Fast-Slow Thinking GRPO for Large Vision-Language Model Reasoning
Authors: Wenyi Xiao
Leilei Gan
Venue: NeurIPS 2025 spotlight ()
Keywords: Large Vision-Language Model
Fast-Slow Thinking
Reasoning
Primary area: applications
TL;DR: A novel Fast-Slow Thinking framework that dynamically adapts reasoning depth based on question characteristics.

Abstract: When applying reinforcement learning—typically through GRPO—to large vision-language model reasoning struggles to effectively scale reasoning length or generates verbose outputs across all tasks with only marginal gains in accuracy.
To address this issue, we present FAST-GRPO, a variant of GRPO that dynamically adapts reasoning depth based on question characteristics. 
Through empirical analysis, we establish the feasibility of fast-slow thinking in LVLMs by investigating how response length and data distribution affect performance.
Inspired by these observations, we introduce two complementary metrics to estimate the difficulty of the questions, guiding the model to determine when fast or slow thinking is more appropriate. 
Next, we incorporate adaptive length-based rewards and difficulty-aware KL divergence into the GRPO algorithm.
Experiments across seven reasoning benchmarks demonstrate that FAST achieves state-of-the-art accuracy with over 10% relative improvement compared to the base model, while reducing token usage by 32.7-67.3% compared to previous slow-thinking approaches, effectively balancing reasoning length and accuracy.

Fast-Slow Thinking GRPO for Large Vision-Language Model Reasoning
Wenyi Xiao Zhejiang University wenyix1a002j..et edu. on
Leilei Gan
Zhejiang University lei leileiganezju edu cn
Abstract
When applying reinforcement learning typically through GRPO to large vision- language model reasoning struggles to effectively scale reasoning length or gen- erates verbose outputs across all tasks with only marginal gains in accuracy. To address this issue, we present FAST-GRPO, variant of GRPO that dynamically adapts reasoning depth based on question characteristics. Through empirical analy- sis, we establish the feasibility of fast-slow thinking in LVLMs by investigating how response length and data distribution affect performance. Inspired by these observations, introduce two complementary metrics to estimate the difficulty of the questions, guiding the model to determine when fast or slow thinking is more ap- propriate. Next, incorporate adaptive
rewards and difficulty -wware KI. divergence into the GRPO algorithm. Experiments across seven reasoning benchmarks demonstrate that FAST achieves state-of-the-an of-the-art accuracy with over 10% relative improvement compared to the base model, while reducing token usage by 32.7-67.3% compared to previous slow-thinking approaches, effectively balancing reasoning length and accuracy.
Introduction
Slow-thinking reasoning has demonstrated remarkable capabilities in solving complex tasks
in Large Language Models (LLMs) [14]] by applying large-scale reinforcement learn-
ing (RL), exemplified by OpenAl's ol (5). DeepSeek-RI
6). and Qwen's QwQ
Unlike fast-thinking models g 9. slow- thinking models undertake more deliberate and
thorough reasoning before reaching an answer, which facilitates the exploration of diverse solu- tion paths for a given problem.
Average Accuracy (%)
55
MM R1
Openk/Thinkar-788
R1-OreVision-11
Researchers 10 have begun exploring sim- ilar slow thinking approaches for large vision- language models (LVLMs) to enhance visual reasoning, which can be categorized into SFT-
FAST-3B
Owen2: SAVL-8
50
MM-R1-9R
RL two-stage methods [0 15-18 and RL- only methods [9H22]] SFT-RL methods col-
45
Curr ReFT 38
VL
lect large-scale distilled data from slow-thinking models before applying reinforcement learning, while RL-only methods directly employ rein- forcement learning on curated high-quality data.
Average Tokens
Figure I: FAST achieves higher average accuracy with shorter average response lengths across seven benchmarks. All methods are built upon Qwen2.5- VL.
Despite these efforts, several challenges persist in slow-thinking for LVLM reasoning. First,
https://github. com/Kr- Loevan/FAST Correspondence to Leilci Gan.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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while RL-only methods enable slow-thinking LVLMs to improve reasoning accuracy, they strug- gle to effectively scale reasoning length [9 -20% to +10% compared to base models. This limited adaptability in reasoning length may constrain their effectiveness on complex tasks. Second, in contrast, we observe that slow- thinking LVLMs with SFT-RL. methods [23 nomenon-producing overly verbose responses across tasks while yielding only marginal im- provements in accuracy. This observation suggests that excessive verbosity may arise from the SET stage, which performs behavior cloning from distilled data. As evidenced in Ta- ble I RI-OneVision (one slow thinking model with SFT-RL) produces reasoning chains approx- imately 2x longer than its base model across all difficulty levels on the Geometry (24) test set. Notably, this overthinking proves detrimental for simpler questions, where extended reasoning results in accuracy degradation (69.5% vs. 72.7%), highlighting the need for adaptive fast-slow thinking.
21 17
with observed changes ranging only from
15
10 [6] exhibit a pronounced overthinking phe-
We notice that current research on addressing the overthinking phenomenon primarily focuses on large language models (LLMs) and can be classified into two categories based on the stage of application. In the training stage, they design length reward shaping in RL training to explic- itly encourage concise model responses. [23]
Table 1: Comparison of accuracy and response
length on Geometry 3K 24 test set across diffi- culty levels for Qwen2.5-VL VL--B, RI-One RI-Oneisiion and FAST.
Qwen2.5-V2 VL
RI-OneVision
FAST
Test
28 In the inference stage, they enforce concise reasoning via prompts, c.g., use less than 50 tokens, to constrain response length [29] 30.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Easy
72.7
318
69.5
623
78.2
189
Med
33.9
406
40.4
661
49.2
220
However, these methods to address overthinking in LLMs ignore challenges of visual inputs and
Hard
5.5
412
10.2
835
12.3
304
question characteristics in visual reasoning [25
All
37.7
378
40.3
731
46.4
239
277. leaving their effectiveness in LVLMs largely unexplored. To our knowledge, no existing work
effectively balances fast and slow thinking in LVLMs.
To address these issues, we propose FAST-GRPO, a tailored variant of GRPO 6 that balances fast and slow reasoning by incorporating adaptive length-based based rewards and dynamic regularization conditioned on the characteristics of multimodal inputs. Our approach begins with an investigation of the relationship between reasoning length and accuracy in LVLMss empirically demonstrating how length rewards and data distributions impact reasoning performance. Based on these findings, our methodology first introduces two complementary metrics estimate the difficulty of the questions, guiding the model to determine when fast or slow thinking is more appropriate. Next, we incorporate adaptive length-based rewards and difficulty-wware KL divergence into the GRPO algorithm. The former dynamically incentivizes concise or detailed reasoning based on question characteristics, while the latter modulates exploration constraints based on the estimated difficulty of each question.
We conduct extensive experiments on a range of reasoning benchmarks for LVLMs, and the experi- mental results have demonstrated the effect of the proposed method. As shown in Figure compared with slow thinking or fast thinking methods, our model achieves state-of-the-art reasoning accuracy with average accuracy improvement of over 10% compared to the base model, while significantly reducing reasoning length against slow thinking models from 32.7 7% to 67.3%.
2 Background: Group Relative Policy Optimization
Group Relative Policy Optimization (GRPO: 6 8) extends PPO [3] by replacing the value model with group relative rewards estimation, optimizing the objective in Equation I
Ne(or.1l,, or,ce)
(GSPO(TS) =
(
min
Tumee (oi 14 o6,es)
(1)
(olo..lg,on.cc (oiaaooi,e (4. oe)
clip
e, ( Aie
3Dxt (To || Tee))
where and B3 are the clipping hyperparameter and the coefficient controlling the KL regularization [
Ås, is the advantage, estimated through group relative rewards A Y -- Pa...r) with two rule-based rewards: (1) accuracy reward (ra) gives reward when the response is equivalent to the answer, and (2) format reward (ry) ensures responses adhere to the specified format.

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3 Pilot Experiments
As discussed in | when applying reinforcement learning-typpinee through GRPO to LVLM rea-
soning struggles to effectively scale reasoning length (RL-only methods; [9 17) generates ver-
bose outputs across all tasks with only marginal gains accuracy (SFT-RL methods; 23 To better understand the factors affecting re- sponse length and overall performance in GRPO [6] for LVLM reasoning, conduct series of experiments on the Geometry 3K dataset [24]. In particular, analyze the impact of length- based reward strategies ($3.1) and the influence
15 10 I6)..
Length Effect
10C
longthy roward (orange color)
CG2
GRNO
short roward (grean colort
0.4
Length Isalid line)
Respronse Length
Accur acy (cashed line)
of data distribution characteristics 4.2
Accuracy
400
0.43
3.1 Length Rewards Analysis
493
Prior research has established that while GRPO effectively scales response length in text-only LLMs 16 20 32 this effect does not trans- To verify this phe- nomenon and explore potential solutions, we
0.35
for to LVLMS 199 222..
:50
Step
0.30
Figure 2: Effect of length rewards on reasoning length and accuracy.
performed GRPO- on Qwen2.5- L [33]
with rule-based accuracy reward, and tested ex-
plicit length rewards that either encourage longer correct responses (Nlangthy reward = Leorrect/ / Lmaw) )
or shorter correct ones (Tshort reward = Tecorrect/ [mmax) as extended rewards, where Toman the maximum token length, Tecorrect denotes the length of the correct response. As shown in Figure 2 with increasing training steps, GRPO with lengthy reward steadily increases to 700 tokens, GRPO with short reward decreases to 180 tokens, while Naive GRPO remains stable around 330 tokens. These length rewards successfully manipulated response length, producing variations from 180 to 700 tokens, but with only modest changes in accuracy (+3%). This decoupling between length and accuracy suggests that LVLMs can maintain reasoning performance across different response lengths, challenging the assumption that longer reasoning is always better.
Based on the findings above, we can draw the following conclusions:
Observation 1: LVLMs can produce significantly different reasoning lengths with modest changes in accuracy via length rewards, suggesting potential for balancing reasoning depth and performance.
3.2 Data Distribution Analysis
Distribution Effect
mimuutty
Considering that overthinking models tend to generate verbose reasoning responses regardless of question difficulty, we next investigated how data distribution particularly the presence of samples with varying difficulty levels-might naturally influence reasoning length and perfor- mance.
503
Difficlity
Hord Difficuity
0.55
Length
Accuracy
Accuracy
-0.5
To this end, we stratified the Geometry3K train- ing dataset into three difficulty tiers using the pass @8 metric (i.e., the probability of correctly solving a question within eight attempts): Easy (0.75 S pass@8), Medium (0.25 < pass@8
300
Step
Figure 3: Effect of data distribution, especially difficulty on reasoning length and accuracy.
0.75), and Hard (pass@8~ < 0.25). This catego- rization resulted in approximately 35% Easy, 25% Medium, and 40% Hard samples.
Figure 3 illustrates how training on these different difficulty distributions affected model behavior. Models trained exclusively on Hard samples generated significantly longer responses but showed only
3

