Reasoning-Aligned Perception Decoupling for Scalable Multi-modal Reasoning
Authors: Yunhao Gou
Kai Chen
Zhili Liu
Lanqing HONG
Xin Jin
Zhenguo Li
James Kwok
Yu Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: MLLM
multi-modal
reasoning
Primary area: foundation or frontier models, including LLMs

Abstract: Recent breakthroughs in reasoning language models have significantly advanced text-based reasoning. On the other hand, Multi-modal Large Language Models (MLLMs) still lag behind, hindered by their outdated internal LLMs. Upgrading these LLMs is often prohibitively expensive, as it requires costly vision-language alignment retraining. To address this issue, we introduce Perception-Reasoning Decoupling,  which modularizes the MLLM’s reasoning component and makes it easily replaceable. This approach redefines the MLLM's role to convert multi-modal inputs into detailed textual outputs that can be processed by any powerful, external, text-only LLM reasoners. To align the MLLM's perceptual output with the final reasoning task, we propose a novel reinforcement learning algorithm called Visual Perception Optimization (VPO). VPO rewards the MLLM based on the correctness of answers generated by the external reasoner to produce faithful and query-relevant captions. Together, this decoupling pipeline and VPO form our Reasoning-Aligned PerceptIon Decoupling (RAPID) approach. Empirical results show that RAPID achieves significant performance gains on multi-modal reasoning benchmarks. Crucially, RAPID enables a novel inference-time scaling paradigm: Once trained with VPO, the MLLM can be paired with any state-of-the-art LLM reasoner for consistent performance improvement without retraining.

Published as a conference paper at ICLR 2026
REASONING-ALIGNER PERCEPTION DECOUPLING FOR SCALABLE MULTI-MODAL REASONING
Yunhao Gou 1.2+ Kai Chen
Zhili Liu Lanqing Hong"
Xin Jin',
Zhenguo Li James T. Kwok?
Yu Zhang't
Southern University of Science and Technology
"The Hong Kong University of Science and Technology
3 Huawei Noah's 's Ark Lab
Huawei Cloud
Project Page:
ABSTRACT
Recent breakthroughs in reasoning language models have significantly advanced text-based reasoning. On the other hand, Multi-modal Large Language Models (MILMss) still lag behind, hindered by their outdated internal LLMs. Upgrading these LLMS is often prohibitively expensive, as it requires costly vision-language alignment retraining. To address this issue, introduce PerceptionnRRasonnie Decoupling, which modularizes the MLLM's reasoning component and makes it easily replaceable. This approach redefines the MLLM's role to convert multi- modal inputs into detailed textual outputs that can be processed by any powerful, external, text-only LLM reasoners. To align the MLLM's s perceptual output with the final reasoning task, we propose novel reinforcement learning algorithm called Visual Pereeption Optimization (VPO). VPO rewards the MLLM based on the correctness of answers generated by the external reasoner to produce faithful and query-relevant captions. Together, this decoupling pipeline and VPO form our Reasoning Aligned Perception Decoupling (RAPID) approach. Empirical results show that RAPID achieves significant performance gains on multi-modal reasoning benchmarks. Crucially, RAPID enables novel inference-time scaling paradigm: Once trained with VPO, the MLLM can be paired with any state-of-the-art LLM reasoner for consistent performance improvement without retraining.
INTRODUCTION
Recent reasoning language models, such as OpenAl-ol (Jaech et al. 2024) and Qwen3 Yanng et al. 2025a), have driven significant gains in complex math and science tasks. By emulating deliberate, step-by-step reasoning process akin to human reflection, these models avoid superficial shortcuts. As a result, they substantially outperform previous models like GPT-4o (Hurst et al. (024). with improvements exceeding 30% on math benchmarks like AIME24 (AME 2024) and around 10% on
science benchmarks like GPQA (Rein et al.] 2024).
Translating breakthroughs from the uni-modal text to the multi-modal domain remains significant challenge. Existing multi-modal large language models (MLLMs), like Qwen2.5-VL (Bai et al. 2025) )
Gemma3 (Team et al. 2025a), and InternVL3 (Zhu et al. 2025), still struggle with reasoning and math-intensive tasks because their underlying LLMs are outdated or lack slow-thinking capabilities. While approaches like VL-Rethinker (Wang et al. (022aa) and MM-EUREKA (Meng et al.) 2025) try to improve performance with reinforcement learning. their success is fundamentally restricted by the reasoning capability of the base L.M.. The ideal solution, namely, switching the LLM with the most state-of-the-art one, is often prohibitive, as requires repeating the entire, costly vision-language alignment process. This raises the critical question: Can we replace the LLM within an MLLM to unlock advanced reasoning" efficiently, without undertaking redundant vision-language retraining?
To address that, we propose the Perception- Reatonnng Decoupling pipeline, where we re-focus the MLLM's primary role on perception. It first translates the multi-mode modal inputs into comprehensive
"qqual contribution
Corresponnencc to yu.zhang..usi ast @ gmail.com In this paper, we focus on multi-modal math and science reasoning tasks.

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Published as a conference paper at ICLR 2026
textual representation, which is then processed by separate, powerful, external LLM for reasoning. This decoupling allows flexible alteration of the LLM reasoner, offering a path to circumvent the costly retraining cycle. Our key distinction from similar two-stage pipelines (Tiong et al. 2022 Guo et al. 2022 Hu et al. 2022 Gou et al. 2024 Lu et al. 2025) lies in the textual representation, which includes both query-relevant caption and tentafive solution to ensure all essential visual information is captured for subsequent reasoning. However, the critical challenge in this new pipeline that the generated textual outputs are not optimized for correct reasoning.
InternVL3-788 L-8
A
IntemVVL3-388
55
InternVL3-148
InternVL-888
Average Performance
Dvis2-348
50-
X
Ovis2-88
Gemma3-278
Gemma3-128
45-
MM-Eureka--5
MM Eureka 7B
VL-Rethinker:726
VL-Retrinker-78
40
QVQ-72B 728. Preview
Qwen2. 5-V
Qwen2.5.VL.3 V-BL-2B
Qwen2.5 L-V
35
Qwen2.5 5-VL-36
100
152
Qwen2.5:V4 VLVB-228 (RAPID)
5w--22.5VL-77 (RAPID)
Total Model Size (B)
Qwen2.5-VV.33 (RAPID)
Figure 1: Comparisons on multi-modal reasoning benchmarks on average performance and total model size between RAPID-enhanced Qwen2.5-VV VL series of models and the other existing MLLMs.
Check the detailed numerical results in Appendix B and experimental settings in Sec. 4.1
To overcome that, we introduce Visual Perception Optimization (VPO), a novel policy gradient algorithm operating through reinforcement learning feedback loop where, given a user query, the MLLM first generates group of query-relevant captions, which are then considered as contexts for the external LLM reasoner to generate final answers. With a correctness- -aase reward function, the perceptual MLLM is aligned with the reasoning objective, and guided to generate faithful and query-relevant captions optimized for the correctness downstream reasoning. The combination of the Perception Berception-RRessoning Decoupling pipeline with the VPO algorithu forms overall approach, named Reasoning- Beatniingggliinnnne Aligned PerceptIon Decoupling (RAPID)
Empirically, RAPID achieves notable performance gains on challenging benchmarks such as Math- Verse (Zhagg et al., 2024), Math Vision (Wang et al.) (024b) and Logic Vista (Xiao et al.] 2024). Moreover, perception and reasoning are decoupled, the MLLMs trained with VPO generate textual outputs that can be directly fed to any LLM for reasoning. This eliminates the necessity for retraining, and enables RAPID be practical solution for the rapid evolution of MILMS and reasoning LLMs. Figure I compares various MLLMs against the RAPID- -APlD-enhanced Qwen2.55VV series. For each RAPID-enhanced group (e.g., Qwen2.5-VL-3B) we optimize the MLLM with VPO using minimal data (39K). The resulting performance curves are generated simply by pairing the optimized MLLM with increasingly powerful external LLMs (see Appendix [ for the choice of configurations), demonstrating novel inference-time scaling paradigm.
Our contributions can be summarized as follows:
We introduce the Perception-Reaseee multi-modal perception, allowing the reasoning component to be flexibly replaced by any advanced external LLM without burdensome retraining.
Decoupling pipeline, which redefines MLLMs' focus to
We propose Visual Perception Optimization (VPO), a novel policy gradient algorithm that aligns the MLLM's perceptual outputs by using the correctness of the external LLM's final the perceptual outputs as contexts for reward signals.
with
Combining both, RAPID achieves significant performance gains and introduces an efficient, novel "plug-and aad---ndd-pyyyy play" inference-time scaling approach. By eliminating the costly retraining required by traditional methods, an one-time optimized MLLM can be paired with any stronger LLM for continual performance improvements, demonstrated in Figure]]
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Published as a conference paper at ICLR 2026
Visual Perception Optimization (VPO)
Transfer to any LLM
V&L aiginemnt
QwQ
Qwen3
Policy Updata
1,
if
Ver
0,
otherwise
y
!!!
Pre-train
Pre-train
data
Qwen3
Trillions tokens
SFT
SFT
Serception-Reasoning Decoupling
QwQ
LLM
Redo
RL
RL
MLLM
Textaai Outputs
...
elingment
MLLM-1
MLLM-n
R1-32B
LLMs
Image
(a) Existing MILM alignment methods.
(b) RAPID (ours).
Figure 2: Comparisons between RAPID and existing alignment methods for reasoning MLLMs. For novel LLMs, existing methods (a) repeatedly conduct the compute-intensiig alignment procedure, while (b) RAPID decouples the visual perception from text-only reasoning (Sec. B.I] by learning to
extract reasoning-aligned visual contexts with the proposed VPO algorithm (Sec. 3.2). Note that the
caption penalty, as in Eq. 3 is omitted here for simplicity. The flame and snowflake icons indicate the models are trainable and frozen, respectively, during the process.
RELATED WORK
Improving the Reasoning Ability of MILMs.
Start with existing MLLM (e-g., Qwen2.5-
VL (Bai et al. ). a widely adopted approach is to perform reinforcement learning or knowledge
distillation. For example, VL-Rethinker (Wang al. 2025a), MM-EUREKA (Meng et al. 2025)
and NoisyRollout @Liu et al. (2255) apply GRPO (Shao et al. 2024 (or its variant (Liu et al. )025ch) to MLLMs to learn deliberate reasoning patterns. Distillation based methods, such as RI- OneVision Yang et al. 2025b), Vision-R1 (Huang et al. (025)) and Re ReVisull-R1 (Chen et al. 2025h) perform supervised fine-tuning (SFT) on reasoning data. However, both methods are restricted by the base LLMs (e.g.. Qwen2.5 (Yang et al. 2024 which lags behind state-of-the-at reasoning models (e.g. Qwen3-8B (Yang et al. 2025a)) While adopting a stronger LLM is an intuitive solution, re-aligning vision and language through full retraining on trillions of tokens is prohibitively costly.
Caption- -eaee-tthe---easasso Pipelines. To leverage LLM reasoning without intensive retraining, prior work explores similar theepiiionttee--easoon pipelines that decouple perception from reasoning. These approaches use Vision-Language Models (VLMs) (Radford et al. [202] [i et al. 2022; Yu et al.) 2022) or MLLMs for the perception task, while a separate LLM handles reasoning. Efforts this area primarily focus improving caption generation, for instance by selecting query-relevant image patches for captioning (Tiong et al. 2022 Guo et al. 2022), prompting MLLMs for query-aware captions (Gou et al. 2024). enhancing captioning datasets (Hu et al. 2022 Lu et. 2025). RAPID differs from these works in two key aspects. First, it includes a tentative solution in its generated output to better capture critical visual information. Second, while existing methods do not optimize captions for the final outcome, RAPID rewards the captioning process based on the correctness the final answer produced by the reasoning LLM.
METHODOLOGY
This section describes the two main components of RAPID: perception-reasoning decoupling (Sec. and visual perception optimization (Sec. 3.2) Figure 2 gives an overview of the approach.
3.1
3.1
PERCEPTION-REASSONE
DECOUPLING
Given an image / and a relevant query y. our perceptiion-reasoning decoupling pipeline involves two consecutive stages: (i) Perception, where an MI.MM (e.g., Qwen2.5-VI. (Bai al., (025)) acts as perception module to generate group of textual outputs Op (detailed below) with respect to the image 1 and a perception prompt.
(ii) Reasoning, where a powerful text-only LLM reaonser (e.g., R1-Distilled-75 (Guo al. 2025) or Qwen3-8B (Yang al. 2025a)) receives the original query q and a consolidated set of perceptual outputs, Op, which are structured by a reasoning prompt P. (shown in Fig. 12 y LLM(P, O,)).
key advantage of this decoupling pipeline is that the textural outputs form a universal interface between perception (MILMMs) and reasoning (L.LMs). This allows the reasoning L.MMs to be upgraded
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independently, boosting performance without the necessity retrain the MLLMs or alignment. A detailed empirical analysis is provided in Sec. 4.3
Strategies for Visual Perception Op.
We explore strate-
gies generate precise perceptual outputs for reasoning:
only
MY
Owen3-88
WT
R1-78
none: An empty set of perceptual outputs Op, which serves as the control reference group.
50
Avg. Accuracy
45
42.0
40
cap (Lu et al.
2025): A standard image caption Ocap
PI, with the template Peop in Fig. 13
35
30
query-relevant caption Oqcap = MLLM(7, quap (4)) with P geap in Fig. [4
gcap (Gou et 2024):
25
20
sol: A tentative solution Osel MLLM(I, Pan(()) with the template Put in Fig. [5 which "tentative"
15
none
cap
qran
sel
cap+-ol
vap+sol
as it acts contexts for LLMs instead of final answers.
Figure Comparison of the strategies for visual perception Op.
To evaluate how different compositions of the perceptual output set Op affect performance, perform an experi-
ment on seven multi-modal reasoning benchmarks (details in Sec. 4.1 In particular, we set Op to: (i) none: (ii) {ocap): 1; (iii) {0 ): (iv) {o ): (v) {ocap: O }; and (vi) {O O J- The reasoning
prompt P, (shown in Fig. 12 is designed to provide a unified structure for all the above cases. We
Qwen2.5-VI.-7B for perception and adopt Qwen3-8B and R1 R1-Distilled-77 (refered as R1-7B)
for reasoning. Figure 3 shows the average accuracies obtained. As can be seen,
Standard captions outperform query-relevant counterparts. This can be attributed to the MLLM's 's extensive training on standard image captioning tasks (Bai et al. 2025). whereas query- relevant captioning remains less optimized. However, with proper optimization (.2),, query- relevant captioning can offer an advantage by extracting contextually relevant visual details.
Combining tentative responses and standard captions achieves best results, delivering sig- nificant improvement (+7% w/ Qwen3-8B) over the original MLLM. This success is due to the complementary roles played by the caption and tentative response in reasoning. The caption provides the LLM with essential contexts for problem-solving. while the tentative response serves as a reference.
While Figure shows that cap+sol performs best, we will adopt qcaptsol as the default in the sequel. The reason is empirical. Our findings in Section 4.2 reveal that qcapt outperforms captsol once VPO (to be introduced in Section 3.2p is applied. This indicates that the query- relevant approach, while less optimized initially, possesses greater potential.
3.2 VISUAL PERCEPTION OPTIMIZATION (VPO)
Although the combination of caption and tentative solution (i.e., both cap+sol and qcap+sol) demonstrates superior results Figure 3 they are not optimized for the correctness of the final reasoning outcome. In other words, the MLLM generates its perception outputs without any feedback on whether these outputs actually guide the reasoning LLM to the correct answer. To address this limitation, we introduce Visual Perception Optimization (VPO), As illustrated in Figure 4 VPO establishes a reinforcement learning feedback loop that fine-tunes the MLLM for better captioning. explicitly rewarding it based the correctness of the final answer produced by the reasoning LLM.
Objective Design. Without loss of generality, we describe VPO using the query-relevant caption (qcap) setting. VPO is inspired by Group Relative Policy Optimization (GRPO) (Shao et al. [024). a policy optimization algorithm originally developed for text-only L.LMs. In our setting, the policy Ty to optimize is the MLLM performing visual captioning. For given input pair (1, q) from the training set pp, the old policy generates caption rollouts (o ~ Te (-14, P Paeap (q))}. Let R; be the
reward for the ith rollout. The normalized advantage is A, R-- where o(R) is the standard
a(I)
deviation of rewards within the group R {R,} and R y/ Σ R; is the baseline reward. Thus,
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Reference Model
f/1
F11
A
(1.4)
Rossoner ULM
Reward Punction
F2
Group Computation
A2
OG
MG
TG
Ac
Policy Update
Figure 4: Visual Perception Optimization (VPO) reinforces captions that induce correct reasoning results via reinforcement learning with verifiable rewards. Here we omit caption penalty for simplicity.
the objective of VPO, following the formulation of GRPO, can be represented as:
L(0) = E(I.g)~pp.oo oo (sn)))
To(0; I, P. Pecap(99 (q)) A clip
To(o; I, P (eap(())) 1 c1. 1 1 =1)
Tiaa (o; I, P geap (4))
Tioia (o; L, geap (q))
which incorporates a surrogate loss clipped to 61, + (e > 0, ch > 0)) and Kl.-penalty
DKL. (oo [o weighted by B (not shown) to stabilize optimization.
