50 and 100 text tokens per reasoning step, respectively, while processing ~100 visual tokens through dynamic image operations. We control the number of visual tokens by limiting the reasoner’s maximum steps, while our verifier selects the optimal stopping point (marked by *).\n\nKey findings:\n- Non-monotonic scaling: Accuracy improves with more visual tokens initially, but may decline if reasoning becomes unnecessarily long.\n- Verifier-guided optimality: Our VTS-V verifier consistently identifies the best stopping point, balancing depth and efficiency.\n- Robust reasoning: Even beyond the optimal step, accuracy remains higher than with under-reasoning, highlighting the benefits of sufficient visual grounding.\n\nWe will incorporate these scaling trends and supporting visualizations into the revised manuscript.\n\n> **Response to W3: Robustness and Generalization of the Verifier Trained on VTS-DPO**\n> \n\nWe thank the reviewer for raising concerns regarding the verifier’s dependence on the VTS-DPO dataset and its robustness to unseen domains. We provide further clarification below.\n\nThe VTS-DPO dataset is constructed based on the LLaVA-OneVision (LLaVA-OV) dataset, which is currently among the most comprehensive multi-modal corpora, covering over 80 distinct vision-language task types. Our DPO dataset comprises 301,028 preference pairs, carefully curated to span a wide range of visual reasoning domains. These include document understanding, scientific diagrams, mathematical problem solving, chart QA, OCR, and general commonsense VQA.\n\nThe dataset is divided into the following major categories:\n\n| **Domain Category** | **# Tasks** | **# Examples** |\n| --- | --- | --- |\n| General | 25 | 135,804 |\n| Document/Chart/Screen | 18 | 100,681 |\n| Math/Logical Reasoning | 15 | 52,049 |\n| OCR/Text-grounded Tasks | 6 | 12,494 |\n\nEach category includes examples from highly varied sources. \n\nNotably, all benchmarks used for evaluation in our experiments (e.g., BLINK, V*Bench, MMStar, MathVista) are held-out from the training data. The verifier is therefore evaluated on unseen reasoning tasks and domains. The strong performance observed across these evaluations supports the verifier’s ability to generalize beyond the training distribution.\n\nWe will expand on the construction and coverage of VTS-DPO in the revised Appendix, including a full breakdown of dataset sources and domains.\n\n> **Response to Q1: Why not use Reinforcement Learning (e.g., GRPO) to Train the Reasoner?**\n> \n\nWe appreciate the reviewer’s suggestion to explore GRPO for training the reasoner. We have conducted preliminary experiments and found that GRPO performs poorly in our multi-tool setting, where the reasoning space is large and tools are diverse. While prior works using GRPO (e.g., DeepEyes [1]) focus on limited-tool environments.\n\nTo address this, we adopt supervised fine-tuning (SFT) as a more stable and effective initialization strategy. Our VTS-SFT dataset serves as a strong cold-start foundation for future RL-based methods. While GRPO is not the focus of this paper, we are actively exploring its potential in future work with improved reward design and tool selection policies.\n\n[1] Zheng Z, Yang M, Hong J, et al. *DeepEyes: Incentivizing “Thinking with Images” via Reinforcement Learning*. arXiv preprint arXiv:2505.14362, 2025.\n\n> **Response to Q2: Why Separate the Reasoner and Verifier Instead of Using a Single Unified Model?**\n> \n\nWe thank the reviewer for this thoughtful question. In principle, combining reasoning and verification into a single model is an appealing idea for potential efficiency. However, based on both theoretical motivations and empirical observations, we find that the decoupled design is more effective in practice, especially in the context of multi-modal, tool-augmented reasoning.\n\n**1. Current Models Struggle to Jointly Handle Both Tasks Well:** Reasoning and verification represent distinct capabilities: the reasoner must generate tool-using action plans conditioned on complex context, while the verifier needs to evaluate the overall quality or utility of each reasoning step. In practice, we observe that when both responsibilities are handled by a single model, the performance on one or both tasks deteriorates.\n\n**2. GPT-4o Results Support the Effectiveness of Separation:** Our experimental results (see table below, excerpted from Table 1) show that adding a standalone verifier to GPT-4o leads to significant performance improvements:\n\n| **Model** | **Avg Accuracy (BLINK)** |\n| --- | --- |\n| GPT-4o | 62.25% |\n| GPT-4o + Verifier | **69.15%** (+6.9) |\n\nThis demonstrates that adding a verifier as a separate module to an already-strong base model (GPT-4o) yields substantial gains, especially on tasks that require structured multi-step reasoning (e.g., +18.33 on Counting, +12.91 on Functionally-Correlated tasks).