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marginal accuracy improvements. In contrast, training on Easy samples produced shorter responses while improving accuracy, Models trained on Medium samples showed modest length increase and the highest accuracy. Based on the findings above, we can draw the following conclusions:
Observation 2: Question difficulty acts as an implicit regulator of reasoning length, sug- gesting that data distribution can be strategically leveraged to achieve adaptive fast-slow thinking.
4 Fast-Slow Thinking GRPO
Building upon the aforementioned observations, we begin by introducing two complementary metrics to quantify the difficulty of multimodal questions, which facilitates dynamic data selection during re- inforcement learning( $4.1). Subsequently, we introduce FAST-GRPO, variant of GRPO specifically designed to balance fast and slow reasoning by leveraging adaptive length-based rewards conditioned on question difficulty (44.).
4.1 Multimodal Question Difficulty Estimation
Given our findings that data distribution influences both reasoning length and performance, accurately gauging data difficulty becomes essential for making dynamic adjustments to data distribution. To address this need, we propose two complementary metrics to measure the difficulty of given question for the policy model: one directly evaluates the intrinsic difficulty of the multimodal question itself, while the other measures its difficulty relative to the policy model's current capabilities.
Extrinsic Difficulty. We first quantify question difficulty relative the policy model through the empirical success rate Sextrinsie
pass@k, where pass mass@k k = c/k represents the proportion of correct solutions among k rollouts. This metric is computed online, reflecting the model's evolving capabilities.
Intrinsic Difficulty. While extrinsic difficulty reflects model's ability to solve problems, it may not fully capture the inherent visual complexity of the questions. We therefore introduce image complexity indicator that specifically evaluates the intrinsic difficulty within questions. Specifically, the Gray-Level Co-occurrence Matrix (GLCM) score, which analyzes how frequently pairs of pixels with specific intensity values occur at defined spatial relationships [34 35 However, GLCM captures only low-level image complexity based on pixel-level interactions and fails to account for higher-level semantic information. We therefore additionally employ the ViT classification entropy based on the output of the feature layer [36] 37 for image semantics complexity, providing high-level representation of conceptual difficulty, The image complexity is computed follows:
1 Σ H(gh) - H(v) 1
H Himage =
where 9, represents the GLCM for image patch p. H(gp) is the entropy of the co-occurrence probabilities across multiple radii and orientations; v denotes the feature output from the final layer of the ViT classifier, and (v) over N classes, with p, being the probability for class j.
Σ Pj log P; is the entropy of the predicted probability distribution
We integrate these metrics to get a comprehensive difficulty estimation (Saifiiultt) of a multimodal question. Questions with higher difficulty scores typically correspond to greater visual complexity and greater extrinsic difficulty for the policy model.
Saifiiully
Sextriusic
Hamage
Slow-to-Fas Sampling. We adopt curriculum strategies for the fast-slow thinking paradigm, using online-computed difficulty metries. Two variants are considered: (i) Binary: distinct training phases. In early epochs, exclude easy samples (Sextrinalc < 0.25) to strengthen reasoning on hard

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questions; in later epochs, exclude hard samples (Sextrinsic 2 0.75) to practice concise reasoning. (ii) Continuous: smoothly shift sampling probability from harder easier questions over epochs. enabling a gradual transition from slow to fast thinking. Binary enforces a clear capabilit--effiieney separation, while Continuous offers a gentler progression.
4.2 FAST-GRPO
With the carefully designed difficulty estimation methods for multimodal question, we introduce FAST-GRPO, tailored variant of GRPO that balances fast and slow reasoning by incorporating adaptive length-based rewards conditioned on question difficulty, as illustrated in Algorithm [
Difficulty-wware Length Reward Shaping, In addition the accuracy reward ra and for- mat reward ry. we propose a difficulty-ane length reward re as follows, which guides the model to employ the appropriate reasoning approach based on question difficulty.
Algorithm FAST-GRPO Training
Require:
Base model mT. selected dataset D, image complexity Hing
Initialize ref f- ne
2: for epoch = 1 to N do
if (Sa < 0) (r. 1)
Sample batch {q: D
ri
min( Lass 1-11111 1,
(0 s Sa) (ra-
4: Generate {o { ~ Tt(a))
5: Compute:
otherwise
Sext = 1 - pass@k(g.))
(4) where Sa is the difficulty score, is the 80th percentile difficulty threshold across the batch, and Lavg is the average length computed in the batch of responses. For less complex ques- tions (Sa- < 8), the reward encourages fast thinking for correct trajectories, specifically rewards trajectories towards shorter than aver- age length. Conversely, for complex questions, the reward encourages thorough reasoning for incorrect trajectories. Importantly, this reward is capped at I, preventing excessive verbosity even for complex problems. Difficulty thresh- old 9 is hyperparameter, for which we anal- yse sensitivity in $5.4
Su Sext Himg
3 = Buin + (Amax - Bmia)(
Sext)
6:
Filter samples via Slow-to-Fast Sampling
7: Compute rewards: r! = ra + X + XeTe
iSa < 0) A (ro = 1)
1, if (Sa 0) A (Ta
otherwise
Update policy:
max E
clip
A - -3,DKL (TTO (Tet)
Told
Following Deepseek-RI setting 19 we
9: end for
define the final reward function as a linear combination of these components: ri Fa + Aory Aert. This difficulty-wware length reward necessitates encouraging exploration for complex problems while maintaining efficient, accurate responses for simpler ones.
Difficulty-Awan KL Regularization. In addition the aforementioned length reward that encour- ages adaptive response length for questions of varying difficulty, the KL divergence term constrains the policy model's deviation from the reference model to achieve an exploitation-exploratio balance, which impacts learning effectiveness across questions of different difficulty levels [6] 31). Our KL coefficient sensitivity analysis in $ $5.4 also reveals that no single static / value optimally serves questions across difficulty levels. Lower KL constraints benefit challenging questions by enabling broader exploration, while stronger regularization maintains performance on simpler tasks. To address this issue, we implement a dynamic coefficient 3a for difficulty- regularization.
B Bmin
(Bmax -iiia) (1 Sextrinsi)
(5)
We give simple theoretical analysis to demonstrate how difficulty-wware 3a enhances learning on varying questions by decomposing the gradient coefficient from the gradient Equation
(o Byy ~og and (1w)
[GConrolq o)) Vo log Fo(o.. o
(6)
Tree T (4) To (o.1g)
GCoRpo(g.0)
A
+ Ba
(7)
Advantage Signal
Adaptive KL Regularization
5

---

As shown in Equation 7 the gradient coefficient consists of the advantage signal driving policy improvement and the adaptive KL regularization term. For high-difficulyy questions, Pa approaches 9min. weakening the KI. regularization and allowing the policy update to be dominated by the advantage signal. For low-difficulty questions, 8a approaches Smax. restricting policy deviation to ensure stability. Besides, the length normalization term [o,] explicitly affects gradient updates,
providing theory insight into Observation 2 for incorrect responses, it encourages longer outputs by reducing per-token penalties, while for correct responses, it encourages brevity through stronger per-token updates. This creates implicit bias toward increasing response length for difficult questions where models generate more incorrect rollouts, while naturally promoting shorter responses for simpler questions that yield more correct solutions.
5 Experiments
In this section, we evaluate the efficacy of our method for LVLM reasoning.
5.1 Experimental Setup
Table 2: Comparison of different training methods and training samples.
Training Dataset. Starting with 500K ques- tions from LLaVA-CoT [23), Mulberry [39].
and MathV-3660 [40]. first apply filters for answer verifiability. We deduplicate questions. retain only rule-based verifiable answers [41], and standardize to closed-form questions (e.g.. multiple-choice, numeric answers). Second, apply Slow-to-Fast sampling to remove ques- tions with extreme extrinsic difficulty scores (Sextrinsie = 0 or 1), yielding 18K training ques- tions. We display its distribution in Figure 6 and the specific source in the appendix.
Training Stage
Method
SFT Sample
RL
Sample
Virgo 38
5K
x
Mulberry
260K
X
LMM-RI
X
105K
MM-RI 21
6K
MM-
12
X
56K
Curr-ReFT
18
1.5K
9K
OpenVLThinker 110
35K
15K
Evaluation Benchmarks.
evaluate on
Vision-RI [5
200K
10K
widely used multimodal benchmarks: (1) Math-
R1-One
16
155K
10K
Vision 42 (2) Math Verse (43) (3) Math-
Vista 44 (4) MM-Math [45). (5) WeMath [6).
FAST (Ours)
18K
(6) DynaMath (47), and (7) MM- Vet [48). The
first six cover various mathematical reasoning tasks, while MM-Vet examines general multimodal abilities. We report both accuracy and response length for all benchmarks. We also conduct additional cross-domain evaluations, including science
reasoning (MM-K12 (22 open-domain VQA (Bingo 449]. MMHAL (50), low-level visual per-
ception (MMVP (51). and comprehensive calibrated evaluation (MMEval-Pre (5)). Details are
provided in Appendix K
For slow thinking reasoning, we compare with three categories of approaches: (1) SFT on distilled data (LLaVA-CoT, Mulberry, Virgo): (2) RL-only training (MM-Eureka, LMM-R1, MM-R1); and (3) Two-stage approaches combining SFT and RL (R1-One Vision, Curr-ReFT, Open Vision-RI). 1). comparative analysis of training methodologies and samples across these baselines is presented in Table For fast-slow thinking comparison, we evaluate against fast thinking methods using various reward shaping techniques: Kimi 1.5's length penalty (25) cosine function rewards 226.. and DAST 27]. Table I0 details these different reward formulations.
Baselines.
5.2 Main Results
We report the main results concerning reasoning accuracy and reasoning length.
reports the main results of reasoning performance. First, FAST achieves state-of-the-ee results on Math Vista with 73.8 and Verse with 50.6, outperforming leading-edge closed-source LVLMs like GPT-4o. Second, on more challenging benchmarks, Math Vi- sion and MM-Math, FAST achieves competitive results, validating FAST's ability to solve complex questions. Third, FAST improves Qwwn2.5-VIL-7B, our base model, with an average accuracy improvement of over 10%. Fourth, FAST improves Owen2.5-VL-3B with an average accuracy
Reasoning Accuracy. Table 4