Reward Design. GRPO is often used in math reasoning problems (Shao et al. 2024 Guo et al. 2025), in which the reward is determined by simple rule because the model's output is the final solution itself. However, in our setting. the MLLM generates intermediate caption, from which the reasoning solution cannot be directly extracted. To address this, for each caption rollout o,, we prompt the reasoning LLM generate final answer, and the reward is determined by whether this answer matches the ground-truth. This is formalized as follows:
R4 r(gg 3b) 1 (Ugi parse(y;)); where y, LLM( Prcssoo 0z)),
where ys is the answer produced by the LLM from caption 0,, 1--) is the indicator function, and Presson (g, 0:) (shown in Figure 16) is the reasoning prompt different from that used for inference (template in Figure 12) as it omits the tentative solution. The reward function r(s.)) compares the predicted answer with the ground-trute Bgr-
During training, we observe reward hacking (details in Sec. 4.2p. where the MLLM directly solves the problem instead of performing captioning. Consequently, the model's captioning ability does not improve. To address that, we impose penalty on reward R; if (i) or leads to correct answer; and (ii) o, does not contain a caption (determined by the policy MLLM vy via few-shot prompting):
R = R: A A1 = -hasCap(o:)).
(3)
where À is a penalizing factor, and the function hasCap(-) checks if o, contains caption (template in Figure 17).
In summary, VPO offers two primary advantages:
Generation Reasoning-Alignee Captions: VPO uses the final reasoning outcome as a reward signal to optimize MLLMs, ensuring the captions are not merely descriptive but also functionally aligned for further reasoning. The performance improvement will shown in Sec. 4.4
LLM-Agnostic and Generalizable Improvement: VPO is an M-g-gsssiiic optimization, i.e., the optimized MILM communicates with the LLM reasoner via natural language, and thus, the performance gain generalizable across any LLMs. This enables a one-time alignment, which can be paired with any LLM in plug-and-pll and- way without repeating VPO, shown in Sec. 4.3
In addition to the caption, we further improve the quality of the tentative solution generated by the MILMM. As the tentative solution can be easily verified by a rule-based reward function, we apply GRPO the MLLM. Details can be found in Appendix D In the experiments, we optimize the MLLM with GRPO and VPO in sequential manner, with VPO followed by GRPO.
Other variants of the check function are considered in Appendix E.3
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Published as a conference paper at ICLR 2026
Table I: Comparison on multi-modal reasoning benchmarks with respect to average accuracies. The best results are bold, while second best are underlined. short for GPT-OSS- 120B-ABB. undergone GRPO training.
Model
MathVista Math Vision
Math Verse MMMU WeMath DynaMath LogieVista AVG
Proprictary Models
Claude- 3,7-Sonnet
66.8
41.9
46.7
75.0
49.3
39.7
58.2
53.9
Gemini-2.00 2.0-hlash
70.4
43.6
47.7
72.6
47.4
42.1
52.3
53.7
GPT-40-202411
60.0
31.2
40.6
70.7
45.8
34.5
52.8
47.9
Open- Sour-Souree Models
MM-Eureka-7B
54.9
34.7
48.3
43.9
InterVVL3-881
73.6
29.3
39.8
62.7
37.1
44.1
44.6
VL-Rethinker-7B
74.9
56.9
37.3
43.6
Re ReVisual-R177
70.8
52.7
55.7
40.7
51.2
49.2
Ovis2-8B
71.8
25.9
57.4
27.2
39.4
Intern VLernVL3-14B
75.1
37.2
44.4
67.1
43.0
31.3
51.2
49.9
Ovis2-16B
73.7
30.1
45.8
60.7
45.0
26.3
47.4
47.0
Gemma-3-1 3-1BB
56.1
30.3
21.1
55.2
33.6
20.8
41.2
36.9
HIM-Eureka3322
74.7
36.6
51.5
62.0
37.1
58.2
50.5
Intern VL3-38B
75.1
34,2
48.2
70.1
48.6
35.3
58.4
52.8
Ovis2-34B
76.1
31.9
50.1
66.7
51.9
27.5
49.9
50.6
Gemma-3-27B
59.8
39.8
34.0
64.9
37.9
28.5
47.3
44.6
QVQ-72B-Preview
70.3
34.9
48.2
70.3
39.0
30.7
58.2
50.2
Qwen2.5-VL-72B
74.2
39.3
47.3
68.2
49.1
35.9
55.7
52.8
VL-Rethinker-728
78.2
42.2
54.6
67.2
49.2
34.9
56.6
54.7
Intern V33-78L
79.0
43.1
51.0
72.2
46.0
35.1
55.9
54.6
Verification-augmentte and Tool-enabled MLLMs
Qwen2.5-VL-7BB (Bo8)
76.8
31.6
46.8
58.1
43.1
29.7
48.6
47.8
SRPO-7B
75.8
32.9
57.1
ReVPT-7B
66.0
DeepEyes-7B
70.1
26.6
47.3
38.9
47.7
Prior Caption- then Reason Methods
ECSO
64.6
42.7
42.8
61.4
38.4
25.0
39.4 4
44.9
OmniCaptioner
67.5
43.3
48.0
62.2
38.7
30.5
56.2
49.5
Qwen2.5-V VL series and RAPID-enhanen counterparts
Qwen2.5-VIL-3B
64.5
21.9
28.8
50.1
24.2
13.4
39.6
34.6
w/ RAPID (Qwen3-8B)
69.6
48.6
60.9
39.1
29.3
56.4
49.2
Qwen2.5-VL. VL-77
70.3
25.8
41.0
57.3
34.4
19.4
46.1
42.0
w/ RAPID (Qwen3-8B)
76.1
43.7
52.2
64.7
45.4
32.7
57.7
53.2
Qwen2.5-VL-32B
37.8
69.0
43.1
55.0
$2.2
RAPID (Qwen3-8B)
76.8
47.0
54.4
67.8
48.5
36.5
60.4
55.9
RAPID (GPT-A5B)"
75.9
52.1
54.3
69.8
50.8
38.3
60.4
$7.4
Qwen2.5-VIL-72B
74.2
39.3
47.3
68.2
49.1
35.9
55.7
52.8
w/ RAPID (GPT-A5B)"
75.1
53.4
56.2
72.4
52.1
37.9
59.1
58.0
4
EXPERIMENTS
4.1
MAIN RESULTS
Baselines. We compare our method with the following baselines: (i) Proprietary models, including
Hlaude3.7-Sonnee (Anthropic) 2025). Gemini-2.00Flaas. (DeepMind 2025 and GPT-4o (Hurst
et al. 2024); (ii) Open-source general-purpert MLLMs, including Qwen2.5-V (3B/7B/32B/72B
(Bai et (005)). Intern (BB/14B/38B/7BB (Zhu al.. 2025). Gemma-3 (12B/27B) (Team)
et al. 2025a) and Ovis2 (BB/1) (Lu et al. 2024b); (ii)) Open-source MLLMs specialized
reasoning, including MMr-ureea (7B/32B) (Meng al. 2025). VL--Rthinker (7B/72B) (Wang
et al. 2025a), QVQ-72B-Prevve (Qwen, 2024) and Visusull R1-7B (Chen et al.) 2025b); (iv) Latest
Caption-then-Reason pipelines, such as ECSO (Gou et al., 2024) and OmniCaptioner (Lu al.
2025). We use the GRPO-optimized Qwen2.5-VL-70 as captioner and Qwen3-8B as the reasoner: (v) Verification based methods such as Owen2.5-VL-77 VL-BB (Bo8) that performs best-of-8 sampling with DisualPRM-8B-v... (Wang et al. 2025b), SRPO-7B (Wan al. (025) that is instructed to perform reflection after reasoning. and Tool-enabled MLLMs such as Re VPT-BB (Zhou al. 2025)
and DeepFyes-775 (Zheng et al. 2025) that call tools for better perception.

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Published as a conference paper at ICLR 2026
Table 2: Ablation study of different components of RAPID (with Qwen2.5-VL-77 by default).
VPO VPO without the caption penalty; 4; using captsol for reasoning- decoupling.
Cap.
Math Vista
Math Vision
Math Verse
We Math
Dyna Math
Logic Vista
Decouple
GRPO
VPO
MMMU
AVG
penalty
A
70.3
25.8
41,0
57.3
34,4
19.4
46.1
42.0
B
70.0
40.4
45.2
62.0
39.1
26.3
49.7
47.5
9
72.7
43.2
50.0
63.3
41.1
28.7
54.1
50.5
D
76.0
41.5
50.6
62.9
43.1
33.1
57.7
52.2
P
/
/
76.1
43.7
52.2
64.7
45.4
32.7
57.7
53.2
P
V1
/
71.2
43.8
48.1
64.6
39.9
32.3
57.9
51.1
0
/
74.2
42.5
50.8
62.0
39.4
31.9
56.6
51.1
8
74.2
29.7
44,8
55,9
41.0
27.7
48.1
45,9
75.0
29.8
42.0
55.8
40.8
23.0
46.3
44.7
Evaluation is conducted on a diverse set of multi-modal reasoning benchmarks, e.g., Math Vista
(testmini) (Lu et al. 2024a), Math Vision (test) (Wang et al.], (024b)) MathVerse (vision-only) (Zhang) ct al. 2024). MMMU (val) (Yue et al. 2024), WeMath (Qiao et al. 2024). DynaMath (Zou et al.
2024. and Logic Vista (Xiao et al.J (024). As in recent works (Wang al.) 2025ct (Zhu et al.
2025). we use VLMEvalKit (Duan et al. (0024) for evaluation, and report the worst-case accuracy for DynaMath, the strict accuracy for WeMath, and overall accuracy for the other benchmarks.
Implementation Details of RAPID. We perform RAPID upon the Qwen2.5-V. VL series (3B, 7B, 32B, and 72B) MLLMs. During training, we use RI-Distilled-7D (R1-7B) as the reasoner compute reward signals for all MLLMs. During evaluation, we adopt Qwen3-8B | Yang et al.) 2025a) and GPT-OSS-120B (Agarwal et al., 2025) as the LLM reasoners. For training data, we adopt ViRL39K (Wang al., 2025a), curated dataset of 38,870 verifiable multi-modal question-answer pairs tailored for multi-modal reasoning. We implement GRPO and VPO with verl (Sheng et al. 2025
with a global batch size of 256, rollout temperature of 1.0, and a learning rate of le
Implementation Details of GRPO. We set the number of rollouts to 8 for the 3B/7B MLLMs and 4 for the 32B/72B MLLMs. Following Yu et al. (2025), we remove KL regularization and use the "Clip-Higher" strategy, setting e to 0.2 and eh to 0.25. When reporting performance with GPRO but without VPO (e.g., O and A in Table 2 and the baselines in Table 3). select the hest-performing checkpoints (with perception-reasoniin
decouple applied) at 400, 300, and 100 steps for the 3B, 7B, and 72B MLLMs. respectively, based on the average accuracies across the seven reasoning datasets (evaluated every 50 steps). GRPO is not applied to the 32B variant, as it has already been RL-ttune.
Implementation Details of VPO. We set the number of rollouts to 4, KL-penalty coefficient / to 1e 3, and penalizing constant À in Eq. (3) to 0.1. VPO is applied to the MLLM following 200 steps of GRPO (except for the 32B model, which we directly use the original model) 4 Similar to GRPO, select the best checkpoints 200, 150, 100, and 100 for the 3B, 7B 32B, and 72B models, respectively, according to their average accuracies on the reasoning datasets.
Results. Table T compares the performance of RAPID and baseline MLLMs on seven multi-modaa reasoming
Q-VL-78
Q-VL-7B GRPO
datasets. It highlights two merits of RAPID: (i) It
perfomance 1%)
80
Q-VL-78 GRPO + VPO
achieves significant performance gains on the reason- ing tasks compared to the original MILMMs For exam- ple, applying RAPID to Qwen2.5-VL-7B with similar- sized LLM (Qwen3-8B) yields an average accuracy of 53.2% (+1 1.2% compared to the original MLLM). No- tably, when applying RAPID to Owen2.5-VLL-725 with GPT-OSS- 20B as the LLM, achieve the best average accuracy of 58% across all the models compared, even sur- passing proprietary MLLMs. (ii) RAPID achieves better performance-size trade-off. For example, Qwen2.5-VL-7B with RAPID (Qwen3-8B) with a total size of 15B outperforms larger models such as MM-Eureka-322 InternVL3-388 and Ovis2-34B. Similarly, Qwen2.5-V S.ve2.5-VLL-32B with RAPID (Qwen3-8B)) surpasses VL-Reethinker-72B and Intern VL33 78B. Check Figure I for a better visualization of the performance-sin trade-off. More analysis on the training and inference compute efficiencies is provided in Appendix D (iii) RAPID surpasses
70
MME
MMBB11
MMter
inage
MMStar
RW-OA
MNT
BUNK
Figure 5: General benchmark Results
We do not use R1-7B as we found the similar-sizer Qwen3-8B performs better in Sec. 4.3
"For the 3B model, we observe that training with VPO after GRPO results in slight forgetting of reasoning. To mitigate this, we switch back GRPO optimization for an additional 100 steps after VPO.
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latest caption-then-rease methods (Gou et al. 2024 Lu et al. 2025). mainly due to the usage of tentative responses and VPO.
Evaluation on General Benchmarks Although RAPID is specifically designed for multi-modal math and science reasoning, we verify that it does not hurt general abilities. We evaluated the VPO/GRPO-optinizer
(wen2.5-VI.-777 on general benchmarks in a "non-thinking" mode, per common protocols (Yang et al., 2025a Wang et al. 2025d). As shown in Figure its performance remains on par with the original model. This confirms that our method is a targeted enhancement for reasoning that preserves the model's general abilities. (Benchmark details and Qwen2.5-VL results are in Appendix F.T.
4.2 ABLATION STUDIES
In this section, we first investigate the effectiveness of the proposed components, i.e., reasoning- perception decoupling (denoted "Decouple") and VPO. For VPO, we ablate the choices on reward computation during training. Next, we assess the generalization and scalability of RAPID to different LLMs. We the same training configurations as in Sec. 4. -ren2.5-VL-3BB/ ablations due to resource constraints. Unless otherwise specified, we use R1-7B as the default LLM for training (reward computation) and Qwen3-8B for inference.
are adopted for
Percepptonnee Decoupling & VPO. Table 2 presents detailed ablation study of RAPID's with the 7B MLLM (see Appendix [.2 for the 3B MLLM), which we analyze by incrementally adding each one the baseline. Starting from the baseline MILM (A). we first apply perception-reasonee decoupling. This step alone (B) yields a significant 5.5% average improvement, demonstrating the immediate benefit of leveraging a stronger external LLM (Qwen3-8B) for reasoning. Building on this, we apply GRPO to enhance the MI.M's perception by optimizing its tentative solutions, which adds another 3.0% the average score (C). We then apply VPO without the caption penalty (D), and achieves further 1.7% gain. Finally, incorporating the caption penalty leads to our full model (D), adding another 1.0%. This brings the total improvement from our full VPO method 2.7% over the model with only GRPO (C). This caption penalty is crucial for VPO's effectiveness, as it prevents reward- -aaarddnaaaingggga where the model might generate solutions instead of the intended captions. S this: without the penalty, the ratio of rollouts containing valid captions diminishes rapidly, whereas with the penalty, remains stable above 95% before 150 stens.
The results also highlight that GRPO and VPO are complementary, whose synergy is evident in two ways: 1) Removing either method from the
58
Q-VL-7B 7B (GRPO, 1st stagel
Q-VL-38 (GRPO, 1st stage)
G-VL-78 (VPO, 2nd stage)
Q-VL-B8 (VPO, 2nd stagel
*
Q VL- (Eval Checkpoint)
Q- (GRPO, stage)
Average Accuracy (%)
Q-VL-B8 (Eval Checkpoint)
full decoupled setup (G vs. C and C vs. ) results in suboptimal performance, confirming
54-
52
both are necessary. 2) Figure [6] further visu-
alizes this dynamies: after initial gains from GRPO begin to plateau, VPO provides distinct secondary performance boost. Despite these gains, the decoupling strategy remains the most critical element. An MILLM improved by VPO and GRPO alone (O) still lags far behind the decoupled version (D), underscoring its impor- tance. We also note that VPO does not improve MLLM's reasoning capabilities on its own (F) vs. D); the slight performance drop suggests mi- nor forgetting during sequential training. How- ever, we demonstrate in Appendix E.4 that this issue can be addressed by simple GPRO training without impacting the overall performance of the 7B model.
50
48-
46
44
42
100
200
300
400
500
600
Training Steps
Figure 6: Training dynamics of GRPO and VPO. Performance is evaluated under the perception- reasoning decouple pipeline.
While standard captions (cap+sol) initially outperform query- ones (qcap+sol) as dis- cussed in Section 3.1 this trend reverses after applying VPO (see e and (.). We hypothesize that this is because qcap easier to optimize during VPO, as the query guides the MLLM to focus on relevant visual details. Instead, without such guidance, the MLLM struggles to identify pertinent information for cap. This is confirmed by Figure & which shows that training rewards for qeap increase steadily, while rewards for cap oscillate without consistent growth.