\n\n**3. Modularity and Reusability of Verifier:** Our verifier can be viewed as a plug-in component: it is model-agnostic and can be reused across architectures (e.g., GPT-4o, Qwen, LLaMA) once trained. This improves flexibility, reduces fine-tuning costs, and makes the framework extensible to new tasks or domains.\n\nWe will clarify this design decision in the final version of the paper.\n\n> **Response to Q3: Iterative Bootstrapping of VTS via Self-Teaching**\n> \n\nWe appreciate the reviewer’s insightful suggestion.\n\nUsing the trained VTS-V pipeline to construct additional VTS-style data in a self-bootstrapping fashion is indeed an interesting and promising direction. It aligns well with recent trends in self-improving agents and iterative data refinement.\n\nOne potential challenge, however, lies in maintaining supervision quality during self-generated data collection. Our VTS-SFT and VTS-DPO datasets rely on high-quality reasoning trajectories and carefully curated preference signals. If the model-generated traces contain subtle reasoning errors or invalid tool calls, these could accumulate and introduce bias or instability during future training rounds.\n\nThat said, combining model-generated traces with selective human or verifier-based filtering may offer a scalable way forward. We see this as an exciting avenue for future work and will consider incorporating this direction into our ongoing research agenda."}, {"review_id": "9IuSgVShjV", "reviewer": "Reviewer_XMPf", "summary": "This paper focus on inference-time visual token scaling, via a tool-augmented VLM Reasoner module and a verifier optimized by DPO. The Reasoner can be either API-based models or finetuned open-source models.\nThe proposed framework relies on the self-constructed dataset, a new tool-enhanced CoT-style dataset.\nThis paper also describes engineering details of their data generation pipeline.\nThe method outperforms baselines, both tool-augmented and prompt-based methods, across several visual reasoning benchmarks, demonstrating improved accuracy and tool-using ability. The authors also provide theoretical guarantees that their algorithm ensures a bounded number of reasoning steps, preventing looping or repetitive outputs.", "questions": "1. Please response to Weaknesses.\n2. From Table2, there could be a conclusion that the improvement main comes from the curated dataset. The gain of the framework itself remains unclear.\n3. Is it possible to add additional experiment of w/o reasoner (as the other ablation study in table3)? This could further demonstrate the effectiveness of the entire framework, otherwise the reasoner could be a dispensable module.\n\nI acknowledge that the dataset could be useful, please provide further explanation and evidence to demonstrate the necessity and effectiveness of the framework (as mentioned above) , so that this paper would not remain significant in dataset engineering only. I will raiss my rating if all questions and concerns are solved.\n\nAdditional suggestion: (NOT weakness) \n1. Some simple visualisations of the framework would assist in understanding of the entire work.\n2. Please carefully check the tables and figure in appendix. They are not properly displayed.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths:**\n1. The paper presents a technically solid framework with clear theoretical explanation.\n2. The design and construction of tool-augmented multi-step visual reasoning dataset is well motivated, addressing a notable gap in existing datasets, which would be useful to future research.\n3. The proposed method largely improves the performance of open-source models regarding visual reasoning and grounding tasks.\n\n**Weaknesses:**\n1.Authors claim that their proposed method offers more interpretable reasoning traces. However, no related evaluation or demonstrations of resulting generations of the trained models are provided (authors only provide the example trace in their constructed data).\n  - More discussion about the results from the trained models using their data should be provided to better support the claim of \"more interpretable reasoning traces\". A dataset with longer reasoning traces or traces with diverse tools does not guarantee that the trained models would exhibit exactly desired performance.