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Table 3: Main results reasoning benchmarks compared with slow-thinking methods. For each benchmark, we report both accuracy (acc.) and response length (len.). Tokens are counted with Qwen2.5-VL's tokenizer.
Math Vision
Verse
Math Vista
MM-Math
WeMath
DynaMath
MM-Ve Vet
Method
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Closed-Soure Model
GPT-40
30.4
49.9
63.8
31.8
69.0
63.7
80.8
Claude-3.5 Sonnet
37.9
46.3
67.7
64.8
68.7
Qwen- Ow-n-VL-Max
39.3
47.3
74.2
45.6
73.2
MM-Eureka
26.9
40.4
67.1
60.7
I.L.VA-COT
16.4
20.3
54.8
22.6
44.8
60.3
Base Qwen2-VL-7B
Qwen2-VL
18.8
443.0
31.9
388,9
58.2
265,9
20.2
661.7
50.5
294.3
39.8
298 4
62.0
132.5
Mulberry
23.4
349.2
39.5
364.3
62.1
275.0
23.7
467.0
50.4
372.1
46.8
273.3
43.9
218.3
Virgo
24.0
36.7
Base Owen2.5-VL-3B
Owen2.5-VL-33
21.2
450.6
34.6
362.3
62.3
212.9
33.1
627.9
50.4
323.7
48.2
270.9
61.3
138.8
Cur--ReFT
20.1
240.1
36.3
121.6
61.9
95.9
28.6
301.5
57.3
156.0
43.8
146.4
62.0
117.6
LMM-RI
25.2
447.8
423.9
63.2
245.0
634.5
62.9
53.1
341.6
FAST-3B (Ours)
26.8
323.5
43.0
286.3
66.2
158.7
39.4
425.0
63.1
244.9
54.4
213.7
64.0
112.7
Base Qwen2.5.VL-7B
Qwen2.5-VL-78
25.6
443.0
46.9
388.9
68.2
189.1
34.1
666.7
61.0
294.3
58.0
273.3
67.1
132.5
MM-RI
30.2
324.6
283.9
71.0
185.6
41.9
528.5
67.9
235.7
57.5
254.2
70.6
137.9
Vision-RI
52.4
73.5
40.4
RI-One
29.9
692.8
46.4
631.5
64.1
402.5
34.1
688.6
61.8
591.9
53.5
560.6
71.6
440.7
OpenVLThinker
29.6
457.2
47.9
398.4
70.2
305.7
33.1
549.7
64.5
326.7
57.4
382.1
68.5
312.7
FAST-7B (Ours)
30.6
204.8
50.6
201.0
73.8
120.7
44.3
335.6
68.8
170.3
58.3
164.8
71.2
114.1
Table 4: Main results of accuracy and length compared with fast-thinking reward shaping methods.
MathV
Math Vista
Math Ver.
WeMath
MM-Ves Vet
Avg.
Method
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
Kimi
25.9
78.9
71.1
58.1
48.2
105.8
66.2
75.3
67.1
57.1
55.7
75.0
CosFn
27.9
396.4
72.1
247.2
49.6
383.9
68.1
311.9
71.1
148.9
57.8
297.7
DAST
27.0
281.1
72.9
93.5
48.5
194.5
67.4
148.9
67.6
66.3
56.7
156.9
FAST
30.6
204.8
73.8
120.7
50.6
201.0
68.8
170.3
71.2
114.1
59.0
162.2
improvement of over 14%, demonstrating that our method can be applied to different-sized models. Further scalability results on -aB-aarreetter model are provided in Appendix [ Lastly. FAST maintains its general multimodal ability, evidenced by improved performance on MM-Vet, and further demonstrates strong generalization beyond math-centric benchmarks in science reasoning and open -omiin VQA. In these evaluations, FAST improves its base model by 7-9% in physics, chemistry, and biology, and on open-domain VQA matches or surpasses strong baselines, showing effectiveness across diverse reasoning domains. Detailed results are provided in Appendix K
Reasoning Length. Tables and report the main results of reasoning length. First, FAST achieves a significant reduction of average reasoning length compared to slow thinking methods, from 32.7% against MM-RI 67.3% versus RI-OneVision, while preserving comparable or better reasoning accuracy. Second, compared to other fast thinking methods in LLMs, FAST achieves a modest reasoning length reduction and better reasoning accuracy. Third. FAST achieves slower thinking on more challenging questions, producing 60% longer responses on Hard than Easy of Geometry 3K as shown in Table and averaging 79% more tokens on MM-Math. Lastly, in cross- doos--dmmain evaluations şK). FAST yields substantially shorter responses: on MM-K12, average length drops by 106 tokens (33.8% (838%) vs. its base model and over 30% vs. strong slow-thinking baselines. In open-domain VQA (Bingo, MMHal), outputs are consistently 15-25% shorter, showing effective control of reasoning length beyond math tasks.

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5.3 Ablations
Table Ablation Results on Math Vista, Math Vi- sion, and Verheerse. More details of naive GRPO refer appendix $
We conduct ablation studies to validate the effectiveness of each design of method: Data Sampling, thinking reward shaping, and diffieulty-aware optimization. The results are represented in Table 5] We can draw the fol- lowing conclusions. First, without Data Sam- pling, reasoning accuracy seriously degrades on all benchmarks, highlighting the critical role of proper data distribution. Second, our thinking re- ward significantly reduces relative 42% response length with minor reasoning accuracy degrada- tion, from 31.5 30.6 on Math Vision. Third, the difficulty-awart regularization demonstrates robust improvement across all benchmarks, with a
Model
Math Math
Math Ver. Len.
Qwen-2.5-VL-7B
68.2
25.6
46.9
340.3
FAST
73.8
30.6
50.6
175.5
w/ Data Sampling
69.9
27.2
48.4
257.3
w/o Thinking Reward
73.6
31.5
45.9
302,2
w/o Difficulty Aware
72.0
29.5
49.2
171.6
Naive GRPO early stop
67.2
25.3
47.6
205,4
70.4
28.1
48.9
243.6
1.8-point absolute increase on Math Vista.
5.4 Analyses
Effeet of Slow to Fast Sampling. We further investigate the effect of Slow to Fast sampling by comparing our Slow to Fast sampling with alternative approaches: Fast to Slow, i.e., exclud- ing hard samples early, easy samples later, and Dynamic Sampling (53), i.e., always filtering out Easy and Hard samples). As shown in Ta- ble Fast to Slow yields comparable accuracy but shows degradation on challenging Math Vi- sion, while Dynamic Sampling leads to 80% longer responses without better accuracy improvements, We also compared our binary Slow-to-Fast sampling against a continuous variant to examine the effect of gradual curriculum shifts. This additional comparison is reported in Appendix
Table 6: Results on the effect of Slow-to-Fan Sam- pling.
Method
MathV. Mith Math Ver. Len.
No Selection
25.3
67.2
47.6
205.4
Dynamic Sampling
27.0
73.2
50.3
317,9
Fast to Slow Continuous Slow-to-Fas
26.3
72.9
50.2
266.1
30.9
74.4
51.0
221.2
Binary Slow-to-Fast
30.6
73.8
50.6
175.5
Table Results on the effect of SFT vs GRPO.
Table 8: Correlation between image complexity metrics and human judgments.
Samples Annotator MathV. Math Vis. MathVer.
260K
4o
27.9
64.0
46.5
Metric
SRCC
PLCC
200K
RI
18.8
66.8
47.1
GLCM entropy score
0.75
0.77
18K
30.6
73.8
50.6
Himg
0.49
0.54
Effect of SFT versus GRPO. As shown in Table 7 to further verify the efficacy of our FAST compared to SFT methods, we compare our method with SFT using: (1) 260K structured CoT data from GPT-4o 33 and (2) 200K long CoT from Deepseek-R! [15 SFT on Deepseek-R! data produces overthinking responses with degraded reasoning, while SFT GPT-4o data mimics fixed structures without substantial gains. In contrast, FAST with just 18K samples demonstrates superior performance across all benchmarks.
Validation of Image Complexity. In our image complexity design, we utilize the GLCM entropy score 34 35 to measure texture complexity and ViT classification entropy (36, 37 for semantic complexity. Zhang et al. (34) demonstrated that GLCM entropy achieves strong human alignment with Spearman Rank-order Correlation Coefficient (SRCC) of 0.75 and a Pearson Linear Correlation Coefficient (PLCC) of 0.77. To validate the effectiveness our combined metric Himg on our specific dataset, we followed the methodology in 34 having three participants rate 200 sampled training images on a 5-point scale based on visual detail complexity. As shown in Table 8 while our combined metric H Hsmg demonstrates moderate correlation with human judgments (SRCC=0.49, PLCC=0.54), it maintains well alignment with human perception.
Difficulty Threshold Analysis. We use the 80th percentile of batch difficulty as our threshold Figure 4 shows our grid search results: the 100th percentile yields concise responses (140.8 tokens) but reduces accuracy, while a 0 threshold produces excessive verbosity (486.2 tokens) with
8