Choices on Reward Computation. We study VPO reward computation by varying the reasoning LLM (during training) and its input content. We take the best-performing checkpoint (optimized
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100
800
9:ap
2.5
Caption Ratio (80
0.65
Caption Length
600
Gwen3-88 en
w/ panalty w/o cap. pariely
Reward
0.60
0.55
400
70-
200
50
100
150
200
50
100
150
200
0
50
100
150
200
Training Steps
Training Steps
Training Stops
Figure 7:
Reward hacking Figure 8: Reward dynamics of Figure 9: Caption length trend with various LLMss
without the caption penalty.
adopting qcap and cap.
with GRPO) the baseline and evaluate under the perception penception-reasoningg decoupled paradigm. First, we keep the input content as qcap+sol and test three LLMs with increasing reasoning capacity: Bren2.5-7B-Insteeee (weak), R1-7B (intermediate), and Qwen3-8B (strong), respectively.
As shown in Table 3 the R1-7B LLM performs best. We hypothesize this due to trade-off in reasoning capacity, reflected in caption lengths. FigureDsshove shows the caption lengths during training for various LLMs. We speculate that the stronger Qwen3-8B can succeed with succinct captions, thus veattentently rewarding short captions that miss d while the weaker -wen2.5-Instruut-77 incentivizes over-long captions that even include inaccurate solutions. R1-7B strikes an effective balance, making it our default choice.
Table 3: Ablation studies on (a) LLM types and (b) input to LLM for reward computation.
Configuration
Q-VL-3B
Q-VL-7B
w/o VPO (baseline)
46.1
50.5
(a) LLM Types
Qwen2.5-7B 2--2-----BInstrucct
47.5
51.9
RI-Distilled-7B
47.9
53.2
Qwen3-8B
47.1
51.3
(b) LLM Input Contents
Next, we examine the choice of input content: using caption alone (qcap) versus using the caption plus a tentative solution (qcapt (gcaptsol). As in Table using only the caption is superior. Including tentative solutions allows the LLM to take a shortcut during the solutions while ignoring wwichh generates noisy reward signal ineffective for optimizing caption quality 6 reasoning ability in Appendix E.6
qcap+sol qeap
47.4
49.5
47.9
53.2
training-relying relying
Additionally, we explore fine-tuning the I.I.M for better
4.3 GENERALIZATION AND SCALING WITH DIFFERENT LLMS.
A practical requirement is that our MLLM, once optimized, should generalize to new, unseen LLMs inference time without retraining. To test this, we perform VPO on the GRPO-trained MILM using only R1-7B as the LLM for this optimization step. We then evaluate its performance against the baseline (the MLLM without VPO) by pairing both MLLMs with diverse range of different LLMs at inference time, as shown in Figure T0
fverage Performance
47.5
D-L-78 w/ cape
45.0
QML wi GRPO
We have three observations. First, the performance gain from VPO generalizes effectively. The gap between the VPO-trained model (solid curves) and the baseline (dashed curves) is maintained or widened when using stronger LLMs, revealing that the benefit is not confined to the specific LLM used for training. Second, the RAPID'S 's scal- ability is evident as absolute performance trends upward when using more capable LLMs, although this improve- ment is not strictly monotonic with model size. Additionally, among the LLMs tested, Qwen3-8B strikes the best balance between performance and model size, establishing it to be our default choice for the inference stage. Note that the optimal LLMs for training and inference might differ (c.f..
Q-VL-3 wi VPD e GRPO
42.5
DAL--1 wy GEPO
Qpen3-4g 4g
RJ -B
Quens 40
Owm
R1 00755--208
4B
G Prossson 1208
Figure 10: Performance with different LLMs. (Only R1-7B is used training)
Table and Figure I0..
4.4 EVALUATION ON CAPTION QUALITY
'We further validate this in Appendix E.5
'Notably, this optimal input format difters from that used in the perception-reasoniin decoupling stage.
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Table 4: Effectiveness of different components of RAPID (with Intern VL3-8B by default). VPO
VPO without the caption penalty.
Cap. penalty
Math Vista
Math Vision
Math Verse
We Math
Dyna Math
Logic Vista
Decouple
GRPO
VPO
MMMU
AVG
73.6
29.3
39.8
62.7
37.1
25.5
44.1
44.6
71.3
42.4
39.3
64.4
38.8
29.1
50.1
47.9
73.2
42.6
44.3
64.4
40.2
31.1
52.1
49.7
75.4
43.2
48.5
64.6
43.2
33.2
55.5
51.9
We validate the improved quality of the captions generated
Win
Original
by VPO-optimized MLLMs via a pairwise comparison
MathVista
(Chen et al. 2023 Liu et al. 2024b) using GPT-4o (Ope-
MathVision
nAI 2024) as a judge. With 1000 random samples per
MathVerse
dataset, GPT-4o compares captions from Qwen2.5-VLL VL-33.
MMMU
trained with and without VPO. The judge is instructed
WcMach
to prefer captions with more comprehensive and accu- rate details required to answer the question, while ex- cluding any solving process (the prompt in Appendix F.3 We alternate the caption order to mitigate position bias ZZengg et al., 2023). As shown in Figure [T] the VPO-optimized MLLM's captions shows a clear advan- tage across all datasets, highlighting the VPO's effective- ness (Check the case study caption quality in Appendix
DynaMath
LogicVista
0.0
0.2
0.6
0.8
1.0
Percentage of Votes
Figure 11: Pairwise comparison on the caption quality with and without VPO.
D. Morcover, we extend this comparison to other MLLMs and validate these findings with human assessment in Appendix
4.5 GENERALIZATION ACROSS MLLMS
We confirm RAPID's generalizability across various MLLMs. Applying decoupling (with Qwen3-8B) and VPO to Intern VL.3-8B yields significant gains (Table(4). mirroring our main results (Table This suggests that RAPID does generalize across different MLLMs. Moreover, applying the decoupling pipeline alone to more MLLMs (i.e., Intern VL3-8B, VL-Rethinker--77 7B and MM-Eureka-7B) with different LLMs (i.e.. Qwen3-8B and GPT-OSS- 120B) also shows consistent improvements (Table 17 indicating that decoupling is broadly effective strategy for enhancing MLLM performance.
4.6 COST ANALYSIS
This section analyzes the cost for GRPO and VPO training. based on NVIDIA H20 GPU rentals from LuchenTeetf at approximately $0.56 per GPU/hour. Table 5 details the resource requirements. Our method is remarkably cost-effective, requiring less than $300 for significant performance gains (see Table [). This low cost ensures accessibility for small teams and individual researchers. Furthermore, as detailed in Appendix E. these expenses are less than 0.1 1% of the cost to pre-train or fine-tune an MLLM with a new LLM, making RAPID a highly practical alternative.
Table 5: Training time and cost analysis for different model sizes and training phases in RAPID.
Wall-Clock Time (hours)
Training Steps
Hardware (GPUs)
GPU Hours
Estimated Total Cost (USD)
Model Size
Stage
GRPO
16.7
200
8 x H20
133.6
$74.8
3
VPO
23.9
200
16 x H20
382.4
$214.1
GRPO
24.0
200
8 x 1120
192.0
$107.5
7B
16.3
16 x H20
260.0
$145.6
32B
VPO
13.6
100
32 x 1120
435.2
$243.7
5 CONCLUSION
This paper proposes RAPID, an efficient method for constructing multi-modal reasoning models. By decoupling visual perception (MLLM) from text-only reasoning (LLM),, RAPID leverages the advanced reasoning of frontier L.LMs while avoiding burdensome visual re-alignment. Enhanced with Visual Perception Optimization, this method reinforces precise captions to provide rich visual context, improving reasoning and effectively scaling more advanced LLMs inference time. Our approach achieves significant accuracy gains on multiple multi-moda reasoning benchmarks while remaining computationally efficient.
htaps:/wwwwllccheetcc..com
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ETHICS STATEMENT
We affirm that this work adheres to the ICLR Code of Ethics f Our research does not involve human subjects, personal data, or sensitive attributes, and it does not pose foreseeable risks of physical, psychological, or social harm. All datasets used in our experiments are publicly available and widely adopted in the research community. We have carefully considered potential issues related bias, fairness, and misuse, and we believe that the scope of this study does not introduce additional ethical concerns. Furthermore, our work complies with all relevant legal, institutional, and research integrity requirements, and declare that there that could have influenced this research.
conflicts of interest competing financial relationships
REPRODUCIBILITY STATEMENT
We have taken extensive steps ensure the reproducibility of our work. All model architectures, training procedures, and hyperparameters are described detail in the main text (Section and Section 4 and the Appendix. For empirical results, speciff dataset sources and preprocessing steps in Section 4.1 and we provide implementation details and experimental settings in Section 4.1 Anonymous source code and scripts for reproducing the main experiments will be made available in the link provided in the abstract. We believe these efforts enable full reproducibility our reported results.
ACKNOWLEDGMENT
This work was supported by National Natural Science Foundation of China under Grant no. 62136005 and Shenzhen fundamental research program JCYJ202506611442200033 This research also supported in part by the Research Grants Council of the Hong Kong Special Administrative Region (Grants 16202523 and HKU C7004-22G).
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APPENDIX
CONTENTS
Limitation
16
B Model Configuration for Figure]
17
Prompt Templates
17
Formulations of GRPO
19
More Analysis
19
Analysis on the Training Compute Efficiency of RAPID
19
Analysis the Inference Compute Efficiency of RAPID
22
Analysis on the hasCap() () Check and Other Variants
22
E,4
VPO Hurts Reasoning Ability of the MLLMM
23
Analysis on the Effect of Caption Length
24
E.6
Adapting the LLM to Reason over Captions via Fine- tine-tuning
................................
25
7
Using the same MLLM for Reasoning
25
More Experimental Details
25
Evaluation on General Benchmarks
25
2
Ablation Study Qwen2.5-VL-3B
................................
26
Details for Pairwise Comparisons
26
F4
Extending Decoupling to Other MILMMs.
27
F5
Training Dynamics VPO
28
F.6
Training Dynamics of GRPO
28
More Discussions
28
G.I Advantages of RAPID over Unilied Architecture
28
H Use of Large Language Models (LLMs)
31
Case Study
31
A LIMITATION
Auto-thinking. RAPID is specifically designed for multi-modal reasoning, and it is appealing to explore how flexibly switch between fast and slow thinking dependent on the complexity of input queries, without human prior and prompt engineering.
Domain-Specifie Design. The RAPID architecture, in its current form, is optimized for multi- modal math and science reasoning. Its extension to other domains. such spatial reasoning (Wang et al.) 2024a), would require more than re-evaluation; it would demand specific adaptations to the model itself. The experiments general benchmarks reported in Sec. 4.1 do not test the full reasoning
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Table 6: Model Configurations for each RAPID-enhaneed model group Figure n_" denotes the corresponding item (e.g., LLM reasoner, GRPO/VPO training) is not applied.
Size (B)
LLM
GRPO
VPO
Avg. Performance
Qwen2.5-VL-3B
7
Qwen3-4B
ViRL39K
ViRL39K
47.3
11
Qwen3-8B
ViRL39K
ViRL39K
49.2
17
Qwen3-14B 14B
ViRL39K
ViRL39K
50.1
Qwen2.5-VL-7B
11
Qwen3-4B
ViRL39K
ViRL39K
51.0
15
Qwen3-8B
ViRL39K
ViRL39K
53.2
21
Qwen3-14B
ViRL39K
ViRL39K
53.6
Owen2.5-VL-32B
36
Qwen3-B
ViRL39K
54.6
40
Qwen3-8B
ViRL39K
55.9
152
GPT-OSS-120B
ViRL39K
57.4
Table 7: Index Prompt templates for RAPID.
Component
Purpose
Notation
Prompt Template
MILM
Standard captions
Peap
Figure
13
MLLM
Query-relevant captions
Pgepp
Figure
14
MILM
Tentative response
Psol
Figure
15
MLLM
Caption Penalty
Figure
17
LLM Reasoner
Inference Reward computation
P Preason
Figure
12
LLM Reasoner
Figure
T6
reason
pipeline, the LLM was not activated. Therefore, investigating the adaptations required generalize RAPID remains a key open direction for future research.
Adapting the LLM. In the current implementation of RAPID, the LLM functions static reasoning module with its parameters kept frozen. valuable direction for future work to explore adapting the LLM our perception-reasoning framework, potentially through methods like supervised fine-tuning or reinforcement learning. While this would introduce additional computational overhead for training, remains an open empirical question whether the potential performance gains would justify the increased cost.
B MODEL. CONFIGURATION FOR FIGURE I
For each RAPID- model group (e.g., Qwen2.5-VL-33 (RAPID)) in Figure I we train the original model (e.g., Dwen2.55VL-3BB using both the proposed VPO and GRPO objectives, where the former encourages the MILMM generate query-relevant captions with higher quality while the later optimizes to give better reasoning traces. The details for VPO and GRPO can be found in Sec. [. and Appendix D We then pair the trained MILM with different LLMs under RAPID. 6 shows the configuration for each RAPID-enhanced model group. Specifically, for each model in the group, we report the total model size (B), paired LLMs, data used conduct GRPO and VPO and the average performance across 7 tasks. Note that the results for Qwen2.5-VL-322B
VL-32B group does not involve GRPO training because it has already undergone an RI. stage before release (Bai et 2025). Results for other MILMSs are consistent with Table
C PROMPT TEMPLATES
In Table provide index of the prompt templates used in RAPID.
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System Prompt:
You are helpful assistant.
User Prompt:
the following text, you will receive detailed caption of image and relevant question. In addition, you will provided with a tentative model response. You goal is to answer the question using these information.
#*# The detailed caption of the provided image: 0
#** A problem to be solved: {
#** A tentative model response. 0
#*# Note the above lentative response might be inaccurate (due calculation errors, incorrect logic/rcasoning and so on), under such case, please ignore it and give your own solutions. However, if you do not have enough evidence show it wrong, please output the tentative response.
Figure 12: Prompt templates used by the reasoner LLM for inference.
System Prompt:
are helpful assistant.
User Prompt: Describe this image in detail.
Figure 13: Prompt templates used by the MILM to obtain the standard captions.
System Prompt:
You given image and relevant question. Based the query, please describe the image in detail. Do not try answer the question.
User Prompt:
Question: 0
Please deseribe the image. DO NOT try the question!
Figure 14: Prompt templates used by the MLLM to obtain the query-relevant captions.
System Prompt:
You are helpful assistant.
User Prompt:
Figure 15: Prompt templates used by the MILM to obtain the tentative response. The placeholder for the question.
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System Prompt:
You are helpful assistant.
User Prompt:
### The detailed caption of the provided image: 0
### Question:
Please think step by step. The final answer MUST BE put in Viboxed ().
Figure 16: Prompt templates used by the reasoner LLM for training.
D FORMULATIONS OF GRPO
GRPO (Shao et al. 2024 a policy optimization algorithm originally developed to enhance the reasoning capability of text-only LLMs. In our setting, the policy Te optimize becomes the MLLM. For a given input pair (1 of image and text question from the training set pp. the old policy generates G' rollouts, i.e., 30 (I, Pmn (g)). Denoting R, as the reward for the i-th rollout, the normalized advantage Å, R--Rt where (I)) denotes the standard deviation of rewards within o(R)
the group and the baseline reward R = G Σi=1 R,. The objective incorporates a surrogate loss clipped within -, + e](c 0) and KL-ppnnlty DKL (TL Te... weighted by (not shown here)
to stabilize optimization:
T.0)= p) oonte (wl1)Pu(9))
G min
To(o, I, Psol()))) A,, clip xa (o; I, Psola(()))
1 1 1 1+ ) ]
Te
(o: Ps)((()))
Aoaa (o; Pat))(()))
The reward RG for the i-th rollout is expressed as: R2 = 0;) 1 ( parse(o:)). where y/tt denotes the ground-trutie answer a reasoning question and 1()) is an indicator function that outputs 1 if the final parsed prediction matches the ground-truth and 0 otherwise.
E MORE ANALYSIS
E. ANALYSIS ON THE TRAINING COMPUTE EFFICIENCY OF RAPID
RAPID's decoupled design enables the flexible adoption of recent LLM reasoners, such as Qwen3 (Yang et al. 2025a), without retraining. This raises critical question: how does our efficient approach compare against models that require full and costly retraining of their visual- visual-language alignment to integrate the latest LLMs?
To investigate this trade-off between performance and computational cost, we compare RAPID with two leading MLLMs also built on the Qwen3-8B LLM: Keye-VLe VL (Team et al. 20256) and Intern (Wang et al. (025dd). Table across seven multi-modal reasoning tasks alongside the training tokens and estimated training FL.OPs (calculated as model size training tokens). The number of training tokens for Keye-VL-8B and Intern VL3.5-8B are sourced from their respective technical reports.
comparative analysis, reporting average accuracy
As can be seen, although still inferior to the end-to-end methods, RAPID with Owen2.5-VL-71 can achieve 90.8% of Keye- VL-8B performance with 1250x less training FLOPs, and 88.2% of Intern VL3.5-88 performance with 864.2x training cost reduction. Thanks to the remarkable training efficiency, we can adopt larger MLLMs such as Owen2.5-VL-322B,
VL-32B, we achieve comparable (92.7%) performance with Intern VLB.5-8B but with 1025x less training FLOPPs
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System Prompt:
You are careful assistant check whether text contains description image.