\n  - Manual evaluation or further comparison is required to support the contribution regarding the term, \"more interpretable reasoning trace\". For example, in Line 92-95, these methods is not **limited** to 1-2 steps, many questions can be well solved only via 1-2 steps.\n2. The verifier is similar to existing feedback-based reflective mechanisms. According to Line 103, the proposed method should differ in both tasks and training datasets. However, the proposed framework is also a tailored dataset whose actions are restricted to tool-use.", "was_revised": true, "final_justification": "The authors provide strong evidence supporting the effectiveness of the Reasoner and their proposed framework, which are my primary concerns. I will still increase my rating from 3 to 4 because authors provide persuasive technical clarification for most of my concerns.", "rebuttal": "**Overall Response**\n\nWe appreciate the thoughtful feedback and valuable suggestions. In response, we clarified our definition of interpretability, highlighted how our structured tool-use traces offer stepwise, visually grounded transparency, and provided empirical evidence supporting this claim. We also clarified how our verifier differs from prior reflective mechanisms, distinguished the impact of the VTS-V framework from the dataset, and added ablations isolating the reasoner’s contribution. All corresponding updates and clarifications will be incorporated into the final version if the paper is accepted.\n\n> **Response to W1: Evaluation of the Claim “More Interpretable Reasoning Traces”**\n> \n\nWe thank the reviewer for raising this important question regarding the interpretability of reasoning traces generated by our model. We clarify below what we mean by *interpretability* in the context of our method and why it is supported by the proposed framework and results.\n\n**1. Nature of Interpretability in Our Setting:** Traditional VLMs perform latent, one-shot image encoding and generate answers based on static visual token embeddings. In contrast, our model produces *multi-turn reasoning traces* composed of explicit tool-use steps:\n\n- Each turn consists of a verbalized subgoal, an invoked tool, and a visual feedback observation.\n- These intermediate outputs are grounded in the actual visual content (e.g., cropped regions, OCR text, depth maps), providing a transparent reasoning trajectory.\n\nThis tool-augmented, structured output allows both humans and verifiers to inspect the decision process at each step. As a result, the model’s internal reasoning becomes observable and interpretable, rather than remaining a latent process.\n\n**2. Examples Beyond Dataset Construction:** In addition to the trace examples in our constructed VTS dataset, the trained models retain and generate similar multi-step reasoning traces during inference. These traces are observable in Figure 1 and in Appendix C.3, where models produce dynamic reasoning involving tool selection and verification-guided iteration. Each generation includes a full trajectory with tool actions and outputs.\n\n**3. Empirical Support via Multi-Step Trace Lengths and Tool Diversity:** Across multiple benchmarks (e.g., BLINK, V*Bench), our models often generate longer and more structured reasoning trajectories compared to vanilla baselines. For instance, average reasoning steps increase from ~1.5 (GPT-4o baseline) to ~3.2 (ours with VTS-V), and tool diversity is observed in the trace logs, including frequent use of grounding, depth, OCR and cropping actions.\n\n**4. Future Work on Manual Evaluations:** We agree that a manual or crowdworker-based evaluation of reasoning quality (e.g., alignment between trace and final answer) would further strengthen this claim. We plan to include such analysis in future work, but our current framework already outputs verifiable, human-readable sub-decisions, which is a step beyond traditional black-box VLM inference.\n\nWe will revise our manuscript to clarify this distinction and to emphasize that the interpretability claim refers to the *explicit, grounded, and stepwise trace format* enabled by our model, rather than implying subjective human quality judgments alone.\n\n> **Response to W2: Relation to Existing Feedback-Based Reflective Mechanisms**\n> \n\nWe thank the reviewer for pointing out the need to better clarify how our verifier differs from existing reflective or feedback-based mechanisms. We agree that our original related work discussion could have better distinguished the motivation and contributions of our verifier design.