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Performanie Analysis on Hyperparameters
Effect Diflicuity Throshol
Sptn Compariion
Comporr
Aug Accurdoy --- teugth
72.7
76.3
79.5
68.2
:000
46.3
Anweagg Accunay
Teat Set spttt
33.9
41.3
Text sox spen
5.5
10.9
11.9
15.1
-00
37.7
43.3
100t
3211
53th
Bose Model
Dany
Med
Hard
Dane
p-le: 3-26-2
p-562
Figure 4: Left: Results the effect of difficulty threshold. The average accuracy is computed across Math Vision, MathVerse and Math Vista. Middle: Test set results with different difficulty level training split comparisons Geometry 3K. Right: Test set results with different value comparison in pilot experiments on Geometry 3K. OOD results comparison on MM- Vet benchmark.
performance degradation. The 50th percentile achieves comparable accuracy to our 80th percentile but with 37% longer responses, confirming our choice effectively balances accuracy and conciseness.
Extrinsic Difficulty Analysis. Figure reveells how training on different extrinsic difficulty splits affects model performance. First, training on Medium difficulty samples yields the best overall performance (45.4%), providing optimal balance for learning. Second, we observe clear difficulty- specific transfer effects: Easy training improves Easy test performance (76.3%), Medium training benefits Medium tests (44.4%), and Hard training significantly boosts Hard test performance (15.1 % vs. base 5.5%). However, Hard sample training degrades Easy performance (68.2% vs. base 72.7%), while Easy training shows limited transfer to Hard problems. These findings support our Slow-to-Fad sampling strategy, demonstrating that no single difficulty level optimal for all test cases.
KL Coefficient Analysis. Recent works [53 54] suggest that removing KL constraints can enhance long-form reasoming in language models. We explored this effect in visual reasoning through grid search on the KL coefficient 3 (Figure 4. Our analysis reveals that lower / values significantly improve performance on Hard questions (16.9% at 8
vs. base 5.5%) by enabling greater exploration, but risk catastrophic forgetting on previously mastered tasks. Conversely, higher 3 values maintain strong performance on Easy questions and improve aat-ofddistribttion generalization (69.2% at B = 5e 2 on MM- Vet), but restrict exploration on complex reasoning tasks. These findings demonstrate no static value optimally serves questions across all difficulty levels-Hard questions benefit from looser constraints while Easy ones and generalization require stronger regularization.
In-depth Analysis of Multiplying Estimated Difficulties. The multiplicative form Saificulty Sextrinsic Hamage jointly captures empirical hardness and intrinsic visual complexity. One theoretical concern that this product could give low scores for cases that are hard for the model but visually simple, potentially leading to fast- thitkhinniig behaviour when slow reasoning is needed. In practice, such mismatches are rare (less than 5% of our training set), and our reward design $4.2 assigns zero length reward in these cases, avoiding contradictory signals. We also tested a weighted-sum ((sum) alternative difficulty aSextrimsic + (1 ax) Hunages where a 0.5, and found almost identical performance to the multiplicative form across Math Vista, Math Vision, and Math Verse (differences within 0.5% accuracy). These results confirm that FAST's difficulty estimation is robust to this potential corner case and the choice of combination strategy. Details are provided in H
5.5 Case Studies and Failure Mode Analysis
We complement our quantitative results with qualitative illustrations of FAST's behaviour. Ap- pendix providee examples where FAST adapts its reasoning, from concise answers on simple problems to expanded chains on complex ones, as well as typical failure cases. Here, we focus on a systematic analysis of these failures.
To understand when and why FAST-GRPO succeeds or fails, we analyse all incorrect responses from FAST-7B, RI-OneVisionn-88 and the base model (Qwen2.5-VL-7BB MATHVISTA. We

---

observe three recurring failure patterns (Figure 5 (i) Visual Perception Failures - where the model incorrectly extracts or interprets visual cues (c.g.. scales, chart values, spatial relations); (ii) Reasoning Error Propagation where a mid-chain mistake contaminates subsequent logical steps; and (iii) Knowledge Conflict & Gap - where language priors override contradictory visual evidence, or the model hallucinates in the absence of domain knowledge.
Key Insights. First, adaptive fast-slow think- ing substantially reduces reasoning-relat related fail- ures: FAST-7B euts Reasoning Error Propaga- tion and Knowledge Conflict cases by ~27% and 199 relative its base model. Shorter, targeted reasoning chains leave fewer opportu- nities for mid-proof errors and help suppress hallucinations caused by overextended thought.
Roxeeng Era Phansecer Sauwkody
350
350
Count
Second, perception, reasoning, is the dom- inant bottleneck: over half of FAST-7B's errors stem from visual misinterpretation. Once a spa- tial relation is mis-localised or a key numeric value misread, even perfectly structured reason- ing will converge to an incorrect answer. Future gains will likely come from strengthening the inpul stage, e.g., fine-grained OCR, calibrated scale reading, robust chart and graph value extraction, and accurate spatial grounding, so adaptive reasoning can operate on correct evidence.
KL-Onehhaten-18 0-l-22501--78
Figure 5: Error breakdown by category.
Related Work
We review approaches for LVLM reasoning and methods addressing overthinking in LLMs.
Slow-thinking methods for IVLMs. SFT-RI. two-stage methods leverage high-quality reasoning trajectories while inadvertently behavior cloning overthinking. Examples include Mulberry [39 55
using MCTS from GPT-4o. VLaVA-CoT (33 with structured reasoning stages, and Virgo (38 finetun-
ing on text-only reasoning chains. Vision-RI [5] RI-One Vision [16], and Open VLThinkee 10 first
collect distilled data from advanced models before applying SFT and RL. RL-only methods directly
employ RL to improve reasoning accuracy but struggle with scaling response length [56] 21 22
Visual-RFT [56 uses GRPO for various vision tasks, while MM-R1 22.. LMM-R1
17, and
MM-Eureka 22 apply RL on base models with curated visual reasoning questions.
Fast-Slow thinking methods for LLMs.. Methods addressing overthinking in LLMs include inference-stage approaches include TALE (30 enforcing token budgets prompt and CCoT [2 providing concise examples in context. Training-stage approaches include O1-Pruner [28 using a tailored RL objective to reduce verbosity, CoT-Value (57) fine-tuning on varied-length reason- ing chains to learn dynamic thinking, and Kimi [25 proposing length penalty rewards in RL and
Long2Short DPO [58] to shorten length. DAST 27 and CosineReward [26] encourage shorter
correct responses and longer in- correct responses via curated length rewards. While effective for text-only tasks, these approaches remain largely unexplored for LVLM reasoning.
Conclusion
We presented FAST, framework enabling LVLMs to dynamically adapt reasoning depth based on question characteristics, addressing the overthinking phenomenon. Through empirical analysis, we developed FAST-GRPO with three components: model-based metrics for question characterization, adaptive thinking rewards, and difficulty-aware KL regularization. Extensive experiments demon- strated that FAST achieves state-of-the-ar accuracy with over 10% improvement compared to the base model while reducing token usage compared previous slow-thinking approaches, effectively balancing reasoning length and accuracy.
10