User Prompt:
Example 1
#ifht A text regarding image: The image displays the logo of Huawei, featuring red, fan-like design with the word "Huawei" written below This image corresponds to the question provided which involves calculating the number of components that can be inserted into phone circuit board one minute based on the time it takes insert one component. 'n'nTo solve the problem, we first need to determine how many components can be inserted in one minute. Since the production line lakes (0.011) seconds insert component, we find out how many components can be inserted in one minute by calculating the total number of seconds a minute and then dividing by the time it takes insert component. There components that can be inserted one minute is calculated as follows: (twp://////////tttt///////////// components] = Vifrac (60 \itxt seconds)) (0.01 Vitxt( scconds/component) = 60 Wtimes 100 is (6000000)60003))
60 seconds in minute. So, the number of of
6000mBBjmn TonniijnTTuuu the
### Does the text contains deseription of the image? Please only answer yes no: Yes.
Example 2
#1fl A text regarding an image: To solve for the length of segment WEDD),, we first need to determine the lengths of the segments VACU), W(BC)), and (CCEE)
M(AB 20V) MCC) is the midpoint of MAB:), so V(AC= CB Vifrac (AB) [2) (20) [2) 10%) W(D))
is the midpoint WBCW), so WBBD DC Vifrae (BC) (2) Vfrac [2] 5%) WCC
Wfrac (2) [5]AC- = lifrac (5) Wtimes 10 4W). ininSince WAC = AE + CER) and WAC 108), we need find the length of ((ED)). Since W(EW) is have MAAE = AC CE = 10 6%).. nn'nNow on M(ACA) ((C)) is midpoint (AB:), the coordinates of points Y(Al),, W(EW), and (CC)) can be visualized or calculated in terms of the distances. The distance (ED)) can be found using the coordinates the simpler arithmetic based on the positions:ani(ED> EC + CD 5- 9.1. 9.W]ianuus the length of segment W(DD)) is (((boxee
### Does the text contains a description of the image? Please only answer yes or no: No.
#1i A text regarding an image: {
### Does text contains a description of image? Please only answer yes or no.
Figure 17: Prompt templates used by the MLLM for caption panelty.
Table Training cost comparison. "As we did not apply GRPO Qwen2.5-VL-3225 it consumes less training tokens (100M) than Qwen2.5-VL-77 (550M).
Method
AVG Accuracies
# Tokens
FLOPs (Ratio)
Keye-VLes VL-8B TTam al. 2025b)
58.6
600B
1500
Intern VL3.5-8B (Wang et al.
2025d)
60.3
410B
1025x
Qwen2.5 w/ RAPID (Qwen3-8B)
53.2
550M
1.2x
Qwen2.5-VL-322 w/ RAPID (Qwen3-8B)
55.9
100M*
1x
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System Prompt:
Please act as an impartial judge and evaluate the quality of the captions provided by two multi- modal AI assistants regarding image and question. You will receive image and question regarding it. You should choose the caption that (i) more accurately and comprehensively reflect the content in the image and (ii) contain more details facts required to solve the question. (iii) contain less visual hallucination (describing objects shown the image). Note that the solution to the problem is not considered as facts or details! Note that if the caption contains any solution process, you should ignore (completely delete it) and only consider the remaining when conducting your evaluation. Begin your evaluation by comparing the two captions and provide short explanation. Avoid any position biases and ensure that the order in which the captions were presented does not influence your decision. Do allow the length the captions influence your evaluation. Do not favor cerlain names of the assistants. Be as objective as possible. Afler providing your explanation, output your final verdiet by strictly following this format: "[[A]]] if assistant A is better, \"[[]]]' if assistant B is better, and "[[[]]]" for tic.
User Prompt:
[User Question]
0
[The Start of Assistant A's Caption]
1
[The End of Assistant A's Caption]
[The Start of Assistant B's Caption]
[The End of Assistant B's Caption]
Figure 18: Prompt templates used for GPT evaluations on caption qualities.
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56
Owen2.5-VL-328
55
Owen2.5-VL-33 (R1-78)
lntemVL3-788
VL-Rethinker-728
Average Accuracy (%)
54
Models
IntemVL3-788
Qwen2.5-VL-77 RAPID (Qwen3-8B)
53
Qwen-2.5-VL-726
Qwen-2.5-VL-728
VL-Rethinker-72B
Qwen 2.5-VL
Qwen-2.5-VL-33
ReVisual-RI. -R--B
Qwen 7B RAPID
Qwen 32B w/ RAPID
Qwen2.5-ViL -ie-2.5-VL-78 w/ RAPID (R1-78)
50
ReVisual-R1-78
49
2 x0
3 x 10
Estimated Inference Compute (Proportional Model Size x Tokens)
Figure 19: Inference compute versus average accuracy.
E.2 ANALYSIS ON THE INFERENCE COMPUTE EFFICIENCY OF RAPID
To evaluate the inference compute efficiency RAPID, we estimate the computational cost across the seven evaluation datasets from [able For each dataset, we perform inference on a sample of 100 examples and approximate the compute as model size x number of generated tokens. For our staged RAPID approach, the total compute is the sum from the perception and reasoning stages, with the compute for each stage calculated using its respective model size. We benchmark these results against top-peere pop-erffrrnnng MLLMs from Table Figure 19 plots the resulting average accuracy against inference compute for both RAPlD-enhanced models and their basclines.
The analysis reveals two key findings:
RAPID achieves a favorable trade-off between accuracy and inference compute. This efficiency highlighted by specific configurations that demonstrate Pareto-optimality For instance, Qwen2.5-VI.-7B w/ RAPID (R1-7B) provides better accuracy-to-compute tio than Re ReVisual-R11785 In another example, Qwen2.5-V1--7B w/ RAPID (Qwen3-8B) outperforms the much larger Qwen2.5-VL-72B while being more computationally efficient.
RAPID demonstrates strong scalability with inference compute. The architecture is designed such that allocating more computational resources at fnference-for example, by swapping in a more powerful LLM reasoner-consistent yields higher accuracy.
E.3 ANALYSIS ON THE HASCAP(-) CHECK AND OTHER VARIANTS
Rationale for the use of hasCap(-). Our initial goal was to discourage the captioning MILM from simply outputting final solution instead of a descriptive caption. key empirical finding, however, was that strictly penalizing any text containing solution-like elements suboptimal. For many visual reasoning tasks, a descriptive caption naturally and concisely includes the answer. For instance, if asked for the time clock face, good caption might be "The image shows clock with the hands pointing to 3:15," which contains both description and solution.
To test this, part the solution was detected the output. As shown Table 9 this variant hasSol(-) performed even worse in the decoupled pipeline than check ("None"), confirming hypothesis that forcing
ablation study using stricter checker that penalized the model whenever any
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Table 9: Comparisons of different checking strategies during VPO (Qwen2.5-VL-77B)
(Penalty) Check Math Vista
Math Vision MathVerse MMMU
WeMath DynaMath LogicVista AVG
None
76.0
41.5
50.6
62.9
43.1
33.1
57.7
52.1
hasCap() 76.1
43.7
52.2
64.7
45,4
32.7
57.7
53.2
hasSol(-) 75.8
40.8
48.7
61.3
42.4
33.0
55.5
51.1
strict separation can harm performance by preventing the model from generating natural and direct descriptions.
Therefore, hasCap(-) was designed balanced heuristic: it ensures that a caption is present but does not have to strictly forbid the co-existence of solution.
Quantitative audit of the hasCap(-) heuristic. We manually audited a random sample of 400 generations from our MLLM trained with VPO. We classified each generation into two ground-truth categories:
Positive Class: The generation a valid caption, which may or may not contain solution
elements. (381 samples)
Negative Class:
The generation could be simply solution or an invalid caption, such pure solution disguised with minimal boilerplate text (e.g., "Here is a description... [solution]"). (19 samples)
The hasCap(-) prompt-based check produced the following results on this
True Positives (TP): 379 (Correctly identified valid caption)
False Negatives (FN): 2 (Incorrectly flagged valid caption invalid)
True Negatives (TN): 14 (Conrecty identified gamed/invalid caption solution)
False Positives (FP): (Incorrectly identified gamed/invalid caption solution as valid)
From these numbers, can derive the following metrics for the hasCap(-) detector:
False Negative Rate: 2/(379 + 2) 0.525%
False Positive Rate: 5/(5 14) 26.32%
This audit demonstrates that the hasCap(-) check is highly accurate and reliable.
Analysis of Failure Modes The failure cases mostly consist of false positives (or the invalid caption ignored by the "hasCap()" check). We found they exhibit similar pattern (hiding pure solution in caption-like text) as shown below:
# Example of invalid output (incorrectly identified positive by check);
Ok, here is description of the image regarding the query. To find the circumfer- ence. .. [detailed mathematical derivation] ... Therefore, the circumference of the circle is 25.13 25.12 cm. This description aligns with the mathematical calculation...
Though such occur, they infrequent (5 out of 400 total samples) impact the downstream performance.
E.4 VPO HURTS REASONING ABILITY OF THE MLLM
We note a performance decrease in the MLLM's reasoning ability after VPO training (Table rows A ()) and have investigated it further.
Our analysis reveals two key findings:
The decrease in reasoning is not permanent and can be fully recovered with a simple, subsequent fine-tuning step.
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Table 10: Comparisons of reasoning ability of Qwen2.5-VL-33/7B different stages.
MLLM
Math Vista Math Vision Math Verse MMMU
We Math
Dyna Math Logic Vista AVG
3B (GRPO)
69.1
26.9
38.2
56,9
34,0
20.0
42.5
41.1
3B (GRPO+VPO)
68.8
26,9
39.8
49,4
33.0
21.6
46.3
40,8
3B (GRPO+VPO-GPRO)
69.1
26.9
39.8
55.1
33.3
20.5
44.0
41.2
7B (GRPO)
74.2
29.7
44,8
55.9
41.0
27.7
48.1
45.9
7B (GRPO+VPO)
75.0
29.8
42.0
55.8
40.8
23.00
46.3
44.7
7B (GRPO-VPO-GPRO)
74.5
29.8
44.3
55.9
40.7
28.5
48.1
46.0
Table
Decoupling results of V at different stages.
MILM
Math Vista Math Vision Math Verse MMMU
We Math Dyna Math Logle Vista JAVG
(GRPO+VPO) Qwen3-8B (CRPO+-PO+CPROO) Qwen3-8B
76.1
43.7
52.2
64.7
45.4
32.7
57.7
53.2
76.5
52.4
63.9
44.8
33.3
57.3
53.1
The impact of this temporary decrease on the final, decoupled system's performance is primarily significant for smaller models, while larger models are more robust to this effect.
Below, we elaborate on these two points.
Recovering reasoning performance with additional GRPO. To counteract this, we performed brief, additional 100-step GRPO training stage after the VPO stage. As demonstrated in Table I0 this additional GRPO stage successfully restores the reasoning performance for both the 3B and 7B MLLMs, bringing them back to the levels seen before VPO was applied.
The impact on the decoupled framework is model-scale dependent. Interestingly, we discovered that the necessity of this recovery step depends on the scale of the MLLM backbone.
For the Model: We observed that the drop reasoning after VPO did negatively impact the performance of the full decoupled pipeline. Our hypothesis is that for a smaller model, this degradation leads to lower-quality "tentative solutions" being passed to the reasoner, thereby creating bottleneck. For this reason, we had already incorporated this additional GRPO stage for the 3B model in our original paper, as illustrated in Figure This step was crucial for achieving the strong performance gains reported for the 3B model.
For the 7B Model: Although applying the extra GRPO stage the 7B model restored its own reasoning ability (Table 10), yielded no significant improvement for the final decoupled system (Table ITI. Therefore, to maintain the methodological simplicity of RAPID, we omitted this non-essential step for the 7B model our paper.
E.5 ANALYSIS THE EFFECT OF CAPTION LENGTH
In our original analysis (Figure 9 in Section 4.2 the final performance correlates with both the choice of LLM for reward computation and the length the generated captions. This raises the question of whether caption length is the primary causal factor for the performance difference.
To isolate the effect of caption length, we conducted a controlled experiment. Our goal was to decouple the reward model's identity from the resulting caption length. We started with the setup that uses, Qwen3-8B, the stronger reasoner, to compute the VPO reward, which normally results in shorter captions (average 153 tokens) and worse performance. We then introduced an explicit length-controlled reward to encourage the perception model (Qwen2.5 5-VL-BB) to generate longer captions, matching the average length produced when using R1-7B for rewards (approx. 654 tokens).
To achieve this, we added length penalty term to the reward function, as formulated in Aggarwal & 650, n. is the token count
Welleck (2025): Tlen (y, Nurgaa) -a Murget nlyl Here, Rearge of the generated caption and the weight a was set to 0.0003 as per Aggarwal & Welleck (2025)
This approach successfully controlled the output length; the average caption length for the model trained with Qwen3-8B rewards increased from around 153 to around 627 tokens, as intended. We then evaluated this MI. MI.LM our benchmark suite, with the results presented in Table 12 The model
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Table 12: Correlation between the choices of LLM, the length the captions and final performance.
LLM
Length Math Math Vision Math Verse
MMMU
WeMath DynaMath LogieVista AVG
R1-7B
653.7
76.1
43.7
52.2
64.7
45.4
32.7
57.7
53.2
Qwen3-8B
153.1
75.8
40.8
48.7
61.3
42.4
33.0
55.5
51.1
Qwen3-8B (lengh-controlled)
627.1
75.8
40.8
48.7
61.3
42.4
33.0
55.5
51.1
Table 13: Adapting the LLM to reason over captions via GPRO training.
Models
Math MathVision MathVerse MMMU WeMath DynaMath LigicVista AVG
RAPID
76.1
43.7
52.2
64.7
45,4
32.7
$7.7
53.2
RAPID (LLM trained)
77.1
43.4
53.2
63.3
45.1
33.3
57.5
53.3
trained with length-controlled rewards showed minor performance improvement over the baseline model trained with standard Qwen3-8B rewards. However, its performance still significantly lags behind the model trained with R1-7B the reward source.
This outcome leads to a clear conclusion. Forcing the MLLM to generate longer text does not guarantee more comprehensive useful descriptions. Instead, the model may produce verbose but less informative content to satisfy the length constraint. This result allows us to climinate caption length confounding variable, confirming that the performance gap is attributable the reasoning ability of the LLM that generates the reward signal.
E.6 ADAPTING THE LLM TO REASON OVER CAPTIONS VIA FINE-TUNING
We conducted an experiment where we fine-tuned the LLM reasoner (Qwen3-8B) in a separate stage after VPO the ViRL-39K dataset. The training data for the LLM consisted of the captions generated by our VPO-trained MLLM (Qwen2.5-VL-7B) We then applied the same GRPO objective (with group-size of 4) to optimize the reasoner.
However, the experiment did not yield significant improvements. During training, we observed that the reward signal was highly unstable, fluctuating without consistent upward trend. The final evaluation results, as shown in Table [3 confirmed this observation, revealing only marginal gains.
Our hypothesis is that a powerful, pre-trained LLM like Qwen3-8B already possesses robust reasoning capabilities that generalize effectively to understanding captions. Consequently, further fine-tuning provides diminishing returns, especially when the base model's reasoning is already strong.
E.7 USING THE SAME MLLM FOR REASONING
We conducted new experiment using the same trained MILM,, Qwen2.5-VL-77. (GRPO+VPO), for both the perception (captioning) and reasoning stages our decoupled pipeline. Note that for this case, it is not actually "decoupling" result the image is visible to the reasoner. In Table [4] we compare this "decouple with self" approach against the standard end-to-end usage of the same MLLM, where it processes the image and question simultaneously.
As the table shows, applying our decoupled pipeline even with the same model for both stages yields tangible performance improvement (46.1% 44.7% average). This demonstrates that the structured two-stage process of first externalizing perception into text and then performing reasoning beneficial in itself. However, it still lags behind when using Qwen3-8B, the default setting of our main paper, as the reasoner, which could be possibly attributed to their gap in reasoning capacity.
F MORE EXPERIMENTAL DETAILS
F.1 EVALUATION ON GENERAL BENCHMARKS
We select MME (uu et al. 2024a). MMBench-vl.1 LLu al. 2024a), MM- Met (Yu al. 2023). SEED-Image
9 LL et al. 2023). MMstar (Chen et al. 2024). Borld-r (RW-QA) (AAl 2024).
We evaluated the "Image" split.
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Table 14: Performance comparison between decoupling (the same MLLM performing both captioning and reasoning) and an end-to-end MLLM. Qwen2.5- Dwen2.5-VL-7B (GRPO+VPO) is adopted.
LLM
Math Vista Math Vision Math Verse MMMU
WeMath DynaMath Logic AVG
Decouple End-to-end
73.7 75.0
30.0
44.0
57.3
41.0
27.3
49.2
46.1
29.8
42.0
55.8
40.8
23.0
46.3
44.7
Table 15: Ablation study of different components of RAPID (with Qwen2.5-VL-3BB. VPO1: VPO without the caption penalty; 1 using sap+sol for reasoning reasoning-perreption decoupling. ": After VPO,
we additionally conduct GRPO recover its reasoning ability.