\n\nWhile prior works such as V-STaR and step-level math verifiers adopt reflective paradigms for single-domain problems (e.g., mathematical reasoning), our verifier is designed for multi-modal, tool-augmented, and multi-step visual reasoning. Most existing verifiers operate in textual domains, generate scalar scores or binary accept/reject signals, and are trained with task-specific preference data.\n\nOur method differs in the following key aspects:\n\n- We design a verifier that operates over multi-modal reasoning trajectories involving visual tools and structured actions, rather than purely textual rationales.\n- We train the verifier using multi-step preference comparisons derived from our large-scale and diverse VTS-DPO dataset, which is constructed from the LLaVA-OneVision corpus and covers over 80 real-world task types.\n- Our verifier is not just a reward model but actively controls reasoning flow during inference, enabling early stopping and action rejection.\n\nWe will revise our related work section accordingly to better reflect these distinctions.\n\n> **Response to Q2: Clarifying the Contribution of the Framework vs. the Dataset**\n> \n\nThanks for the thoughtful question. We agree that distinguishing between the impact of the framework (VTS-V) and the curated dataset (VTS-SFT) is important.\n\nOur experimental results (see table below, excerpted from Table 1) demonstrates that the framework alone leads to substantial improvements when applied to a capable model like GPT-4o *without any fine-tuning*:\n\n| **Model** | **Avg Accuracy (BLINK)** |\n| --- | --- |\n| GPT-4o | 62.25% |\n| GPT-4o + VTS-V | **69.15% (+6.9)** |\n\nThis indicates that the VTS-V framework itself is effective, assuming the base model can understand multi-turn instructions and tool-augmented reasoning workflows.\n\nIn Table 2, applying the same framework to open-source models without fine-tuning leads to performance degradation. This is not a limitation of the framework, but rather a reflection of the lack of tool-use priors and alignment tuning in these models. Specifically:\n\n- Open-source models have no pretraining exposure to structured reasoning formats like: Plan → Action → Tool → Observation → Continue/Stop.\n- They often misinterpret verifier signals or fail to produce valid tool-use outputs without explicit instruction.\n\nBy contrast, GPT-4o benefits from strong instruction-following and alignment capabilities, allowing it to integrate seamlessly with VTS-V.\n\nAfter fine-tuning open-source models with VTS-SFT, they learn to properly use the framework and outperform their original baselines (e.g., Qwen2VL-7B improves from 48.01% to 52.19%).\n\nWe will clarify this distinction in the revision.\n\n> **Response to Q3: Ablation Without the Reasoner**\n> \n\nThanks for the suggestion. To directly evaluate the contribution of the **reasoner module**, we compare models with:\n\n- **w/o Reasoner**: The base model uses verifier guidance but no trained reasoner (tool actions are generated directly).\n- **w/ Reasoner**: Our full VTS-V framework, with both trained reasoner and verifier.\n\nWe report the results below:\n\n| Model Variant | V*Bench | MMStar | MathVista |\n| --- | --- | --- | --- |\n| Qwen2.5VL-7B + Verifier (w/o R) | 67.54 | 55.93 | 7.80 |\n| Qwen2.5VL-7B + VTS-V (w/ R) | 75.13 | 57.93 | 23.52 |\n| Qwen2VL-7B + Verifier (w/o R) | 50.80 | 44.29 | 20.24 |\n| Qwen2VL-7B + VTS-V (w/ R) | 66.67 | 55.26 | 23.80 |\n\nThe results demonstrate that incorporating the trained **reasoner** significantly improves performance across all benchmarks. Without the reasoner (Verifier-only), models struggle to perform reliable multi-step reasoning—especially on complex tasks like MathVista. Adding the reasoner consistently leads to large gains (e.g., +15.72 on MathVista for Qwen2.5VL-7B), highlighting its importance in executing valid tool-use actions and following verifier guidance effectively.\n\nWe will highlight this finding more clearly in the revised version.\n\n> **Response to AQ1 & AQ2: Framework Visualization and Appendix Formatting**\n> \n\nThanks for the feedback. We have added improved visualizations of the framework and corrected the formatting issues in the appendix. These updates will be reflected in the revised version of the paper."