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8 Acknowledgement
This work was supported in part by the "Pioneer" and "Leading Goose" R&D Program of Zhejiang (No. 2025C02037), the Earth System Big Data Platform of the School of Earth Sciences, Zhejiang University, Alibaba-Zhejiang University Joint Research Institute of Frontier Technologies, and the Science and Technology Project of State Grid Beijing Electric Power Company (Project Title: Research on Urban Cable Network Operation Status Detection and Risk Identification Technology Based on Soft Robots and Artificial Intelligence, Project Number: 520246250003).
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This Appendix for "Fast-Slow Thinking GRPO for Large Vision-Language Model Reasoning" is organized as follows:
Experimental Setup and Reproducibility. In SB we detail the implementation settings; $C describes the training and evaluation datasets; $D compares different length reward shaping methods; providee the human evaluation prompt for image complexity.
A Additional Experimental Analyses. F analyses naive GRPO behaviors; G reports statistical significance of main results; $ presents case studies and failure mode examples;
$K gives cross-domain evaluation results (science reasoning, open-domain VQA, low-
level visual perception, calibrated evaluation);
shows scalability experiments on S
52B-parameter LVLM.
Discussion and Limitations. directions for future work.
A discusses potential limitations of FAST-GRPO and
A Limitations
While our FAST framework demonstrates significant improvements in balancing reasoning length and accuracy, we acknowledge several limitations in our current work. Due to computational resource constraints, we were only able to evaluate our approach on models up to 32B parameters (Qwen2.5- VL-32B). The effectiveness of fast-slow thinking mechanisms may scale differently with larger models (e.g., models with 70B+ parameters), which could potentially exhibit different reasoning patterns and overthinking behaviors.
B Implementation Details
Table 9: Training Hyperparameters
We implement FAST using Qwen2.5-VL-3B and 7B as our base models. Below we detail our training setup and hyperparameters.
Hyperparameter
Value
Model
Qwen2.5-VL
Epochs
10
Learning Rate
1e-6
General Training Hyperparame- ters. For FAST training, we use our 18K dataset with a learning rate of 1e-6, a batch size of 512. We the maximum sequence length to 4096 for both prompts and generation, and apply BF16 precision through- out training. The training process runs for 10 epochs, requiring ap- proximately 600 H100 GPU hours. We use the prompt: You FIRST think about the reasoning process as an internal monologue and then pro- vide the final answer. The reasoning process MUST BE enclosed within <. Uhink < [think > lags. The final answer MUST BE pul < answer < /onswer > tags.
Train Batch Size
512
Temperature
1.0
Rollout per Prompt Prompt Max Length Generation Max Length
8
4096
4096
Max KL Coefficient Min KL Coefficient
0.03
0,001
Precision Max Pixels
BF16
1000000
Xy
0.5
A
0.5
Easy if 0.75 < pass@k if pass@k < 0.25
Difficulty
Hard
Medium
otherwise 80th percentile
Difficulty Threshold
Method-specific Training Hyperparameters. For reinforcement learning approach, employ a temperature of 1.0, 8 rollouts per question, and a KL coefficient ranging from 0.001 (min) to 0.03 (max). The reward weighting factors are set to 0.5. The difficulty threshold is set at the 80th percentile. For GLCM computation, following prior setting [34], Ip is derived from local patch p in the original image with 64 gray levels, defined by radius 8 = [1, 2, 3, 4] and orientation 0 = [0 45% 999P, 135%]. In practice, we divide the gray image into local patches of size 64.
Computation Environment. All training experiments were conducted using H20 GPUs. Model in- ference evaluations performed using the vLJ.M framework [59], and our training implementation extends the VeRL codebase (60).
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The complete set of hyperparameters is provided in Table 9 We commit to releasing all the code, data, and model checkpoints for experimental results reproducibility.
C
Datasets
Our training dataset comprises samples from four main categories: (1) Mathematical prob-
lems, including data from MathV360K, Ge- ometry3K, and other mathematical reasoning datasets; (2) Visual QA tasks, sourced from SPareGPPTV, Vizwiz, and additional visual question answering benchmarks; (3) Science problems from AI2D, ScienceQA, and other scientific reasoning datasets; and (4) Figure Understanding tasks from VQA, ChartQA, and other document and chart comprehension datasets. The distribution is balanced across these categories, with Mathematical problems constituting the largest portion, followed by Figure Understanding, Science, and Visual QA tasks.
Science
3546
Mathematical
6649
Visual QA
4433
Figure Understanding
Figure 6: Distribution of Training Dataset Sources by Category.
D Length Rewards
We provide comparison of different length rewards in Talbe I0
Table 10: Comparison of different length reward shaping methods.
Method
Length Reward
0.5
len(i) len
if correct otherwise
Kimi Length Penalty 25
max len-min
minn0, 0.5
lenl))-mint max max men Jon
CosFn 26
Mmin 1/2 (fmma M1 (1 + cas( cos(f)))
where generation length, T maximum length
Tmmin/ Ifmaz min/max rewards
For correct answers: Thuin r Mmna rT.
For wrong answers: Mmin = 30 Tmaa rz
(max(--0 -0.5 0.5, 0.1) if correct
DAST 27
[min (0.92 0.1,-0.1) if incorrect
where Lorngge Lobudges and Lbudget = P lor
p) Iimax p N
if Satficuity < 0 and ra 0 < Sameulty and ra otherwise
Tragy min Tang
FAST
1,1)
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E
Human Evaluation Prompt
Image Complexity Rating Instructions for Visual Reasoning Tasks
Please rate the complexity of the given image scale of 1-5, considering how challenging would be for visual reasoning tasks, Focus on aspects that affect the difficulty analyzing, interpreting, and reasoning about the image content.
Rating Scale:
Very Simple
Clear, uncluttered images with few objects
Simple spatial relationships
High contrast and clear visibility
Minimal text or numbers if present
Straightforward visual patterns
Somewhat Simple
Moderately clear images with a manageable number of objects
Basic spatial relationships requiring minimal analysis
Good visibility with minor distractions
Limited text or numerical information
Recognizable patterns with minimal complexity
3 Moderate Complexity
Multiple objects with varied relationships
Moderate spatial reasoning required
Some visual clutter or distractions
Moderate amount of text, numbers, or symbols
Patterns requiring some analysis
Complex
Numerous objects with intricate relationships
Challenging spatial reasoning required
Significant visual clutter
Substantial text, numbers, or symbols requiring careful reading
Complex patterns requiring detailed analysis
5 Very Complex
Dense arrangement of many objects with intricate relationships
Advanced spatial reasoning required
Heavy visual clutter making object identification difficult
Extensive text, numbers, or symbols with complex relationships
Intricate patterns requiring sophisticated analysis
When rating, consider: number of objects, visual clarity, amount of information, spatial relationships, and reasoning steps needed to understand the image content.
Naive GRPO Results
As shown Figure 7 the training accuracy naive GRPO continues increase throughout the training process, similar to other methods like Dynamic Sampling and FAST. However, when
17