Cap. penalty
Math Vista
Math Vision
Math Verse
We Math
Dyna Math
Logic Vista
Decouple
GRPO
VPO
MMMU
A
64.5
21.9
28.8
50.1
24.2
13.4
39.6
34.6
B
65.5
39.1
31.9
59.0
31.1
24.8
48.3
42.8
68.5
40.0
39.2
61.0
35.1
26.9
51.7
46.1
68.5
39.4
43.4
59.9
27.9
55.3
P
69.0
44.3
60.9
27.3
55.3
47.9
P
69.6
40.8
48.6
60.9
39.1
29.3
56.4
49.2
G
V
67.0
40,9
44.3
58.0
33.2
28.9
54.4
46.7
8
68.8
41.0
43.8
59.8
34.8
28.7
54.4
47.3
(
69.1
26.9
38.2
56,9
34.0
20.0
42.5
41.1
68.8
26.9
39.8
49.4
33.0
21.6
46.3
40.8
MMT-Bench (MMT) (Ying et al. 2024). and BLINK (Fu et al. 2024b) to assess foundational vision-language capabilities, which cover tasks such as object recognition, text recognition (OCR), spatial awareness and
Figure 20 presents the results for Q -LL-3...........LL Similar to the observations for the 7B model (Figure 5). the VPO/GRPO-optimize model performs comparably the original MILM (Note we do not report results with Owen2.5-VLL-32B1/ same observations). This confirms that RAPID preserves general-purpose purpose abilities across different model scales.
they show the
F.2 ABLATION STUDY ON OWEN2.5-VL-33
In this section, we extend our ablation study to the smaller Owen2.5-VL-33 model, with results presented in Table 15 While the results are largely consistent with those from 7B counterpart (Table 2). critical difference emerges. The 3B model necessitates an additional GRPO stage (D) following VPO to restore its reasoning capabilitie TT) which turn yields considerable accuracy gains. We at-
90
Q-VL-3B
Q-V-3R +. GRPO
Q-VL-3B GRPO VPO
Parforance
70-
60
tribute this requirement the limited capacity of the 3B model, where optimizing for the VPO task appears to de- grade its inherent reasoning performance-a a trade-off that is less pronounced in the larger 7B model.
40
MME
MMMBV1. Het
SEED image
MiMStar
mw-a dr
Bi BLAKK
F.3 DETAILS FOR PAIRWISE COMPARISONS
Figure 20: General benchmark Re-
sults. (Qwen-2.5-VL-3B)
Extended comparisons with OmniCaptioner-77 and MM-Eureka-7Bs Following the setting in Sec. 4.4 we conducted head-to-head comparison of our model, Dwwn2.5-VL-T (GRPO+VPO), against two strong baselines: O (an MILM enhanced for standard captioning) and MM-Bureka- 7B (an MLLM specially optimized for reasoning)
The win/tic/lose rates for Qwen2.5-VL-7B (GRPO+VPO) are reported in Figure where we observe the following:
10We hypothesize that VPO degrades the quality of the intermediate reasoning steps passed to the LLM, an effect always visible in the final accuracy.
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VPO Win
OmniCaptioner-77
VPO Win
Tie
MM-Eureka-77 7B Win
MathVista
MathVista
MathVision
MathVision
MathVerse
MathVerse-
MMMU-
MMMU
WeMath
WeMath
DynaMath
DynaMath
LogicVista
LogicVista
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
Percentage Vates
Percentage of Votes
(a) Ours vs. OmniCaptioner-71B
(b) Ours vs. MM-Eureka-7BB
Figure 21: Pairwise comparisons caption quality among ours and MmmiCaptionee-7BMMMBBBBBBee
RAPID vs. OmniCaptioner-7B: Our model's advantage from its focus on generating query-relevant captions, in contrast to OmniCaptioner's standard captions, Our model also benefits from more advanced base model (0wen2.5-VL-77 vs. Qwen2-VL--7B..
RAPID vs. MM-Eureka-7B: Our model performs better because VPO directly optimizes for captioning quality, whereas MM-Eureka-7B is optimized for end-to-end reasoning.
This validates that VPO significantly enhances the MLLM's ability to generate high-quality, task- relevant descriptions, outperforming MLLMs specialized for either standard captioning or reasoning.
Prompt for GPT evaluations. We provide the prompt for GPT evaluations on the quality of the caption in Figure I8] Consistent with the details in Sec, 4.4 this instructs the GPT to (1) choose captions that include more comprehensive and accurate details required to answer the question and (2) exclude any solving process in the captions.
Human evaluations. We present the details of the human evaluation conducted for the pairwise comparison experiment. For this, 100 questions are randomly sampled from the testmini set of Math Vista, and captions are generated using Qwen2.5-VL-33 trained with and without VPO. A total of trained human annotators are recruited, with each annotator comparing all the captions pairs to determine winner or a tie. For each caption pair, aggregate the results from different annotators by taking the majority of the decisions. Specifically, there are annotators and only 3 decisions (win, tie and lose), there is at least one decision that occurs twice. We compute the inter-annotator consistency following Zheng et al. (2023) by calculating the ratio of identical decision pairs out of all possible decision pairs and average them across all samples.
In Table 16 we report the win/tie/lose ratio (i.e., "win" means captions generated by MILMs with VPO is better) and additional measure of GPT-human consistency, calculated by the agreement rate between GPT-4o and human judgments. As can be seen, Qwen2.5- VL-3B trained with VPO demonstrates superior caption quality under human evaluation. This aligns with the result in Figure [I] which further supported by the high consistency of 87%. This supports the rationale of using GPT-4o a judge for evaluating caption quality.
Table 16: Human evaluation on pairwise comparison of the caption quality.
Win
Tie
Lose
GPT-human consistency
Inter-annotator consistency
62%
32%
6%
87%
85%
F.4 EXTENDING DECOUPLING TO OTHER MLLMS.
We apply the decoupling pipeline alone to more MLLMs (i.e., Intern VL3-8B, VL-Rethinker-7B and AMM-Eurek-77B with different LLMs (i.e., Qwen3-8B and GPT-OSS- 120B) and report the results in Table 17
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Table 17: Decoupling (using Qwen3-8B and GPT-OSS-120B) performance of different MLLMs. The best results are bold.
Model
Math Vista
Math Vision Math Verse MMMU
WeMath DynaMath LogicVista
AVG
73.6
29.3
39.8
62.7
37.1
25.5
44.1
44.6
w/ Qwen3-8B
71.3
42.4
39.3
64.4
38.8
29.1
50.1
47.9
w/ GPT-OSS-120B
70.6
47.1
41.2
68.1
41.0
29.1
51.0
49.7
VL-Rethinker-7B
74.9
30.0
47.5
56.9
37.3
21.4
43.6
44.5
w/ Qwen3-8B
72.8
43.0
51.9
59.7
41.1
30.9
50.2
w/ GPT-OSS- -20B
72.8
47.8
50.0
68.1
46.3
30.7
55.0
53.0
MM-Eureka-7B
73.0
27.9
46.1
54.9
34.7
22.6
48.3
43.9
w/ Qwen3-8B
72.2
42.1
47.7
61.4
35.9
28.9
51.2
48.5
w/ GPT-OSS-120B
70.5
47.5
51.8
68.2
43.9
33.5
50.8
52.3
F.5 TRAINING DYNAMICS OF VPO
We show the average reward and caption lengths over training in Figures and 23 We observe that:
Rewards increased training progresses. This confirms the effectiveness of VPO
allows the MLLM to generate captions that lead to higher reasoning accuracy.
Caption lengths grow as training progresses. An explanation for this phenomenon that the MILM learns to generate more comprehensive captions during training, which is reflected by longer lengths. This also confirmed in the Appendix [] where we visualize the captions.
F.6 TRAINING DYNAMICS OF GRPO
We visualize the training dynamics of GRPO in Figure 24 For 3B and 7B MLLMs, the rewards fluctuate and eventually drop after an initial convergence. contrast, the 72B model exhibits a more stable convergence. In both cases, subsequent VPO stage continues to improve the performance under the perception-reassoinn pipelines.
G MORE DISCUSSIONS
G.1 ADVANTAGES OF RAPID OVER UNIFIED ARCHITECTURE
We are aware that RAPID is modular framework rather than unified architecture that is adopted by most existing MLLMs. Our perspective is that RAPID are not to replace these unified systems, but rather to serve a dual, complementary role. Specifically, could serve as data engine build future powerful unified models. However, under limited budget, it could be a pragmatic and economic solution to address capacity gap of unified models.
RAPID as Data Engine for Future Unified Models. We agree that powerful, unified MLLM the ultimate goal. However, training such models is hampered by the scarcity of nigh-quality, multi-modal reasoning data. Our modular framework directly addresses this bottleneck by serving as a data engine (Gou et al. 2024, 2025). The RAPID pipeline can generate vast amounts of complex reasoning trajectories. This high-quality, model-generated data can then be used train and significantly improve a future unified MLLM (Chen et al. 2025a a technique proven effective in prior work Yang al.
2025b Huang al. 2025).
RAPID-like Methods Bridge Current Ability Gap. At present, general-purpose MLLMMs still
lag behind specialized models in critical perception tasks like object counting (Tamarapalli et al.) 2025), fine-grained OCR CCen et al. 2025c), depth estimation (Fu et al. 2024b) and semantic segmentation (Anonymous) 2025). ). However, expert-agent-bere based systems could pragmatically bridge
this gap by integrating these "expert" models (Zhou et al.) 2025; Su et al.) 2025 Liu et al. (225bb]
Gou et al. 2023 Liu et al.] (024b). This allows the system to leverage SoTA performance on these sub-tasks immediately, achieving higher overall accuracy.
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0.70
Rewend
Reward
0.60
0.45
VPO (0wen2.5A4 -33 Smoothed
VPO (0wen2.5-ML-7
200
300
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Training Steps
Training
Qwen2.5-VI.-3B
(b) Qwen2.55VVL-7B
0.70
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Reward
0.60
M7
(Qwen2.5
(Qwen2.5 VL-7722
0.50
Smoothed (CMA=0.6)
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20
40
60
80
100
120
140
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Training Steps
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(c) Qwen2.5 VL-3BBB
(d) Qwen2.5 V-VL-BBB
Roward
0.55
VPO (InternVL3-88) 8B)
Smooth ed (EMA-0.6)
0.45
100
150
250
300 350
Training Steps
(e) InternVL3-33
Figure 22: Rewards over training steps for VPO.
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800
600
Captin Length
Caption Lengih
600
500
400
600
300
300
VPD (Owen2. 5-VL-88)
VPO (QWen2.55V-78))
200
100
200
300
50
100
150
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250
Training Steps
Training Steps
(a) Qwen2.5 Dwe-2.5-VL-3B VL-BB
(b) Qwen2.5-VVe VLLBBB
800
Caplion Length
800
Caption
700
800
600
500
VPO (Qwen2.5-ML3326)
500
VPD (QHen2.5MML-72))
120
Training Steps
Steps
(c) V.vc22.5-IL-32BB
(d) Qwen2.5-VIL-72B
700
500
Caption Length
500
300
200
VPO OnternVL3-08)
50
100
150
200
250
300
350
Training Steps
(c) Intern VL3-8B
Figure 23: Caption length over training steps for VPO.
0.50
0.6
0.65
0.75
0.5
0.60
0.70
0.4
0.35
0.3
330
503
400
Taiiiing Steps
Trairiing
(a) Qwen2.5-VL.. VL-3B
(b) Owen2.5-VL-7B
(c) 2wwe2255VLL-77
Figure 24: Rewards over training steps for GRPO.
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RAPID Economic Solution with Limited Compute. While unified architecture is compelling goal. RAPID is a more pragmatic solution under restricted training budgets. circumvents the prohibitive cost of training unified model massive data. For example, RAPID could enjoy the advanced reasoning ability of new LLMss without training a new MILM from scratch.
H USE OF LARGE LANGUAGE MODELS (LLMs)
In this paper, the role of Large Language Models (LLMs) was confined to a minor, supporting capacity for polishing the writing. They were not involved in the core research process, such as ideation or analysis.
I CASE STUDY
Caption qualities. We conduct case study on the generated query-relevant captions. Specifically, for multi-modal reasoning question and image, we investigate the quality of the generated captions. For MLLMs, we consider Qwen2.5-VV VL series (3B/32B) both with and without VPO. We visualize the question, image and captions in Tables [8 24 for Dwen2.5-VL-3B and Tables 25 29 for
Qwen2.5-VI-333.
Comparing the captions generated by MILMs with and without VPO, we discover the following:
VPO leads to more visual details. We highlight these visual details in red in the table. Notably, these details are important clues required to correctly solve the question. This shows that VPO effective in improving the quality (especially comprehensiveness) of the query-relevant captions.
VPO leads to captions with more organized and hierarchical structures. For example, in Table 23 the MLLM with VPO describes the images at three levels, i.e., Tropic level, Terrestrial food chain and aquatic food chain. This allows the reasoner to quickly locate important information in the captions. However, the original MILM uses sequence of sentences that are less clear.
Large-sized MILMs generate more comprehensive captions. We found the captions generated by Qwen2.5-VL-33 model. This is because larger MILMs have better reasoning abilities that allow it to describe the image from multiple perspectives and in more logically coherent way. This leads to longer captions.
are significantly longer than those generated by the 3B
we provide a complete comparison of captions (generated by Qwen2.5-VL--3B with and without VPO) and the resulting reasoning results (produced by R1-7B) Similarly to the case study on caption quality, MILMs trained with VPO generate captions that capture more details. This is critical to the correctness of the reasoning process. As can be seen, the reasoner that receives captions with VPO arrives at the correct answer after several rounds of thinking and reflection. However, the reasoner that accepts the under-optimized caption experiences multiple contradictions and confusion (highlighted brown), which leads to responses that exceeds the maximum context length and finally fails this problem.
Reasoning accuracies. In Table 30
Table 18: Case Study with Qwen2.5-VL-3B. Additional visual details that relevant to the question but are only generated by MILMS with VPO are highlighted red.
Image:
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Fuel Consumption (miles to the gallon)
48
City driving
Motorway driving
38
33
28
Taber
Ursa
Velvo
Tink
Xtam
Car
Max. Speed (mph)
Cost to Purchase (E)
Taber
65
12,500
Ursa
60
15,250
Velvo
125
37,500
Tink
55,250
Xtam
110
62,500
Question:
If a driver travels average of 4,250 miles month driving only along motorways in an Xtam car, what the predicted annual consumption of fuel (in gallons)? Select from A, B, C, and E.
(A)Cannot say (B) 1, 1,500 (C) 125 (D) 150 (E) 1,250
Query-relevant Captions (Qwen2.5VVL-3)) w/ VPO):
The image is bar graph titled "Fuel Consumption (miles to the gallon)" that compares the fuel efficiency of five different cars, labeled as Taber, Ursa, Velvo, Tink, and Xtam. The graph is divided into categories: "City driving" and "Motorway driving."
For each car, there are two bars:
The light blue bar represents fuel consumption for city driving.
The dark blue bar represents fuel consumption for motorway driving.
The data for each car as follows:
Taber:
City driving: 48 miles per gallon
Motorway driving: 43 miles per gallon
Ursa::
City driving: 39 miles per gallon
Motorway driving: 43 miles per gallon
Velvo:
City driving: 35 miles per gallon
Motorway driving: 33 miles per gallon
Tink:
City driving: 33 miles per gallon
Motorway driving: 28 miles per gallon
Xtam:
City driving: 33 miles per gallon
Motorway driving: 33 miles per gallon
Below the bar graph, there is table that provides additional information about each car:
Max. Speed (mph): Taber (65), Ursa (60), Velvo (125), Tink (95), Xtam (110)
Cost Purchase (E): Taber (12,500), Ursa (15,250), Velvo (37,500), Tink (55,250), Xtam (62,500)
The image does not contain any information related to the question about fuel consumption for a specific car model.
Query-relevant Captions (Qwen2.5-VL-33%)
The image is a bar graph titled "Fuel Consumption (miles to the gallon)" that compares the fuel efficiency of five different cars, Taber, Ursa, Velvo, Tink, and Xtam, under two driving conditions: city driving and motorway driving. The graph uses two colors to differentiate between these conditions: light blue for city driving and dark blue for motorway driving.
Below the graph, there a table that provides additional information about each car, including:
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Max. Speed (mph): The maximum speed each achieve.
Cost to Purchase (&): The price each car in pounds.
The table entries are as follows:
Taber:
Max. Speed: 65 mph
Cost to Purchase: f12,500
Ursa:
Max. Speed: 60 mph
Cost to Purchase: f15,250
Velvo:
Max. Speed: 125 mph
Cost to Purchase: f37,500
Tink:
Max. Speed: 95 mph
Cost Purchase: f55,250
Xtam:
Max. Speed: 110 mph
Cost to Purchase: $62.500
The graph shows that the Taber and Ursa cars have higher fuel efficiency in city driving compared motorway driving, while the Velvo, Tink, and Xtam cars have higher fuel efficiency in motorway driving compared city driving.
Table 19:
Case Study with Qwen2.5-VL-3B, Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted red.
Image:
shown the figure, AB parallel CD, EG bisects angle BEF, then angle is equal to ()
Choices: A:50" B:60
A
Cood
2
C
F
G
D
50
Question:
According to the question shown in the image, please directly answer the question and provide the correct option letter, e.g., A, B. C, D.