}, {"review_id": "ziBghesdgV", "reviewer": "Reviewer_CE1C", "summary": "This research addresses the limitations of the static visual encoding paradigm in current Multimodal Large Language Models (MLLMs). It highlights how their pre-processing approach, which relies on fixed visual tokens, hinders dynamic reasoning capabilities and fundamentally differs from the iterative feedback mechanism of human perception. The authors propose a framework: inference-time visual token scaling. This framework models the process using a Markov Decision Process and dynamically adjusts the inference process with a multi-step DPO-trained validator. This allows the model to achieve adaptive, refined analysis of visual content. To validate the effectiveness of their method, the researchers also constructed a specialized dataset called VTS, which includes both supervised trajectories and preference comparisons.", "questions": "see the weakness", "limitations": "N/A", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n1. The paper proposes a dataset which may help the training of the reward model.\n\n2. The proposed method is effective for some image-based visual reasoning tasks\n\n\n**Weakness**\n\n1. Figures 1 and 2 are not clear.\n\n2. If the \"reasoning reinforcement polishing\" (likely referring to your iterative refinement process) involves multiple rounds of actions, please elaborate on the key distinctions between your proposed reinforcement learning method and existing multi-round reinforcement learning approaches. Specifically, how does your inference-time visual token scaling mechanism and the use of a multi-step DPO trained validator differentiate it from, or build upon, traditional multi-round reinforcement learning paradigms?\n\n3. Your core motivation is to address the limitations of static visual information input, which leads to incomplete attention during contextual reasoning. While the self-attention mechanism in large language models does allow for varying attention to visual tokens during training and inference, your work introduces a novel approach to dynamic attention adjustment for visual information. It's crucial to acknowledge and explicitly compare your method with prior work that has also tackled dynamic visual attention or iterative perception in MLLMs. Please discuss how your approach, particularly inference-time visual token scaling and the Markov Decision Process modeling, differs from and potentially advances solutions proposed in works such as:\nLMEye: Iterative Perception Network; InstructBLIP; V*\nA clear comparative analysis against these established methods would significantly strengthen your paper's contribution and highlight the novelty of your proposed framework.\n\n4. The experimental results show limited improvement in some datasets, and the improvement may be largely relevant to the sft stage.", "was_revised": true, "final_justification": "My concerns have now been addressed. The authors promise to revise the paper further to include some new complementary experiments and discussions with other methods.", "rebuttal": "**Overall Response**\n\nWe appreciate the insightful feedback and detailed questions. In response, we clarified key conceptual differences from traditional RL and dynamic attention methods, emphasizing our verifier-guided, multi-step MDP formulation and inference-time visual token scaling. We also updated Figures 1 and 2 for clarity, and clarified the respective roles of our framework and fine-tuning, supported by both GPT-4o and open-source model results. These clarifications and improvements will be included in the revised version.\n\n> **Response to W1: Clarity of Figures 1 and 2**\n> \n\nThanks for the feedback. We have improved the clarity of Figures 1 and 2, and the revised versions will appear in the updated paper.\n\n> **Response to W2: Differences from Traditional Multi-Round Reinforcement Learning**\n> \n\nThanks for the thoughtful question. While our method is formally cast as a Markov Decision Process (MDP), it departs significantly from traditional multi-round reinforcement learning (RL) paradigms in both its state formulation and guidance mechanism.\n\n**1. Dynamic Visual Token Scaling at Inference Time**: Traditional RL agents operate over fixed state encodings (e.g., static image tokens). In contrast, our framework performs inference-time visual token scaling, allowing the model to dynamically generate new visual tokens through actions such as zooming, OCR, grounding, and depth estimation.\n\n- This enables iterative refinement of visual context, rather than reasoning over a one-shot encoding.\n- Actions are selected conditionally based on prior steps, supporting context-aware visual exploration.\n\n**2. Verifier-Guided Reasoning via Multi-Step DPO (Not Reward Maximization)**: Instead of using scalar rewards to optimize policy, we guide reasoning using a multi-step DPO-trained verifier, which evaluates entire reasoning trajectories based on preference comparisons.\n\n- The verifier provides step-wise utility signals, assessing both intermediate tool actions and final outputs.