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Figure 7: Training accuracy of Naive GRPO.
Figure 8: Validation accuracy of Naive GRPO.
IBMA tmaothwo.di
Hold our Val dobcn Accuracy to Triiiing Stops
Eycaniic
341
Nake GAPO
6.7
232
310
examine the validation accuracy in Figure g we observe concerning trend. The validation accuracy of naive GRPO initially increases, reaching peak of 0.40 around step 150, but then begins to decline despite continued improvements in training accuracy.
This discrepancy between training and validation performance indicates a clear overfitting phe- nomenon in naive GRPO. Upon closer examination of the model outputs in later training stages (e.g.. case in Figure 9), we observe an increasing inconsistency between the chain-of ohtiin- reasoning and the final answers produced by the model. Specifically, the model develops tendency generate reasoning chains that do not logically support its final conclusions, suggesting that it is memorizing training examples rather than learning generalizable reasoning patterns.
This overfitting behavior explains why the validation accuracy deteriorates even as training accuracy continues improve. The model optimizes for the training distribution the expense of generaliza- tion capability. Therefore, implementing early stopping based on validation performance is crucial when using naive GRPO select the optimal checkpoint (around step 150 in our experiments) before overfitting severely impacts the model's 's reasoning abilities.
Example Case: Inconsistent Reasoning in Naive GRPO on Training Dataset
Question: What is the measure of LGHI? Chain of Thought:
Since the lines AB and CD are parallel, and EF is transversal, the angles created by the transversal with the parallel lines have specific relationships. Specifically, the angle at point E that adjacent to 40" and the angle point F that is adjacent to 70" are supplementary angles with the angle GHI.
G
A
E
B
40
The angle point E is 40% and since EF is straight line, the angle adjacent to it on the other side of the transversal is 180 -0 140 Similarly, the angle point F is 70%, and the adjacent angle on the other side of the transversal is 180 70 110
H
70
F
C
D
Since GHI is the angle formed by the intersection of the transversal with the parallel lines, it is the angle that is supplementary to the 110 angle. Therefore, the measure of angle GHI is 180 110 70%
Geometry problem with angles
So, the measure of LGHI is 70%.
Final Answer: 110
Figure 9: Example of reasoning inconsistency naive GRPO on training dataset: The model produces the correct final answer (110%) despite having flawed reasoning its CoT (which incorrectly concludes 70%). This suggests memorization rather than proper understanding of geometric principles.
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G Statistical Significance Analysis
Table 11:
Main results on reasoning benchmarks. We report accuracy (Acc.) and response length
(Len.) with standard deviation across 5 runs with temperature set to 0.1. indicates statistical significance (p<0.05).
Qwen2.5-VLL 5-VL-3B
FAST-3B
Qwen2.5 Swen2.5-VL-7B
FAST-7B
Benchmark
Acc.
Len.
Acc.
Len.
Acc.
Len.
Acc.
Len.
MathVision
21.2
450.6
26.8+0.3*
323.5+14.2'
25.6
443.0
30.620.4*
204.8=12.3*
Vetse
34.6
362.3
43.0#0.4
286.3+12.8'
46.9
388.9
50.6+0,5*
201.0=10,5*
Math
62.3
212.9
66.2+0.5*
158.7+9.3*
68.2
189.1
73.8=0.6*
120.7+8.22
MM-Math
33.1
627.9
39.4+0.6'
425.0=16.7'
34.1
666.7
44.3=0.7"
335.6+15.3"
WeMath
50.4
323.7
63.120.4*
244.9=11.5'
294.3
68.8+0.5*
170.3+9.8*
DynaMath
48.2
270.9
54.4#0.3"
213.7+10.6*
58.0
273.3
58.3+0.4
164.8=11.2
MM-Vet
61.3
138.8
64.0+0.5*
112.746.9'
67.1
132.5
71,240.6
114.147.5*
To rigorously evaluate the effectiveness of approach, conducted statistical signif- icance analysis across all benchmarks. Table presents comprehensive results comparing our FAST models with their respective Qwen2.5-VV baselines, including standard deviations from multiple runs.
Figure TO visualizes the performance differ- ences between FAST-7B and Qwen2.5-VL.-7B. The top panel illustrates accuracy improvements in percentage points, while the bottom panel shows response length reduction percentages. Error bars represent standard deviation across 5 runs with temperature set to 0.1, and asterisks (*) indicate statistically significant differences (p<0.05).
Figure 10: Performance comparison between FAST-7B and Qwen2.5-VL-7B across multiple benchmarks.
Our analysis reveals that FAST-7B achieves statistically significant accuracy improvements on out of 7 benchmarks, with only DynaMath showing non-significant improvement (0.3 percentage points). The most substantial accuracy gains are observed on mathematical reasoning tasks (Math Vision: +5.0%, Math Verse: +3.7%, MM-Math: +10.2%) demonstrating method's particular effectiveness on complex reasoning problems.
Regarding response length, FAST-7B consistently produces significantly more concise responses across all benchmarks, with length reductions ranging from 13.9% to 53.8%. This confirms that approach successfully achieves both improved accuracy and enhanced efficiency in generating responses. The statistical significance of these improvements provides strong evidence for the effectiveness of our FAST framework in enhancing both the reasoning capabilities and efficiency.
H Analysis of Multiplicative Difficulty Formulation and Weighted-Sum Alternative
The multiplicative combination
Saifiiuulty
Sextrinsie
H Hunage
was designed to jointly capture a model's empirical success rate and the intrinsic visual complexity of a question. One concern raised in review is that when Sextrimsic is high (model finds the problem hard) but Himage very low (visually simple), the product may close to zero, potentially signalling "fast thinking" in case that is actually challenging.
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Reward design avoids conflict
As shown in Algorithm (T. the lifficulty-wwar length reward rt applies non-zero shaping only in two aligned cases:
Correct and Not Complex (Saifiiullty R): encourage shorter responses.
Incorrect and Complex (Saiffieulty 2 0): encourage longer responses.
The misaligned case in question (Incorrect but Not Complex, Correct but Complex) yields so no penalty or incorrect encouragement is applied.
Empirical rarity of corner cases
We ranked 1,000 random training samples and computed correlations between Sextrinsies H iingge and Saifficulty- High Sextrinsic combined with low Hinage was rare (< 5% of samples).
Weighted-sum alternative
We compared the multiplicatiie form with a weighted sum: s(sum) difficulty = aeSettninsic + (1 a)) a = 0.5.
Table 12 shows near-identical results.
Table 12: Multiplicative vs weighted-sum difficulty formulation.
Formulation
Math Vision
Math Vista
Math
Avg. Len.
Multiplicative 30.6
73.8
50.6
175.5
Weighted Sum
29.1
73.9
50.2
183.8
These results confirm (i) corner cases are rare in our actual training distribution, (ii) reward shap- ing avoids contradictory signals for such cases, and (iii) performance is robust the choice of multiplicative sum combination.
I Continuous Slow-to-Fast Sampling
In the main (Section 5.4 we compared our Slow-to-Fast sampling strategy against alternative approaches such as Fast-to-Slow and Dynamic Sampling [3 Here, we further contrast a continuous variant of Slow-to-Far scheduling:
Binary Slow-to-Fast. In this setting, the training curriculum makes hard switch at the halfway point of total epochs: the first half samples only hard and medium questions, and the second half incorporates easy questions, following the procedure in Algorithm
Continuous Slow-to-Fast. Here, the probability of drawing easy sample, Peasy. increases linearly with the training epoch from at the start to a maximum Praxx at the final epoch:
b
Peasy (t) =P Pmaxx
T
where is the total number of epochs. We set Pmaxx = 0.4 following initial tuning, ensuring a gradual transition from hard/medium-foous more balanced sampling.
Results. Table compares the two schedules under identical training settings on MATHVISTA, MATIVVISON,, and MATHVERSE.
Findings. Continuous scheduling provides accuracy gains (e.g., +0.6pp on MATHVISTA) and increases average output length by 26%, reducing efficiency. We hypothesize that the chosen Piaxx was insufficient sample a large enough proportion of easy questions later epochs, limiting potential efficiency gains. Additional tuning adaptive Pmax may yield more favourable trade-offs.
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Table 13: Binary vs. Continuous Slow-to-Fast scheduling. Accuracy (%) Avg. length (tokens).
Method
MATHVISTA
MATHVISION
MATHVERSE
Avg. Len.
Binary Continuous
73.8
30.6
50.6
175.5 221.2
74.4
30.9
51.0
Scalability to Larger Models
To evaluate the scalability of FAST-GRPO beyond mid-sized LVLMs, train and test the framework on the 32B-parameter model Qwen 225--2--53322 using the same 18K-question training set as in our main experiments. Due to compute constraints, training stopped after epochs (~1,200 GPU hours), which likely results in a sub-optimal checkpoint. We compare FAST-32B to strong slow- thinking baselines including Vision-R1-333 and IM-Bureka-322 six benchmarks, including MM-K 2 [22], a 2,000-question scientific reasoning benchmark evenly covering math, physics, chemistry, and biology. Due compute constraints, we stopped training after three epochs (1200 GPU hours), resulting in a likely sub-optimal checkpoint.
Table 14: Performance of FAST-GRPO 32B models compared to baselines. Accuracy (%) / Avg
length (tokens).
Model
MATHVISION
MATHVISTA
MATHVERSE
WEMATH
MM-K12
MM-VET
Avg Acc / Ten
Qwen-2.5-VL-52B
38.4/651
71.7 / 331
/5.9/550
69.1/515
66.8/ 840
71.1 /312
61.1/5332
Vision-RI-320
39.1 1976
440
60.9 818
74.2/637
64.8/ 1039
72.2
64.6/7106
MM-Fureka-52B
34.4/639
74.8 /552
56.5 560
7
72.2/857
73.4 344
64.1 /46600
FAST-32B
37.2/531
75.4/
57.6/430
74.4/
68.4/ 629
72.6/254
64.3/422.
Findings. Despite shorter training. FAST-32B matches or slightly exceeds the accuracy of stronger slow-thinking baselines while using notably fewer tokens:
Versus Vision-RR -isoonn----22- R1-32B, average output length is reduced by 40% (422.1 vs. 710.6 tokens) with comparable accuracy (64.3% vs. 64.6%)
Versus MM--ureka-338 32B, length is reduced by ~ 22% (422.1 vs. 546.0 tokens) while slightly improving average accuracy (64.3% vs. 64.1%).
These results indicate that FAST-GRPO scales effectively to larger LVLMs, maintaining its accuracy- efficiency trade-ofT. We leave exploration on ultra-large (2 70B) LVLMs for future work.
K Cross-Domain Evaluation
To validate FAST-GRPO beyond math-intensive benchmarks, conducted additional experiments on science reasoning, open-domain VQA, hallucination analysis, and low-level visual perception. These evaluations were added in response reviewer requests for broader task coverage.
K.1 MM-K12 Scientific Reasoning
The MM-K12 benchmark [22] consists of 2,000 multimodal reasoning questions evenly covering four domains: mathematics, physics, chemistry, and biology.
Findings. Compared to its base model, FAST-7B improves accuracy by +8. in physics, +7.0pp chemistry, and +8.8pp in biology, while reducing output length by ~ 33.8%. Even against strong slow-thinking models such as MM-Eureka-7B, accuracy remains comparable with ~ 30% fewer tokens.
K.2 Additional General Benchmarks
We further evaluate on four benchmarks covering open-domain VQA and visual robustness:
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Table 15: Accuracy (%) and average output length (tokens) on MM-K12 across subjects.
Model
Math
Physics
Chemistry
Biology
Avg Acc Len
Qwen-2.5-VL-7B
58.4
45.4
56.4
54.0
53.6 477.6
FAST-7B
69.0
53.8
63.4
62.8
62.2 371..
MM--urrka-777
71.2
56.2
65.2
65.2
64.5 537.8
Open OpenkLThinneer-B
63.0
53.8
60.6
65.0
60.6 561.0
RI-OneVision-
44.8
33.8
39.8
40.8
39.8 817.5
FAST-3B
56.0
50.6
56.2
57.6
55.1 318.1
Table 16:
Performance across diverse benchmarks.
Model
Bingo 1
MMHALU1 1
MMVP f MMEval-Pre Prll--P-Po
MM-K12 1
Qwen2.5-VL-7B
3.70
3.50
47.3
76.0
53.6
FAST-7B
3.72
3.40
47.0
75.0
62.2
Vision-R1-7B
3.62
3.10
44.0
72.2
MM- HMM-Eurea-77B 7B
3.69
3.20
46.7
74.8
64.5
Open VLThinkkr-B
3.45
3.00
46.5
71.5
60.6
Bingo Score
49
Open-domain VQA benchmark for hallucination analysis.
MMHal 55]:
Hallucination and informativeness evaluation open-domain VQA.
MMVP
51
Low-level visual perception probing.
MMEvval-Pro
52
Calibrated multimodal benchmark spanning math, science, and general
VQA.
Findings. FAST matches or slightly outperforms strong
baselines in open-domain
VQA and vallucination-robustenn benchmarks, while producing shorter outputs. This supports the observation that adaptive reasoning length mitigates hallucination risk in multimodal reasoning (61]
L
Case Study
Figure [] illustrates how FAST balances reasoning length and accuracy. For simple coordinate identification, RI-One Vision exhibits overthinking with 349 tokens output (highlighted in green), while FAST delivers a concise 59-token solution. For complex geometry, the base model makes critical error in angle calculations, while RI-One produces correct but verbose 676-token solution. FAST demonstrates adaptive slow thinking with more efficient and correct 375-token solution. validating our approach's ability adjust reasoning depth based on question complexity.
In addition to these affficiencyffeuuseee examples, we present three representative error cases illus- trating the main failure categories discussed in Section 5.5) each for Visual Perception Failure, Reasoning Error Propagation, and Knowledge Conflict & Gap. These cases are shown in Fig- ures 14 14 and provide visual, task-specific instances of how such errors manifest across different problem types.
22