Query-relevant Captions (Qwen2.5-VL-3B w/ VPO):
The image is geometric diagram with the following elements:
- Two parallel lines labeled AB and CDD
line segment EF.
A point G where line segment EG intersects line segment C.D.
An angle labeled 50t point F.
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An angle labeled 2 point G.
A question asking about the measure of angle 2, with choices:
A: 50
B: 60
C: 65
90
The diagram shows a triangle EFG with angle at point F and angle 2 at point G. The angle at point F is given as 50%.
The question asks for the measure of angle 2, given that AB || CD and EG bisects angle LBEF.
Query-relevant Captions (Qwen2.5-VL-3B):
The image shows geometric figure with lines AB and CD parallel to each other. Line EG bisects angle BEF Angle marked as 50 degrees.
Table 20:
Case Study with Qwen2.5-VL-3B, Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted red.
Image:
Start Binary To Decimal
Get Binary Number Call it B
D
Power
Yes
B% (Power)))
D 2*woerr
B B Power
Power ++
Say The Answer
Stop
Question:
Input binary number B 11000, find the corresponding decimal value by the algorithm shown in image.
Quera-relevant Captions (Qwen2.5.VL-33 VPO):
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The image is flowchart titled "Start Binary To Decimal." It outlines process to convert a binary number to its decimal equivalent. The flowehart starts with the instruction "Get Binary Number Call it BB" which is followed by initializing variables and Power to O. The flowchart then checks if is greater than O. If B is greater than 0, it checks if B modulo 10 raised to the power of (Power 1) is equal O. If this condition false, it updates D by adding raised to the power of Power, and then updates B by subtracting 10 raised to the power of Power. If the condition is true, it increments Power. This process continues until B is no longer greater than O. Finally, it states "Say The Answer is D" and "Stop."
The image does not contain any visual elements additional information beyond the flowchart itself.
Query-relevant Captions (Qwen2.5-VL-3B):
Start Binary Decimal
Get Binary Number Call it B
D=
Power 0
B >0 0
B%10'Power + 1) = 0
D D + Power
B = B Power
Yes
Power ++
Table 21: Case Study with Qwen2.5-VL--BB. Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted in red.
Image:
Number of Students in Each Grade
79
91
58
96
Grade
73
Grade 2
Grade
Grade
Grade 5
Question:
The pie chart below represents the number of each grade at a United States elementary school, What the percentage of Grade 2? The answer should be percentage between and 100.
Query-relevant Captions (Qwen2.5-VL-3B w/ VPO):
The image is pie chart titled "Number Students in Each Grade." The chart is divided into five
segments, each representing different grade level and the number of students in that grade. The
grades and their corresponding numbers are as follows:
Grade 1: 79 students
-Gadd 2: 96 students
Grade 3: 73 students
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Published as a conference paper at ICLR 2026
Grade 4: 58 students
Grade 5: 91 students
The pie chart visually represents the distribution of students across these grades. The segments are color-coded for each grade, with Grade in red, Grade 2 in blue, Grade 3 in green, Grade 4 in orange, and Grade 5 in purple. The chart provides a clear visual representation of the number of students in each grade at the elementary school.
Query-relevant Captions (Qwen2.5-VL-3B))
The pic chart below represents the number of each grade at a United States elementary school. What is the percentage of Grade 2? The answer should be percentage between and 100.
Table 22:
Case Study with Qwen2.5-VI-33. Additional visual details that are relevant to the question but are only generated by MILMs with VPO are highlighted in red.
Image:
3
Question:
Is the left graph isomorphic with the right graph? choice: (A) Yes (B) No
Query-relevant Captions (Qwen2.5-VL-3B w/ VPO):
The image consists of two graphs. The left graph a connected graph with the following vertices and edges: A, B. C, D, E, F, G, and H. The edges to F, H is connected to E, B is connected to F, F connected to E, E is connected to G, Fis connected to G. and E is connected to D.
follows: A is connected to H, A is connected
The right graph is simple cycle graph with 8 vertices, labeled 1, 1,2,3,4, 5, 6, and and edges connecting each vertex to the next a circular manner.
Based on the description, the left graph is not isomorphic to the right graph. The left graph has a more complex structure with multiple connections and central node (E), while the right graph is simple cycle with such central node and different number of vertices.
Query-relevant Captions (Qwen2.5-VL-3B2)
The left graph is graph with 8 vertices and 10 edges. The right graph is graph with vertices and 8 edges. The left graph is not isomorphic to the right graph.
Table 23: Case Study with Qwen2.5-VL-33 Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted red.
Image:
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Trophic
Terrestrial food
Aquatic
level
Tertaayy consumer
(secondary carnivore)
Hopps
Secondary consumer (carnivore)
Fish
Lizard
Primary consumer (herbivore)
Caterpillar
Zoo- plankton
Primary producer (autotroph)
Phyto- plankton
Plant
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, at the end. Question: What happens fish if pelicans CChoices: (A) decrease (B) nothing (C) increase (D) none of the above
Question:
Query-relevant Captions (Qwen2.5-VL-33 w/ VPO):
The image depicts food chain diagram showing the trophic levels and different types of consumers in both terrestrial and aquatic environments. Here is a detailed description of the image:
Trophic Level:
Primary producer (autotroph): This level includes plants and phytoplankton, which are the base of the food chain.
Primary consumer (herbivore): This level includes caterpillars and zooplankton, which feed on the primary producers.
Secondary consumer (carnivore): This level includes lizards and fish, which feed on the primary
consumers.
Tertiary consumer (secondary carnivore): This level includes snakes and pelicans, which feed on the secondary consumers.
2. Terrestrial food chain:
Primary producer (autotroph): Plant
Primary consumer (herbivore): Caterpillar
Secondary consumer (carnivore): Lizard
Tertiary consumer (secondary carnivore): Snake
3. Aquatic food chain:
Primary producer (autotroph): Phytoplankton
Primary consumer (herbivore): Zooplankton
Secondary consumer (carnivore): Fish
Tertiary consumer (secondary carnivore): Pelican
The image also shows arrows indicating the direction of energy flow from one trophic level to the
next, emphasizing the flow of energy through different ecosystems.
Query-relevant Captions (Qwen2.5-VL-3BB: The image shows a food chain diagram with two types of food chains: terrestrial and aquatic. The terrestrial food chain includes caterpillar, lizard, fish, and snake, with the caterpillar being the primary producer and the snake being the tertiary consumer. The aquatic food chain includes zooplankton, phytoplankton, fish, and a pelican, with the zooplankton being the primary producer and the pelican being the tertiary consumer.
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Table 24: Case Study with Qwen2.5-VL-3B Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted red.
Image:
Snakes
Howks
Frogs
Mice
Deer
Crickets
Grassas
Decompoeers
Question:
Hint: Please answer the question and provide the correct option letter, c.g., A, B, C, D, at the end. Question: If frogs were removed from this environment what animal would potentially see an increase in its population? Choices:(A) crickets (B) deer (C) snakes (D) hawks
Query-relevant Captions (Qwen2.5-VL-33 w/ VPO):
The image is food web diagram depicting various organisms and their interactions within ecosystem. The diagram includes the following elements:
Deer (at the bottom left) consuming Trees.
Mice (in the center) consuming Grasses.
Crickets (in the center right) consuming Grasses.
Snakes (at the top left) consuming Mice.
Hawks (at the top center) consuming Snakes.
Owls (at the top right) consuming Mice.
Frogs (in the center right) consuming Crickets.
Decomposers (at the bottom center) breaking down organic matter.
The arrows indicate the direction of energy flow from one organism to another, showing the relationships between the different species in the ecosystem.
Query-relevare Captions (Qwen2.5-VL-3B) The image is a food web diagram depicting various organisms and their interactions within an ecosystem. It includes a deer, trees, grasses, mice, crickets, frogs, hawks, and owls. The arrows indicate the direction of energy flow from producers (trees and grasses) to consumers (deer, mice, crickets, frogs, hawks, and owls), and decomposers (decomposers). The diagram shows how energy moves through the ecosystem, with each organism feeding on others, and how the removal of frogs could potentially lead to an increase in the population of crickets, they are primary food source for frogs.
Table 25:
Case Study with Qwen2.5-VL-32B. Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted in red.
Image:
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A
B
Question:
Hint: Please answer the question and provide the correct option letter, e.g., A, B. C, D, at the end.
Question: Which option is correct? Choices: (A) A (B) B (C) C
Query-relevant Captions (Qwen2.5-VL--32B w/ VPO):
The image presents logic puzzle involving patterns and shapes. Here is detailed description of the
image:
Left Side: Grid with Shapes
The grid is 3x3 matrix.
Each cell contains a shape with a specific pattern or design.
The shapes include circles, diamonds, and triangles, each with different internal designs (e.g., stars, squares, etc.).
Row 1:
1. Cell 1: A cirele with a star inside.
2. Cell A diamond with star inside.
3. Cell A triangle with inside.
Row 2:
1. Cell 1: Empty.
2. Cell A circle with a square inside.
3. Cell A diamond with a square inside.
Row 3:
1. Cell 1: Empty.
2. Cell 2: A triangle with downward arrow inside.
3. Cell 3: Empty.
Right Side: Multiple Choice Options
There three options labeled A, B, and C. Each option shows sequence of three shapes, The task is to determine the correct pattern that fits the logic of the grid.
Option A:
1. A diamond with downward arrow inside.
2. A triangle with a square inside.
3. A circle with a star inside.
Option B:
A diamond with downward arrow inside.
2. A triangle with a square inside.
3. A circle with downward arrow inside.
Option C:
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1. A diamond with downward arrow inside.
2. A triangle with a square inside.
3. A diamond with downward arrow inside.
Analysis of the Grid Patterns
Column-wise Observation:
Column 1:
Row 1: Circle with star.
Row 2: Empty.
Row Empty.
Column 2:
Row 1: Diamond with a star.
Row 2: Circle with square.
Row Triangle with downward arrow.
Columm 3:
Row 1: Triangle with star.
Row 2: Diamond with square.
Row Empty (to be determined).
Row-wise Observation:
Row 1: Circle (star), Diamond (star), Triangle (star)
Row 2: Empty, Circle (square), Diamond (square)
Row Empty, Triangle (downward arrow), (to be determined)
Shape Progression:
TTe shapes in each row and column follow specific order: Circle Diamond - Triangle.
The internal designs also follow pattern: Star - Square Downward Arrow.
Query-relevant Captions (Qwen2.5-VL-32BB:
The image consists two main sections:
Left Section:
A 3x3 grid with various shapes and patterns.
The grid contains:
circle with a star inside the top-left cell.
A diamond with a star inside in the top-middle cell.
A triangle with star inside in the top-right cell.
A circle with square inside in the middle-left cell.
diamond with a square inside in the middle-middle cell.
triangle with a square inside in the middle-right cell.
triangle with downward- downward-pointing arrow inside in the bottom-left cell.
The bottom-middl and bottom-right cells are empty.
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Right Section:
Three options labeled A, B, and C.
Each option contains three shapes:
Option A: A diamond with a nownward-pointingg arrow inside, a triangle with a square inside, and circle with star inside.
Option A circle with howwwward-pointinn arrow inside, a triangle with square inside, and another circle with a downward -eaynadd--piiiinggg arrow inside.
Option C: A circle with nownward-pointiee arrow inside, triangle with square inside, and a diamond with a Lownward-pointing arrow inside.
The task appears to involve identifying a pattern sequence based on the shapes and their internal symbols in the grid and selecting the correct option from the choices provided.
Table 26: Case Study with Qwen2.5-VL-32B. Additional visual details that relevant to the question but are only generated by MLLMs with VPO are highlighted in red.
Image:
Model Performance
GPT3-3B
GPT4
GPT3-8B
GPT3-12B
GPT3-1758
LLaMA-7B
LLaMA-138
LLaMA2-138
LLaMA-33B
LLaMAz-708
60
LLaMA-65B
A58
LLaMA2-708
LLaM 338
LLaMA2-708
Acc
GPT-4
LLaM 450
40
LLa 7B
LLaM4-33B
LLaMAR-138
GP 1-B
20
LLBB
GPT--38
2-78
LL
2.0
1.8
1.6
1.4
1.2
Pretrain Loss
Figure 2: The performance of SFT (blue lines) and ICL (red lines) settings on GSM8K. GPT-4 states they use some part of the GSM8K data in pre-training, and suggest others consider its performance between SFT and ICL.
Question:
Hint: Please answer the question requiring an integer answer and provide the final value, e.g., 1, 2, at the end. Question: How many models in the figure achieve an Acc score greater than 60?
Query-relevant Captions (Qwen2.5-VL-32B w/ VPO):
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The image is scatter plot titled "Model Performance," which compares the performance of various large language models on a specific task. likely related to the GSM8K dataset. The plot uses different colors and line styles distinguish between models and their training settings. Here is detailed deseription of the image: Title and Labels:
Title: "Model Performance"
X-axis: Labeled "Pretrain Loss," ranging from approximately 1.2 2.0.
Y-axis: Labeled "ACC" (presumably short for Accuracy), ranging from 0 to 80.
Legend:
The legend on the left side lists various models and their corresponding colors and markers:
GPT3-3B (pink), GPT3-6B (orange), GPT3-12B (yellow), GPT3-175B (dark green)
LLaMA-7B (light green), LLaMAA-7B (teal), LLaMA-13B (dark teal), LLaMMA213B
(light blue)
LLLaMA333B (blue), LLaMA-65B (purple), LLaMA2-70B (pink), GPT-4 (dark pink)
Line Styles:
Blue Lines: Represent the SFT (Supervised Fine-Tuning) setting.
Red Lines: Represent the ICL (In-Context Learning) setting.
Dotted lines connect points for each model, showing trends in performance.
Data Points:
Each model is represented by a series of points on the plot, with the position determined by:
X-axis (Pretrain Loss): Lower values indicate better pretraining.
Y-axis (ACC): Higher values indicate better accuracy.
Key Observations:
1. GPT-4 Performance:
GPT-4 (dark pink) achieves the highest accuracy (ACC) score, well above 60, and has low pretraining loss.
is plotted as a single point at the top-right of the graph.
2. LLaMA and LLaMA2 Models:
Various LLaMA and LLaMA2 models (e.g., LLaMA-7B, LLaMA2-7B, LLaMA-13B, etc.) are scattered across the plot.
Larger models (e.g., LLaMA2-70B) tend to have higher accuracy scores.
3. GPT3 Models:
GPT3 models (GPT3-3B, GPT3-6B, GPT3-12B, GPT3-175B) are plotted with lower accuracy scores compared to LLaMA and LLaMA2 models.
GPT3-175B performs better than smaller GPT3 models but still lags behind the larger LLaMA models.
4. Accuracy Threshold (ACC > 60):
Models achieving an ACC score greater than are primarily from the LLaMA2 series and GPT-4.
Notable models include:
-LLaMA2-70B
-LLMM2-65BB
LLaMA2-33B
GPT-4
Text Caption:
The caption below the figure provides additional context:
Figure 2: Describes the performance of SFT (blue lines) and ICL (red lines) settings on GSMSK.
Notes that GPT-4 uses some part of the GSM8K data in pretraining and suggests its performance lies between SFT and IC},

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Published as a conference paper at ICLR 2026
Query-relevant Captions (Qwen2.5-VL-32B):
The image is scatter plot titled "Model Performance." " It compares the performance of various large language models on a task, likely related to the GSM8K dataset, based on two metrics: "ACC" (accuracy) the y-axis and "Pretrain Loss" the x-axis. The models represented by different colored dots, and the legend on the left identifies each model by name and color. The models include various versions of GPT-3 (3B, 6B, 12B, 175B), LLaMA (7B, 13B, 33B, 65B, 70B). LLaMA2 (7B, 13B, 33B, 65B, 70B), and GPT-4.
Key Features:
Axes:
Y-axis (ACC): Ranges from 0 80, representing accuracy scores.
X-axis (Pretrain Loss): Ranges from 1.2 to 2.0, representing pretraining loss values.
2. Models:
Each model is represented by colored dot, with the model name labeled near the dot.
Models include the GPT-3 series, LLaMA series, LLaMA2 series, and GPT-4.
3. Trends:
There are two sets of lines:
Blue lines (SFT settings): Represent the performance of models under supervised
fine-tuning (SFT).
Red lines (ICL settings): Represent the performance of models under in-context
learning (ICL).
GPT-4 is shown as single point, suggesting its unique position in the performance landscape.
4. Legend:
The legend on the left provides a color-coded list of models, including:
GPT-3 variants: 3B, 6B, 12B, 175B
LLaMA variants: 7B, 13B, 33B, 65B, 70B
LLaMA2 variants: 7B, 13B, 33B, 65B, 70B
GPT-4
5. Caption:
The caption explains that the figure shows the performance of SFT (blue lines) and ICL (red lines) settings on GSMSK.
notes that GPT-4 uses some part of the GSM8K data in pretraining and suggests its performance lies between SFT and ICL.
Question:
The question asks how many models in the figure achieve an ACC score greater than 60. The task is to count the number models that meet this criterion based on the scatter plot. However, the instruction is to describe the image without answering the question.
Table 27:
Case Study with Qwen2.5-VL-32B. Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted in red.