\n- This enables fine-grained control and inference-time termination based on theoretical bounds (Theorem 3.2), which is typically lacking in RL agents prone to over-exploration or loops.\n\nWe will clarify these distinctions in the revised draft.\n\n> **Response to W3: Comparison with Prior Work on Dynamic Visual Attention**\n> \n\nThanks for raising this important point. We agree that dynamic visual perception is a growing area, and we appreciate the opportunity to clarify how our framework differs from prior methods like LMEye, InstructBLIP, and V*.\n\nOur proposed framework introduces a general, verifier-guided inference-time reasoning process built on a Markov Decision Process (MDP). It enables multi-step refinement of visual understanding via a flexible set of visual tools—something that existing approaches do not fully support.\n\n**Comparison with Prior Work:**\n\n- LMEye allows LLMs to request new visual evidence, but lacks a structured action space and termination control. In contrast, we model perception as MDP-driven tool selection and pair it with a multi-step DPO-trained verifier that decides when to stop.\n- InstructBLIP enhances initial visual encoding using instruction tuning, but performs single-pass perception. Our approach allows iterative, adaptive reasoning during inference, where the model can invoke tools like OCR, zoom, or grounding based on ongoing context.\n- V* performs recursive visual search, mainly for locating objects in high-res images. Our framework is more general-purpose, supporting a wider range of tasks (e.g., math, OCR, charts), and termination is based on verifier-guided reasoning quality, not a binary search objective.\n\n**Our Core Innovations:**\n\n1. **Inference-Time Visual Token Scaling** – Dynamically adjusts which image regions are processed in more detail via tool-use, not fixed at input time.\n2. **MDP-Based Multi-Step Reasoning** – Each state-action step is formally defined, supporting structured perception and tool-based decision-making.\n3. **Verifier-Guided Termination** – A learned verifier trained via multi-step DPO provides step-wise feedback and enforces bounded reasoning (Theorem 3.2), improving efficiency and robustness.\n\nWe will update the manuscript to explicitly include this comparative discussion.\n\n> **Response to W4: Clarifying Dataset-Wise Improvements and the Role of SFT**\n> \n\nThanks for pointing this out. We agree that some datasets show more modest improvements, and we welcome the opportunity to clarify the role of our framework vs. fine-tuning in these results.\n\nAs shown in Table 1, applying the VTS-V framework to GPT-4o—without any fine-tuning—already results in substantial gains:\n\n| **Model** | **Avg Accuracy (BLINK)** |\n| --- | --- |\n| GPT-4o | 62.25% |\n| GPT-4o + VTS-V | **69.15% (+6.9)** |\n\nThis demonstrates that the framework itself is effective, particularly when the base model (like GPT-4o) is well-aligned and capable of interpreting multi-step instructions and tool-use signals.\n\nIn Table 2, open-source models (e.g., Qwen2-VL, LLaMA3.2) show degraded performance when using VTS-V without fine-tuning. This is not due to the framework’s limitations, but rather:\n\n- These models lack tool-use priors and have no exposure to structured reasoning loops (e.g., Plan → Action → Tool → Feedback → Stop/Continue).\n- They also lack the instruction-following robustness of GPT-4o and thus cannot properly interpret verifier feedback or generate well-formed tool commands.\n\nOnce fine-tuned with our VTS-SFT dataset, these models learn to align with verifier signals, producing valid reasoning trajectories and improving beyond their baselines (e.g., Qwen2VL-7B improves from 48.01% to 52.19%).\n\nWe will clarify this distinction in the revision."}]

Author rebuttal:

Meta-review: This paper introduces an inference-time visual token scaling approach by modeling visual reasoning as a Markov Decision Process with two main components: a reasoner and a verifier. The authors also present a dataset with supervised reasoning trajectories incorporating tool use for training purposes. Experimental results demonstrate consistent improvements across several benchmarks.

The reviewers agreed that the verifier-guided reasoning is a unique contribution. They also noted that the proposed dataset has strong potential to inspire future work in the field. While reviewers initially raised concerns about novelty, training details, and the need for additional analysis, these were well addressed during the rebuttal phase and confirmed by the reviewers.

The AC agrees with the reviewers’ recommendation of acceptance.
Decision: Accept (poster)