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?
Q: Ar elephent is located of (4, 3), which cornasannds to which paint the disgram?
Bann Model
Faee(Oung)
Narh
1C, nend conn the can atout 1lim
feturnit point ahophat
rthado Shay S ti out the dighart
(1.)
dishant lectted
hige
the orihe and untt obert the erignn Th
sinhhare oolara
The skiphor or (4.23 mapp, po ct
(1J
left.
3
ranower bowed03 vonuuerr
0
bother Luniing grvd, puint H420
contitenty ohireeee
cre were which comuppcco Arowen vireoerr
?
angle then degrea engle Choices 130", S0", 100"
Bese Mode!
Fant/Ours)
circk. Theak Thed
and respectvvll The legge shona ther sot cnd2
pmpport tenyen toone
cemmil ingle The canmal angle
Foom let's fooes propertics of tongento and
Since and
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conaitan sC syruee See of engins a0k
Hergente ergles CuP and OSP are bork right eight (507)
the wes seglerie cut and cann 18et..
Sheee reic of the
cocorenddd Accendio Aczurding
aofo Thasd 1000-201 mussuee
Siece CADE the
commupaatingg
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183
The storr the dagres of engier 207///-ee
Figure 11: Case studies of different models' reasoning. Mistakes and overthinking are highlighted in red and green.
Example Case: Visual Perception Failure
Question: What is the highest amount this class mea- sures?
Ground Truth: 400 (ml) Model Answer: 600 (ml) Error Analysis:
A2
The image shows beaker with markings up 400 ml and a label indicating a total capacity of 600 ml. The question asks for the highest amount measured, which refers to the highest marked graduation (400 ml), not the container's maximum capacity. The model misinterprets the labeling and outputs 600 ml.
Beaker with scale markings
Error Type: Misinterpretation of visual context, confus- ing scale markings with container capacity.
Figure 12:
Visual Perception Failure example: Model confuses the beaker's maximum capacity label with the highest visible measurement marking, leading to an incorrect answer. This highlights the bottleneck in visual extraction accuracy.
23