Image:
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Insurance Coverage Nonalderly 6-64: Employer, 2013
NT
OR
MEN
WI
IN
Pb
NV
IL
NC
OK
AL
LA
AK
281,900- 2,024,500
2,098,300- 4,79,300
4,757,100- 6,467,400
7,133,900- 36,665,500
SOURCE: Kaber Parily Toundadio's State Health Facts.
Question:
Please answer the question and provide the correct option letter, c.g., A, B. C. D, at the end. Hint:
Question: Does South Carolina have the highest value in the South ? Choices: (A) Yes (B) No
Query-relevant Captions (Qwen2.5-VL-320 w/ VPO):
The image is a choropleth map the United States, depicting the distribution of health insurance coverage for nonelderly individuals (ages 0 64) through employer-sponsoree plans in 2013. Here is a detailed description of the image:
Title and Subtitle:
Title: "Health Insurance Coverage of Nonelderly 0-64: Employer, 2013"
This indicates that the map shows the number of nonelderly individuals (aged 0-64) who had employer--ponsorred health insurance 2013.
Color Coding:
The map uses gradient of blue shades to represent different ranges of employer-sponsored health insurance coverage. The legend at the bottom explains the color coding:
Lightest Blue: 281,900 - 2,024,500
Light Blue: 2,098,300 4,739,300
Medium Blue: 4,757,100 -,446,4400
Darkest Blue: 7,133,900 16,665,500
State Colors:
Darkest Blue (Highest Coverage): States in this category include California (CA), New York (NY), Texas (TX), and Florida (FL). These states have the highest number of nonelderly individuals with employer-sponsored health insurance.
Medium Blue: States like Illinois (IL), Ohio (OH), Pennsylvania (PA), and Michigan (MI)
fall into this category.
Light Blue: States such Colorado (CO), Arizona (AZ), and Tennessee (TN) are in this range.
Lightest Blue (Lowest Coverage): States with the lowest coverage include Alaska (AK), Hawaii (HI), Wyoming (WY), and several others in the Midwest and Northeast.
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South Region Analysis:
Highest Value in the South: The darkest blue states in the South are Texas (TX) and Florida (FL), indicating they have the highest employer-sponsoree health insurance
coverage in the region.
South Carolina (SC): South Carolina is colored a light blue shade, indicating it falls into the range of 2,098,3000 4,739,300. This is not the highest value in the South.
Other Observations:
Northeast: New York (NY) Pennsylvania (PA) have high coverage, with NY in the darkest blue category.
Midwest: States like Illinois (IL) and Ohio (OH) have medium to high coverage.
West: California (CA) stands out with the darkest blue, indicating the highest coverage in the West.
Source:
The map is sourced from the Kaiser Family Foundation's State Health Facts, as noted at the bottom of the image.
Question Analysis:
The question asks whether South Carolina has the highest value the South. Based on the map:
South Carolina a light blue category, not the darkest blue.
The highest values in the South are represented by Texas and Florida, which are in the darkest blue category.
Query-relevant Captions (Qwen2.5-VL-32B) The image is choropleth map of the United States, illustrating the distribution of health insurance coverage for nonelderly individuals aged 0-64 through employer-sponsore plans in 2013. The map uses varying shades of blue to represent different ranges of coverage numbers across the states. The legend at the bottom indicates four categories of coverage:
Lightest Blue: 281,900 - 2,024,500
Light Blue: 2,098,300- 4,739,300
Medium Blue: 4,757,100 6,467.400
Darkest Blue: 7,133,900 16,665,500
Key observations from the map:
States like California (CA), Texas (TX), and Florida (FI.) are shaded the darkest blue, indicating the highest range of employer-sponsored health insurance coverage.
Many states in the Midwest and West are shaded in lighter blues, indicating lower coverage numbers.
The source of the data cited the Kaiser Family Foundation's 's State Health Facts.
The question asks whether South Carolina (SC) has the highest value in the South. The map shows South Carolina in a light blue shade, indicating it falls into the second-lowed category of coverage.
Table 28: Case Study with Qwen2.5-V1L-32B. Additional visual details that relevant to the question but are only generated by MLLMs with VPO are highlighted in red.
Image:
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202
A
Battery
300
Question:
<image 1>A battery, an ammeter, three resistors, and a switch are connected to form the simple circuit shown above. When the switch is closed what would happen to the potential difference across the 15 ohm resistor?
Query-relevant Captions (Qwen2.5-VL-321) w/ VPO):
The image depicts an electrical circuit involving a battery, an ammeter, three resistors, and a switch. Here detailed description of the components and their arrangement: Components in the Circuit:
1. Battery:
Located on the left side of the circuit.
Serves the power source, providing the electromotive force (EMF) to the circuit.
2. Ammeter (A):
Placed immediately after the battery.
Used to measure the current flowing through the circuit.
It is connected in series with the rest of the circuit.
3. Resistors:
There are three resistors with the following resistances:
A 20 Ω resistor
- A 15 Ω resistor
30 resistor
The resistors are connected in combination of series and parallel configurations.
4. Switch (S):
Located on the right side of the circuit.
Controls the flow of current in the circuit. When closed, the circuit is complete, and current can flow.
Circuit Configuration:
The Q resistor connected in series with the rest the circuit.
The Ω and 30 resistors are connected in parallel.
The parallel combination is then connected in series with the 20 Ω resistor.
The ammeter is in series with all the resistors, measuring the total current.
The switch is placed after the parallel combination, completing the circuit when closed.
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Path of Current:
1. Current flows from the positive terminal of the battery.
2. It passes through the ammeter.
3. It then encounters the 20 Ω resistor.
4. After the 20 Ω resistor, the current splits:
One part flows through the 15 Ω resistor.
The other part flows through the 30 Ω resistor.
5. The currents recombine after the parallel branch.
6. The combined current continues through the rest of the circuit and returns to the battery.
Analysis of Potential Difference:
When the switch is closed, current flows through the circuit and potential differences develop across each resistor.
The Q2 and 30 resistors are in parallel.
In parallel configuration, the potential difference across each branch is the same.
Therefore, the potential difference across the 15 Ω resistor is equal to that across the 30 f resistor.
Query-relevant Captions Diven2.5-VL-32213
The image depicts simple electrical circuit consisting following components:
Battery: power source labeled as "Battery" is shown on the left side of the circuit.
Ammeter (A): A device used to measure the current the circuit connected series with the battery.
Resistors: Three resistors are present in the circuit:
A 20 Ω resistor is connected in series with the ammeter.
A 15 Ω resistor is connected in parallel with 30 Ω resistor.
Switch (S): A switch is placed the circuit, which can be opened or closed to control the flow of current.
Wires: The components are connected by wires to form complete circuit.
Circuit Configuration:
The Ω resistor series with the ammeter and the battery.
The 15 Ω resistor and the 30 Ω resistor connected in parallel with each other.
The switch is placed in the branch that includes the parallel combination of the 15 Ω and 30 Ω2 resistors.
Key Observations:
When the switch is closed, the parallel combination of the 15 Ω and 30 Ω resistors will be active, allowing current flow through both resistors.
The ammeter measures the total current flowing through the circuit.
This description provides detailed overview of the circuit's components and their arrangement,
Table 29: Case Study with Owen2.5-VL-32BB. Additional visual details that are relevant to the question but are only generated by MLLMs with VPO are highlighted in red.
Image:
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Asaal
JareJ
B
Question:
Please answer the question and provide the correct option letter, c.g., A, B, C, D, at the end. Question:o:: Misty the cat has five kittens: two of them are striped, spotty, the rest of them absolutely white. In which picture can we see the kittens of Misty, knowing that the ears of one of them of different colour? Choices: (A) A (B) B (C) C (D) (E)
Hint:
Query- Query-relevant Captions (Qwen2.5-VL-322 w/ VPO):
The image presents a multiple-choice question involving illustrations of cats. Here detailed description of the image:
Overall Structure:
The image contains five labeled sections, each representing a different option: A, B, C, D, and E.
Each section features group of cartoon-style cat illustrations.
The question describes a specific scenario about cat named Misty who has five kittens with particular characteristics.
The task is to identify which section correctly represents Misty's kittens based the given clues.
Clues from the Question:
1. Misty has five kittens.
2. Two of the kittens are striped.
3. One kitten spotty.
4. The rest (two kittens) absolutely white.
5. One of the kittens has ears of a different color.
Analysis of Each Section: Section A:
1 striped, spotty, 2 white kittens.
No kitten has ears of different color.
Section B:
striped, spotty, 2 white kittens.
No kitten with differently colored ears.
Section C:
2 striped, spotty, 2 white, gray kittens.
* One kitten has ears of different color.
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Section D:
2 striped, spotty, 2 white kittens.
. One kitten has ears of different color.
Section E:
I striped, 3 spotty, 1 white kittens.
One kitten has ears of a different color.
Query-relevant Captions (Qwen2.5-VL-32B):
The image shows five groups of cartoon-style cats, each labeled with letter (A, B, C, D, E). Each group contains multiple cats with various patterns and colors, including striped, spotty, and solid-colored cats. The cats are depicted in different poses, such as sitting, lying down, or standing. The question asks to identify the group that matches the description of Misty's 's kittens, which includes two striped, one spotty, and white kittens, with one having differently colored ears. Detailed Description of Each Group:
Group A: Contains cats with striped and spotty patterns. Some cats have differently colored ears.
Group Features cats with striped and solid-colored patterns. No cats have differently colored ears.
Group C: Includes cats with striped, spotty, and solid-colored patterns. No cats have differently colored ears.
Group D: Shows cats with striped and solid-colored patterns. No cats have differently colored ears
Group Contains cats with striped, spotty, and solid-colored patterns. No cats have differently colored ears.
The task is identify the group that matches the specific description of Misty's kittens.
Misty's 's Kittens:
Two striped kittens
One spotty kitten
Two white (solid-colored) kittens
One kitten has differently colored ears
Conclusion: Only Group A meets all the criteria, including the presence of differently colored ears.
A
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Published as a conference paper at ICLR 2026
Table 30: Reasoning Case Study with Qwen2.5-VL-3B Additional visual details that relevant to the question but are only generated by MLLMs with VPO are highlighted in red. Reasoning process that show confusing and contradiction are highlighted in brown.
Image:
B
D
C
Question:
O is the circumcircle of AABC, with AB BC 16. The are AB is folded down along the chord AB to intersect BC at point D. point D is the midpoint of BC, what is the length of AC?
Query-relevant Captions (Qwen2.5-VL-33 w/ VPO):
The image is geometric diagram of triangle AABC inscribed in circle with center O. The diagram shows the following elements:
Points A. B. and C' are the vertices of the triangle.
Point O the center of the circumeircle of AABC.
Line segment AB is chord of the circle.
Line segment BC another chord the circle.
Point D is point the circle such that the are AB is folded down along the chord AB to intersect BC at D.
The diagram includes dashed line segment AD and dashed line segment BD. The image does not provide any numerical values or specific measurements, and does not contain any text or additional information. The focus is purely on the geometric relationships and the diagram itself.
Captions (Qwen2.5-VL-3BB: The image shows circle with center O and points A. B, and C on its circumference. The line segment AB is diameter the circle, and the are AB is folded down along the chord AB to intersect BC at point D. Point D is the midpoint of BC.
Query-relevant
Reasoning Result of R1-7B (captions from Qwen2.5- VL-3B w/ VPO):
Alright, let me try to figure out this geometry problem step by step. So, we have triangle ABC inscribed in a circle with center O. AB and BC are both 16 units long, making it an isosceles triangle with AB = BC. The diagram shows that when are AB is folded along chord AB, intersects BC at point D, which is the midpoint of BC. So, BD DC 8 units.
First, need to visualize this. Since ABC is isosceles with AB BC, the base is AC, and the two equal sides are AB and BC. The circle is the circumcircle, so all three vertices lie on the circumference.
When the are AB is folded along AB, point D is where the fold intersects BC. Since the midpoint, BD = DC = 8. Folding along AB suggests that point D is the reflection of point C over the line AB. But since D lies on BC, maybe there's some symmetry here.
I think should consider the properties of the cireumcirele. perpendicular bisectors of the sides meet at the center O. Since AB BC', the triangle is isosceles, so the median from to AC should also the altitude and the angle bisector.
triangle inscribed circle, the
Wait, but we' we're dealing with fold along AB. When you fold along AB, point C would map to some point on BC. Since D is the midpoint, maybe there's 's reflection involved here. Let me try to see triangle ABD congruent or similar to another triangle.
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Alternatively, maybe using the Law Cosines would help. Let's denote angle at B as angle ABC. Since AB BC 16, the triangle is isosceles, angles at and C' are equal. But when we fold are AB over A AB, point D is created on BC. Since D is the midpoint, perhaps there's a relationship between the angles the lengths.
Wait, another approach: when you fold along AB, point C' maps to D. So, AD should equal AC' because reflection preserves distances. So, AD AC. Also, since D is the midpoint of BC, BD DC 8. So, triangle ABD, we have AB 16, BD 8, and AD AC.
So, triangle ABD has sides AB 16, BD 8, and AD AC = x. Maybe can apply the Law of Cosines here. Let's denote AC as Then, AD well.
In triangle ABD:
AB + BD2 - AB BD
B co0ccoss(BD) = AD2
Which is:
162 + 8² 2. cos(<<BB)) = x²
256 64 256 cos( (ABD) x²²
320 256 cos(<ABB))
x²
But don't know angle ABD. Maybe I can relate to the original triangle ABC. Since ABC isosceles with AB BC = 16, angle ABC is equal to angle B BAC and angle BCA? Wait, no, in an isosceles triangle, the angles opposite the equal sides are equal. So, since AB BC, the angles opposite them, which would be angle ACB and angle BAC, are equal.
Wait, no, in triangle ABC, AB BC 16, so the sides opposite angles C and A respectively. So, angle at C (angle ACIB) equals angle at A (angle BAC). Let's denote angle BAC as 0, so angle ACB is also 0, and angle ABC is 180 20 degrees.
When we fold along AB, point C maps to on BC. So, the reflection over AB takes point C D. Therefore, AD = AC and angle BAD = angle BAC = 0.
Wait, but AD is equal to AC because reflection preserves length. So, triangle ABD has sides AB 16, BD = 8, and AD AC x. Maybe can use the Law of Cosines here as well.
Alternatively, maybe using the Law Sines in triangle ABC. Since ABC is isosceles with AB BC 16, the circumradius can be found using the formula:
R
2 sin (A)
Where a is the length of a side, and A is the opposite angle.
Wait, but I' I'm not sure if that's the right approach. Let me think again.
Since ABC' is isosceles with AB = BC' = 16, then angle at A equals angle at C. Let me denote angle B as Φb. So, in triangle ABC, angles are & at B, and (180 Φ)/2 at A and each.
Now, when we fold along AB, point C' is reflected over AB to point D on BC. So, AD = AC, and BD = 8, DC 8.
So, in triangle ABD, AB 16, BD 8, AD
51

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Published as a conference paper at ICLR 2026
So, using the Law of Cosines on triangle ABD:
AB + BD - 2.AB BD cos(LABD) AD2
162 8 2- cos( (ABD)) x²
256 64 256 cos LABD) = x²²
320 256 cos( LABD) = x²²
But angle ABD is the same as angle ABC, which Φb So, cos(LABD) = cos()).
From triangle ABC, using the Law of Cosines:
AC AB² + BC 2 AB BC cos(s)
x² = 162 + 162 2 16 16 cos(
x² 512 512 cos
But from triangle ABD, we have x² 320 256 cos(
So, setting them equal:
512 512 cos( 320 256 cos(o)
512 320 512 cos( 256 cos(
192 256 cos(
192 3
cos(
256 4
So, angle @ has cosine 4' Now, substituting back into the equation for x2 from triangle ABC:
3
512 512
4
x² 512 384
128
V128 8v2
Wait, but this contradicts the initial thought that AC is 16 Hmm, maybe made a mistake the reflection part. Let me check.
Wait, when fold along AB, point C. maps D on BC. So, AD should equal AC because reflection preserves distance. So, AD = AC = x.
But in triangle ABD, we have AB = 16, BD = 8, AD = x.
Using Law of Cosines:
162 82 2. 1 8 cos( (LBD) = 2
256 64 256 cos LABD) = x22
320 - 256 cos LABD) = x²
But angle ABD is the same angle ABC, which is á. So, cos www.coo.sss... (LABD) cos(Φ) Thus, x² 320 256 (2) = 320 192 128 r V128 8/2
Wait, that would make AC 8,2, not 16 the initial model response suggested. Hmm, maybe the model response was incorrect.
Alternatively, perhaps made a mistake assuming angle ABD is equal to angle ABC. Let me think again.
52

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Published as a conference paper at ICLR 2026
In triangle ABC, angle ABC is at point B, between AB and BC. When we fold along AB, the angle at B remains the same, but the direction changes. So, the angle ABD in triangle ABD is actually angle between AB and BD, which is different from angle ABC.
Wait, no, BD is part of BC, so angle ABD is actually the same as angle ABC because BD is along BC. So, maybe my initial assumption was correct.
Wait, but then according to this calculation, AC' 8v2, which is about 11.31, but given that AB and BC are 16, that seems plausible.
Alternatively, maybe should consider that when folding, the angle at D is right angle. So, maybe triangle ABD is right triangle.
Wait, in the model response, they concluded that angle BAC is 90 degrees, which might not be correct. Let me see.
angle BAC 90 degrees, then triangle ABC would right-angled isosceles triangle, making AC AB- v2 16v2. But according to my calculation, it's 8.2. So, maybe the model response was wrong.
Wait, perhaps the mistake is in assuming that AD = AC. When you fold along AB, point C maps to D, so the distance from A to should equal the distance from to C, right? So, AD = AC. So, that part seems correct.
Wait, but in the model response, they used Law of Cosines with angle BAC being 90 degrees, which led AC 16 But according to my calculation, angle BAC is not necessarily 90 degrees, and it's actually determined by the folding.
Wait, perhaps should use the fact that the folded diagram, AD = AC because of reflection. So, maybe triangle ABD is congruent to triangle ABC? But no, because BD is only 8, not 16.
Alternatively, perhaps using coordinate geometry would help. Let me place point A at (0,0), point B at (16,0), since AB = 16. Since ABC' is isosceles with AB = BC = 16, point C' would be somewhere such that BC 16.
(rest of the reasoning)
Therefore, the correct answer should be AC 8v2, not 16.2 as in the model response.
But wait, maybe I made mistake in assuming angle ABD is equal to angle ABC. Let me think again.
In triangle ABC, angle at B is o. which we found cos( = 3. When folding along AB, the angle B remains the same, angle ABD is indeed Φ. Therefore, my calculation should be correct.
Therefore, the model response was incorrect, and the correct answer is AC 8v2
Reasoning Result of R1-7B (captions from Qwen2.5-VL Alright, so I'm trying to solve this geometry problem.
Let me read it again carefully. We have triangle ABC with AB BC 16.
So, it's an isosceles triangle with AB and BC equal.
That means angles and C are equal, right?
Wait, no, actually, in triangle ABC, if AB BC, then the base is AC, so the base angles at A and equal.
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Hmm, but I' I'm not sure if that's important right now. The problem mentions that the are AB is folded down along the chord AB to intersect BC at point D.
And D is the midpoint of BC.
So, BC is 16, so BD and DC are each 8.
Got it.
We need to find the length of AC. First, should probably visualize the problem.
Let draw circle with center O, points A, B, and C on the cireumference.
AB is diameter, but wait, hold on.
The caption says the image shows a circle with center and points A, B, on the circumference.
The line segment AB is diameter, and the are AB is folded down along AB to intersect BC at D, which is the midpoint. Wait, so AB is diameter, which would mean that angle ACB is right angle because any triangle inscribed in semicircle is right triangle.
But hold on, in the problem statement, it says AB BC 16.
AB is diameter, then AB would be the longest side, but BC also 16, so that's interesting because in right triangle, the hypotenuse is the longest side.
So if AB is the diameter and side of the triangle, then AB would be the hypotenuse.
But in the problem, AB BC, so both would be legs, which can't 't be because in right triangle, the hypotenuse is longer than the legs.
Hmm, maybe AB isn't 't the diameter?
Wait, the initial caption says AB is diameter, but the problem statement says AB BC= 16.
That seems conflicting because AB diameter, it should be longer than BC.
Maybe misread the problem.
Let me check.
Wait, no, the problem says O is the circumcircle of triangle ABC.
So O is the circumradius.
If AB is diameter, then the circumradius would be half of AB, which would make the circumradius
But if AB is 16, then the circumradius
However, in that case, triangle ABC would have AB as the diameter, making angle ACB right angle.
But in the problem, AB BC 16, so triangle ABC would have two sides equal to 16 and one side (AC) which we need to find.
But if angle C is 90 degrees, then AC would be the other leg, so AC BC = 16, making it an isosceles right triangle, so AC would be 16
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But wait, that seems straightforward, and maybe that's the answer, but I'm not sure because the folding part might complicate things.
Wait, the problem mentions that the are AB is folded down along AB to intersect BC at D, which is midpoint.
So maybe the initial assumption that AB a diameter isn' correct because when you fold the are AB down along AB, it intersects BC at D, which is the midpoint, maybe AB isn' I diameter.
Hmm, now I'm confused.
Alternatively, let me try think differently.
Maybe AB isn't the diameter, but just chord.
So the circle has center O, and AB is chord, not necessarily the diameter.
Then, the are AB is folded along AB, meaning reflecting the are AB over the chord AB, which would create reflection of point C over AB, landing at point D on BC. Since the midpoint of BC, which is 16, so BD =C=
So, when you fold arc AB over AB, the reflection C over AB is D, which lies on BC.
So, perhaps triangle ABD is congruent to triangle ABC, but I'm not sure.
Alternatively, maybe the reflection of C over AB is D, which is on BC.
So, the distance from C to AB is the same as from D to AB, but since D is on BC, maybe we can use some properties here.
Wait, perhaps using coordinates would help.
Let me try to place the points on a coordinate system.
Let's place point B at the origin (0.0).
Since AB = 16, let me place point A at (16, 0).
Then, since AB is a chord of the circle, the center O is somewhere in the plane.
Let me denote point C as (x, y)-
Since AB BC = 16, the distance from B to 16, so / x2 + y² 16.
Also, since ABC is a triangle, point C is somewhere not on AB. Now, the arc AB is folded over AB, and it intersects BC D, which is the midpoint of BC.
So, since B is at (0,0) and C is (x.y), the midpoint When we fold the are AB over AB, the reflection of point C. over AB is point D.
( ().
So, the reflection of point C over AB is D, which lies on BC.
So, the reflection of point C over AB is point D.
So, to find the reflection of point over AB, let's find the equation of AB first.
Since at (16,0) and B is at (0,0), AB is the x-axis from (0,0) to (16,0).
So, the line AB is y=0.
Reflecting point over the x-axis changes the sign of the y-coordinate.
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So, the reflection of point C=(x.y) over AB (y=0) would be (x, -y).
But the reflection point is D, which is (2, 2)
So, according to the reflection, (x, -y) should equal (2 5)
Wait, that can't 't be unless x 0 and O, which would place C at the origin, but then ABC wouldn't 't be a triangle.
Hmm, that doesn't it make sense. Maybe my assumption that AB is the x-axis is causing confusion because in reality, AB is just chord, not necessarily the x-axis.
Alternatively, perhaps should place AB as horizontal chord but not necessarily aligned with the x-axis.
Let me try that.
Let me place point A at (a, b) and point B at (c, d), but this might complicate things.
Maybe a better approach is to use coordinate geometry with AB as a chord, not necessarily aligned with any axis.
Alternatively, maybe using vectors or geometric properties would be better.
Let's think about the reflection.
When you fold the are AB over AB, point C is reflected over AB to point D on BC.
omitted
When we fold are AB over AB, the reflection of point over AB is point D.
So, reflection C over AB D.
Since AB is the x-axis from (0,0) to (a,0), the reflection over AB would invert the y-coordinate.
So, is at (x.y), then would be at -y).
But D is also the midpoint of BC, which is (B (B=+0c yutve)
(4+ 0+y -62 5)
2
So, setting (x, -y) equal to ():
= x/2 => x
Again, this leads to y=0, which would place on AB, making ABC degenerate.
Hmm, clearly, placing AB on the x-axis isn't working because forces C to on AB. Let me try different approach without coordinate geometry. Let me consider the properties of the reflection.
When we fold are AB over AB, point reflected over AB to point D on BC.
So, AB is the perpendicular bisector of segment CD.
Therefore, AB is perpendicular to CD, and the midpoint of CD lies on AB, Since the midpoint of BC, the midpoint M of CD is also the midpoint of BC, which is D itself.
So, D lies AB and is the midpoint of CD.
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Therefore, AB is the perpendicular bisector of CD, so CD is perpendicular AB, and D is the midpoint of CD and lies on AB. Wait, but D is also the midpoint BC.
So, lies on AB, then BC must intersect AB D, which is the midpoint BC.
So, in triangle ABC, D is the midpoint of BC and lies on AB.
Therefore, AB is a median of the triangle, and since AB is also side, must be that triangle ABC such that AB is both side and median, which is only possible if ABC is an isosceles triangle with AB = AC
But the problem states AB BC = 16, so if AB = AC, then it's an equilateral triangle, but in that case, all sides would be 16, making AC 16, but the answer seems to be 16v2, so maybe that's not the case.
I'm really confused now. Maybe the correct answer is 16v2, as in the initial tentative solution, but I'm not sure why.
Wait, another idea: since the midpoint of BC and lies on AB, and AB a side, then ABC must be such that AB is median and altitude, making it isosceles triangle with AB AC.
So, AB AC= 16. exceeding maximum context length (8192)
57


Reviews:
[{"review_id": "JIdJznn2W8", "reviewer": "Reviewer_cXzG", "summary": "This paper introduces RAPID, a method to enhance the reasoning of Multi-modal Large Language Models (MLLMs) whose internal language models are often outdated and expensive to upgrade. The approach decouples the system, using the MLLM for perception to generate detailed textual descriptions from images, which are then fed to a separate, powerful text-only LLM for reasoning. A novel reinforcement learning algorithm, Visual Perception Optimization (VPO), is used to train the MLLM to produce captions that are optimized for the final reasoning task. This \"plug-and-play\" design allows for easy upgrading of the reasoning LLM, enabling performance improvements without costly retraining of the vision components.", "questions": "N/A", "limitations": "", "rating": 2, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper is very well-written and logically structured, making the core ideas easy to understand. The figures are clear and effectively illustrate the main concepts.\n\n2. The motivation is straightforward.", "weaknesses": "1. This paper lacks novelty. The paper presents a relatively straightforward idea. It uses a multimodal large language model (MLLM) to describe an input image and then relies on a separate language model for textual reasoning. This setup mainly combines existing components rather than introducing a new methodological contribution. The multimodal stage performs description rather than genuine reasoning, which limits the conceptual depth of the approach.\n\n2. The proposed pipeline does not offer clear benefits in performance or efficiency. For example, when using Qwen2.5-VL-7B as the captioner and Qwen3-8B as the reasoner, the results reported in Table 1 remain below those of the single multimodal model Qwen3-8B-Instruct without reasoning. The method also requires roughly twice as many model parameters, which increases computational cost without providing noticeable performance gains.\n\n3. The decoupled architecture is vulnerable to error accumulation. If the perception stage produces an inaccurate or incomplete description, the reasoning model has no way to recover from that mistake. This makes the overall system unstable and limits its reliability compared with end-to-end multimodal reasoning approaches.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "vUKPYcZid0", "reviewer": "Reviewer_DHha", "summary": "This paper introduces VPO, which rewards the MLLM based on the correctness of answers generated by the external reasoner. They use a caption penalty to make sure the MLLM focus on the visual understanding, while the LLM mainly serve as a reasoner. Overall, this framework seems to be simple yet effective.", "questions": "See weakness.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper proposes training a visual captioner using the accuracy of LLM responses as a reward signal. Although combining VLM-based captioning with LLM reasoning has become common, to the best of my knowledge, introducing RL for training a visual captioner is novel. Therefore, the work demonstrates strong originality.\n\n2. The experiments are very solid, particularly as the conclusions are validated across models of multiple scales, with comprehensive ablation studies provided.\n\n3. The paper is easy to understand, and the formulations related to RL training are presented with rigor.\n\n4. The literature review is complete, and the code has been open-sourced.", "weaknesses": "The main limitation of the paper is that it does not provide a sufficiently detailed justification for the necessity of adopting a VLM captioner + LLM reasoner framework. In fact, many existing open-source and closed-source MLLMs still rely on unified reasoning, and the unified model appears to be an important trend in the development of large models. \n\nThe authors could elaborate on their perspective regarding the future direction of large models: whether they believe the field will move toward unified architectures or expert-agent-based systems. If the explanation is convincing, I would be willing to raise my score to 10, as this is already a very solid piece of work.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "36MfbZWf76", "reviewer": "Reviewer_wDxG", "summary": "This paper proposes RAPID (Reasoning-Aligned PerceptIon Decoupling), a two-stage pipeline for multi-modal reasoning that (1) repurposes an MLLM into a perception module that emits rich, query-aware text (caption + tentative solution), and (2) passes that text to a separate, stronger text-only LLM for the actual reasoning. Empirically, RAPID yields large gains on seven vision-math/logic benchmarks (e.g., MathVista, MathVision, MathVerse, MMMU, WeMath, DynaMath, LogicVista), enables inference-time scaling by swapping in stronger LLM reasoners without re-training the MLLM, and preserves general abilities on non-reasoning benchmarks.", "questions": "1. Does RAPID extend to multi-image and video inputs without architectural changes?\n2. You find R1-7B best for training rewards and Qwen3-8B strong for inference. Could you elaborate on the caption-length & difficulty balance hypothesis (Fig. 9) with controlled experiments (e.g., length-controlled rewards)?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The pipeline diagrams and prompt templates (referenced figures/appendices) make it easy to follow the two-stage flow and what exactly is optimized.\n2. Thorough ablations: perception variants (none / cap / qcap / sol / cap+sol / qcap+sol), with and without VPO/GRPO, with/without penalties, and different LLMs for training vs. inference.\n3. VPO is a neat twist on GRPO for caption supervision by outcome: the reward comes from a downstream verifier (the reasoner’s answer correctness), not from caption n-grams or human preferences.", "weaknesses": "1. Comparisons to verification-augmented or tool-enabled LMMs (e.g., visual verification modules, external OCR/detection tools) are missing. This matters because a strong verifier might reduce drift without multi-turn agent interaction.\n2. The method introduces two RL phases (GRPO then VPO) plus group rollouts and external LLM calls for rewards. While appendices mention batch sizes/steps, the wall-clock/cost, GPU hours, and reasoner-call counts per step are not surfaced prominently in the main text. This matters for practical adoption.\n3. The hasCap(·) check is prompt-based. This heuristic may be gamed (e.g., hiding solutions within “caption-like” text) or fail across domains/styles. A small quantitative audit of false positives/negatives (and downstream impact) would be valuable.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "QuJ5DXG8qg", "reviewer": "Reviewer_izU6", "summary": "This paper introduces RAPID, a method to decouple the perception and reasoning capabilities of multi-modal large language models (MLLMs). Compared to prior methods which aim at improving reasoning of MLLMs through end to end reinforcement learning based approaches, RAPID essentially separates the process into two stages; 1. perception: where the MLLM is asked to generate high quality captions describing an image and 2. reasoning, where the captions are fed to a stronger language model to answer the question. They also propose VPO, a policy gradient method to improve the MLLMs capabilities to produce high quality captions by assigning rewards based on a stronger LLM which takes as input the captions and generates the answer. The method shows strong performance on most multi-modal benchmarks, beating existing approaches. They also perform detailed ablations of the different components of their pipeline. Another advantage of RAPID is that it enables multiple LLMs to be used for the same MLLM backbone and allows for inference time scaling where a more powerful LLM can be used to generate solutions as test time.", "questions": "Please refer to the weaknesses section for questions. Additionally, \n\n1. The LLM is kept frozen throughout the process, did you try to fine-tune the LLM as well either jointly or in a separate stage? Would that help align the LLM to better answer questions based on the image descriptions? \n2. did you try any experiments where the same MLLM backbone was used as the reasoner as well? I wonder if training the same backbone for both captioning and reasoning + answering would allow for some transferability in learning.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper introduces an important technique of decoupling perception of MLLMs from reasoning, which allows for modularization and more customizable design choices \n2. The paper introduces VPO, a method to improve the perception and captioning capabilities of MLLMs which further helps improve downstream performance on several multi-modal benchmarks by 3-4%\n3. The various components like decoupling, GRPO, VPO, caption penalty are ablated well which should help other researchers with their design choices while training multi-modal language models with policy gradient methods. The authors also ablate other aspects such as prompts being fed to the MLLM and the LLM and the types of LLMs used during training and inference, providing valuable insights.  \n4. The technique allows for the same MLLM backbone to be used with several LLMs and also allows for inference time compute scaling by using a more powerful LLM.", "weaknesses": "1. In Table 1, the paper lacks comparison of using existing MLLM baselines as the perception module with an LLM (Qwen3-8B/GPT-OSS-120B) as the reasoner. While it is clear that RAPID helps improve performance of Qwen2.5-VL, the table lacks performance of just using the decoupling strategy with the other MLLM baselines. For instance, if we look at Table 2 A vs B, we see that there is a 5.5% boost just from the decoupling. It will be good to include similar performance metrics for the other baselines. \n2. Adding on to point 1, RAPID is only tested with Qwen2.5-VL as the MLLM backbone. While it is clear that RAPID generalizes to different reasoning LLMs, it will be good to show how well RAPID performs with some of the other MLLM backbones like InternVL or Ovis2 to shed light on its generalizability. \n3. Since one of the major claims is that VPO helps improve quality of captions/textual outputs, it will be good to compare how VPO performs against some of the other baselines like OmniCaptioner or MM-Eureka-7B. Currently the authors only include captioning win rates before and after VPO on the same MLLM backbone in Figure 11.\n4. One drawback is that while VPO helps improve the overall performance and the reasoning of the decoupled system, looking at Table 2 (rows H vs I), the reasoning capabilities of the underlying MLLM (using just GRPO vs GRPO + VPO) seems to decrease, which is not great.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)