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Example Case: Reasoning Error Propagation
Question: Find x Choices: (A) 21, (B) 34, (C) 58, (D) 67 Ground Truth: (C) 58 Model Answer: (B) 34
Error Analysis:
The model correctly identifies the problem as right- triangle angle calculation and applies the tangent ratio: tan.r 10/16 5/8. yielding ss 33.75". The mid- chain error occurs when mapping this computed angle the provided options: the model selects option 34%, overlooking that the target quantity the diagram cor- responds to another angle (58%). This incorrect mapping contaminates the final answer choice.
16
10
Geometry diagram
Error Type: A correct method with intermediate mis- take that propagates to the final conclusion.
Figure 13:
Reasoning Error Propagation example: The model applies the correct trigonometric method but misaligns the computed value with the problem's 's actual target, causing subsequent steps be built on a wrong assumption.
Example Case: Knowledge Conflict & Gap
Question: Fig.Q3 shows excerpt of the transmission phase of a TCP connection. Assume the length of the IP header is 20 bytes. What the ACK number message 6?
Peyload - 50 bytes
Ground Truth: 839 Model Answer: 451
Error Analysis:
To compute the ACK number, the model must correctly trace the TCP sequence of events in the diagram and account for byte offsets per message. Here, the model applies general TCP knowledge and standard ACK pro- gression, but fails interpret the specific visual data flow in the diagram (misidentifying the sequence range of mes- sage 3). This leads an underestimated ACK number. Error Type: Domain knowledge misapplication, relying on generic protocol rules over conflicting visual evidence from the figure.
Faybed bytes
5
Fig. Q3
TCP transmission diagram
Figure 14: Knowledge Conflict & Gap example: The model ignores the specific sequence number information in the visual diagram and instead applies incorrect general TCP rule, leading to wrong ACK number.
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NeurIPS Paper Checklist
1. Claims
Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Question:
Answer: [Yes]
Justification: The abstract and introduction accurately reflect the paper's contributions, including the FAST framework for balancing fast-slow thinking in LVLMs, the empirical analysis of reasoning length and accuracy, and the three key components of the approach.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification: The paper includes a dedicated Limitations section that acknowledges computational resource constraints limited evaluation to models up to 7B parameters, and notes that effectiveness may scale differently with larger models (70B+) which could exhibit different reasoning patterns.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed not penalize honesty concerning limitations.
3. Theory assumptions and proofs
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Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
Answer: [NA]
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The answer NA means that the paper does not include theoretical results. All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
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Question:
Answer: [Yes]
Justification:
All the the implementation details can be found in S.1 and
B
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If the contribution is dataset and/or model, the authors should describe the steps taken make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution a specific model and empirical evaluation, may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access to the model. In general. releasing code and data often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
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Question: Does the paper provide open access to the data and code, with sufficient instruc- tions faithfully reproduce the main experimental results, described in supplemental material?
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Reviews:
[{"review_id": "Z9P9a11aoK", "reviewer": "Reviewer_A2xT", "summary": "* This paper proposes FAST-GRPO, which is a variant of the GRPO reinforcement learning method that balances fast and slow reasoning for LVLMs through incorporating adaptive length-based rewards and dynamic regularization determined by question characteristics.\n* To determine the difficulty of questions, they propose 2 metrics — extrinsic and intrinsic difficulty — which provides accurate feedback to guide the model to choose between fast and slow thinking.\n* They improve the GRPO algorithm through including adaptive length-based rewards and difficulty-aware KL divergence.\n  * Empirical results on 7 reasoning benchmarks show the effectiveness of the proposed FAST-GRPO framework in achieving both efficiency in reasoning length and reasoning accuracy.", "questions": "* How does FAST-GRPO perform on reasoning tasks from a broader scope of domains, such as physics and social reasoning?", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### **Strengths**\n* The paper is clearly written with good presentation.\n* The research question is very well-motivated. The authors first conducted pilot experiments to find out limitations of the current GRPO method on LVLMs, the observation which motivates them to explore whether determining and adaptively providing different reward feedback to multimodal questions with different levels of difficulty.\n* The proposed FAST-GRPO method is effective in balancing fast and slow reasoning, achieving effective reasoning length and accuracy performance.\n  * The authors proved this through extensive experiments across reasoning benchmarks and models, as well as conducted ablation experiments in 5.3 to prove the contribution of each method component.\n  * In 5.4, the authors conduct additional analysis to provide more empirical insights.\n\n### **Weakness**\n* Limited scope of reasoning tasks. As discussed in lines 239-245, 6 of the 7 benchmarks evaluated are limited to the domain of math reasoning. This draws questions to the generalizability of the proposed FAST-GRPO method on reasoning tasks in other domains.\n* Section 5.4 could be restructured to provide more clear insights to readers.\n  * For instance, “validation of image complexity”, “difficulty threshold analysis”, and “extrinsic difficulty analysis” are all discussing insights on the difficulty of multimodal question data. These could be organized into a sub-subsection with some higher level summarizations.", "was_revised": true, "final_justification": "Additional clarifications provided by the authors are valid, and I believe that my original positive score already reflects my recognition of their contributions. I will keep my score.", "rebuttal": "We’d like to thank the reviewer for acknowledging the novelty and effectiveness of our proposed approach. We address your raised points as follows.\n\n> **W1, Q1: Generalizability of the proposed FAST-GRPO method on reasoning tasks in other domains.**\n\nWe thank the reviewer for raising the important question regarding the generalizability of FAST-GRPO to other reasoning domains.\n\n**First, we would like to clarify that generalizability was a key consideration in our original design from dataset construction to evaluation.**\n\n**On dataset construction**: Our training dataset was intentionally curated for diversity, encompassing a wide range of tasks beyond mathematics. The dataset is composed of:\n* **Mathematics (~40%)**, with samples from sources including MathV360K and Geometry3K.\n* **Science (~20%)**, with key sources including AI2D and ScienceQA.\n* **Visual QA (~20%)**, sourced from datasets including ShareGPT4V and Vizwiz.\n* **Figure Understanding (~20%)**, drawing from datasets including DocVQA and ChartQA.\n\n**On evaluation**: This method was validated not only on math benchmarks but also on general-purpose evaluations like MM-Vet (achieving 71.2% vs. base model's 67.1%) and multimodal reasoning evaluations like MathVista (73.8% vs. base model's 68.2%), which contains 10.7% scientific reasoning questions covering physics and biology.\n\nSecond, to more directly and comprehensively address your valuable concern, **we have evaluated FAST-3B and FAST-7B on the challenging MM-K12 benchmark** proposed in MM-Eureka[1]. MM-K12 contains 2,000 reasoning questions evenly distributed across math, physics, chemistry, and biology (25% each). We present the results below against strong baselines.\n\n| Model | Math | Physics | Chemistry | Biology | Avg. Acc. | Avg. Len. |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: |\n| GPT-4o | 55.8 | 41.2 | 47.0 | 55.4 | 49.9 | - |\n| Gemini-2.0-Flash | 76.8 | 53.6 | 64.6 | 66.0 | 65.2 | - |\n| Claude-3.7-Sonnet | 57.4 | 53.4 | 55.4 | 55.0 | 55.3 | - |\n| Qwen-2.5-VL-32B | 71.6 | 59.4 | 69.5 | 66.6 | 66.8 | 840.3 |\n| Qwen-2.5-VL-7B | 58.4 | 45.4 | 56.4 | 54.0 | 53.6 | 477.6 |\n| **FAST-3B** | **56.0** | **50.6** | **56.2** | **57.6** | **55.1** | **318.1** |\n| R1-Onevision-7B | 44.8 | 33.8 | 39.8 | 40.8 | 39.8 | 817.5 |\n| OpenVLThinker-7B | 63.0 | 53.8 | 60.6 | 65.0 | 60.6 | 561.0 |\n| MM-Eureka-7B | 71.2 | 56.2 | 65.2 | 65.2 | 64.5 | 537.8 |\n| **FAST-7B** | **69.0** | **53.8** | **63.4** | **62.8** | **62.2** | **371.2** |\n\nThe results demonstrate the strong generalizability of our approach. Specifically:\n\n* **Strong Generalization Across Science Domains**: FAST-7B significantly outperforms its base model (Qwen-2.5-VL-7B) across all science domains: Physics (+8.4), Chemistry (+7.0), and Biology (+8.8). This confirms that FAST-GRPO is effective beyond mathematical reasoning.\n* **Competitive Accuracy with Efficiency**: Compared to strong slow-thinking models like R1-Onevision-7B and OpenVLThinker-7B, FAST-7B achieves better accuracy (62.2% vs 60.6%) in science domains while being more efficient, reducing the average response length by approximately 33.8% (371.2 vs. 561.0 tokens). Even when compared to MM-Eureka-7B, trained on the MM-K12 train set, FAST-7B achieves comparable accuracy (62.2% vs. 64.5%) with a 30% reduction in response length (371.2 vs. 537.8 tokens).\n* **Scalability**: The improvements are consistent across model sizes, with FAST-3B outperforming a larger model Qwen-2.5-VL-7B (55.1% vs 53.6%) with more efficient reasoning (318.1 vs 477.6 tokens).\n\nWe believe this new evidence supports the generalizability of FAST-GRPO. We will incorporate these results and their corresponding analysis into our revision.\n\n[1] Meng, Fanqing, et al. \"Mm-eureka: Exploring the frontiers of multimodal reasoning with rule-based reinforcement learning.\" arXiv:2503.\n\n---\n\n> **W2: Section 5.4 could be restructured to provide more clear insights.**\n\nWe sincerely appreciate this valuable suggestion. Restructuring Section 5.4 would improve its clarity and narrative flow.\nIn the revised manuscript, we will adopt this advice and reorganize the section. Specifically, we will group the analyses on 'Validation of Image Complexity', 'Difficulty Threshold Analysis', and 'Extrinsic Difficulty Analysis' under a new, cohesive sub-subsection titled **'Analysis of Image-Text Question Difficulty'**."}, {"review_id": "rFZdLAJMfy", "reviewer": "Reviewer_jkkr", "summary": "1. The authors identify a key problem in current Large Vision-Language Models (LVLMs): \"slow-thinking\" models often \"overthink\" by generating overly verbose responses for all questions, regardless of their actual difficulty. This can be inefficient and even hurt accuracy on simpler problems. To address this, the authors propose FAST-GRPO- a method that enables the model to adapt its reasoning depth. The core of the approach is to first use two metrics to estimate the difficulty of a question. This difficulty estimation then guides GRPO process in two ways: adaptive length-based rewards to encourage concise answers for easy questions and more detailed reasoning for difficult ones. It uses a difficulty-aware KL divergence to control how much the model's policy can change, allowing for more exploration on complex problems.\n2. The proposed approach forces the model to learn when to apply \"fast thinking\" (short answers) and when to use \"slow thinking\" (detailed reasoning), leading to higher accuracy while significantly reducing the average response length.\n3. Two difficulty metrics are introduced - (a) Extrinsic Difficulty: Based on model's pass@k rate (how often it answers correctly), (b) Intrinsic Difficulty: Based on image complexity, using GLCM entropy and ViT entropy.\n4. A \"Slow-to-Fast\" curriculum is used—early training focuses on hard questions to build depth, then shifts to easier ones to promote concise thinking.\n5. The reward function combines - Accuracy reward, Format reward and Length reward: Encourages brevity on easy questions and thoroughness on hard ones. he KL coefficient is dynamically adjusted—looser for hard questions to allow exploration, tighter for easy ones to prevent overthinking.\nThe model is trained on 18K multimodal reasoning questions (filtered and difficulty-stratified), and evaluated on 7 benchmarks including MathVista, MathVerse, and MM-Vet.", "questions": "1. Could you provide a more robust justification for the multiplicative formulation of the complexity score (S_complexity)? Have you experimented with alternative formulations, such as a weighted sum?\n2. The \"Slow-to-Fast\" curriculum is a binary split. Have you considered a more continuous curriculum where the probability of sampling \"Easy\" questions gradually increases over the course of training?\n3. The ablation study (Table 5) shows that removing Data Sampling causes the largest performance drop. Given the aggressiveness of the filtering, to what extent are the final gains attributable to the highly curated nature of the 18K dataset versus the FAST-GRPO algorithm itself?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths-\n1. Introduces a dynamic RL-based method (FAST-GRPO) that intelligently adapts reasoning depth based on question difficulty—filling a key gap in LVLM reasoning literature.\n2. The paper proposes innovative, complementary difficulty metrics (extrinsic and intrinsic), including a practical image complexity estimation using GLCM and ViT entropy.\n3. The empirical results show that on multiple LVLM reasoning benchmarks, the proposed approach provides SOTA accuracy while significantly reducing token usage compared to existing slow-thinking methods.\n4. The insights presented in the prelimnary investigation are useful.\n\nAreas of Improvement-\n1. The paper's method for calculating complexity, using the formula $S_{complexity} = S_{difficulty} \\cdot H_{img}$, contains a potential flaw in its logic. The issue arises when a problem is very difficult for the model to solve (resulting in a high $S_{difficulty}$) but is paired with a visually simple image (leading to a very low $H_{img}$). Because of the multiplication, the final complexity score for this problem would be close to zero. According to the framework's design, a low complexity score signals the model to use \"fast thinking\" and rewards shorter, more concise answers. This creates a direct contradiction: the model is encouraged to provide a brief solution for a problem that it finds very hard and likely needs a more detailed, step-by-step reasoning process (\"slow thinking\") to solve correctly. This conflicting reward signal could hinder the model's ability to learn how to tackle such challenging problems effectively.\n2. The authors start with ~500K questions and, after two filtering stages, arrive at a final training set of just 18K questions. However, the exact details of filtering strategy is not laid out well.\n3. The current curriculum learning approach from slow-fast has a binary threshold in terms of epochs, however, the authors do not experiment with a graded approach of switching from slow to fast thinking.\n4. All experiments are conducted on models up to 7B parameters; it’s unclear whether FAST-GRPO would maintain gains on larger-scale LVLMs (e.g., 70B+).\n5. The paper lacks sufficient qualitative analysis and error breakdown. While it reports strong quantitative improvements, it provides only a single example of reasoning inconsistency and does not include comparative qualitative outputs that illustrate how FAST-GRPO adapts reasoning depth in practice. Additionally, there is no systematic error analysis to identify failure modes across question types or reasoning stages, which limits interpretability and diagnostic insights into model behavior.", "was_revised": true, "final_justification": "Some of the questions related to boundary case in reward and continuous reward are addressed with further experimental details. Further, during the discussion period, the authors have shared further error analysis which very critical and useful to understand the improvement with FAST-7B in reasoning over easy, medium, hard while showing the primary gap in perception errors of these models. Given this further analysis, I'm modifying my rating.", "rebuttal": "We’d like to thank the reviewer for acknowledging the novelty and effectiveness of our proposed approach. We address your raised insightful points as follows.\n\n> **W1, Q1: The potential conflicting reward signal could hinder the model's ability to learn such challenging problems. Have you experimented with alternative formulations, such as a weighted sum?**\n\nTo ensure clarity, we will adopt the reviewer's terminology for this response, where $S_{difficulty}$ refers to the model's extrinsic difficulty (termed $S_{extrinsic}$ in our paper) and $S_{complexity}$ refers to the final combined score (termed $S_{difficulty}$ in our paper).\n\nIn our method design, the corner case you proposed, a problem with high difficulty ($S_{difficulty}$) but low visual complexity ($H_{image}$) will **indeed result in a low final complexity score ($S_{complexity}$). However, we will demonstrate that this does not create a conflicting reward signal.**\n\nOur analysis is twofold:\n1. Our **reward design** avoids conflicting signals from this corner case.\n2. **Empirical evidence** shows that using a weighted sum yields nearly identical results, suggesting the practical impact is negligible. \n---\n\n**Analysis 1: Reward Design Avoids Conflicting Signals**\n\nAs detailed in the below reward equation (Equation 4 in paper), our difficulty-aware length reward ($r_t$) is applied based on three distinct cases:\n\n$$r_t =\n\\begin{cases}\n1 - \\frac{L}{L_{avg}} & \\text{if } (S_d < \\theta) \\wedge (r_a = 1) \\\\\\\\\n\\min\\left(\\frac{L}{L_{avg}} - 1, 1\\right) & \\text{if } (S_d \\ge \\theta) \\wedge (r_a = 0) \\\\\\\\\n0 & \\text{otherwise}\n\\end{cases}$$\n\nCase 1:  When the solution is **correct** and the question is categorized as **\"Not Complex\"** ($S_{complexity} < \\theta$), the length reward $r_t$ encourages shorter responses. Specifically, it penalizes responses where the length $L$ exceeds the batch average length $L_{avg}$.\n\nCase 2:  When the solution is **incorrect** and the question is categorized as **\"Complex\"** ($S_{complexity} \\ge \\theta$), the reward $r_t$ moderately encourages longer responses.\n\nCase 3:  Otherwise. This category includes two scenarios: **a) the solution is incorrect and the question is \"Not Complex\"**, and b) the solution is correct and the question is \"Complex\". In these cases, $r_t$ is 0, providing neither a reward nor a penalty.\n\nFirst, since the problem is inherently difficult for the model, the majority of its sampled responses will be incorrect ($r_a=0$). This situation falls into **Case 3**. In this case, the length reward $r_t$ is zero. This means the model is **not penalized for generating longer, exploratory reasoning chains for most of its attempts**. This directly avoids the conflicting reward you were concerned about.\n\nSecond, in the rarer event that the model produces a correct solution ($r_a=1$), it falls into **Case 1**. Here, a modest length penalty is only applied if the response is longer than the batch average length $L_{avg}$. Additionally, **the final reward is dominated by the primary accuracy reward ($r_a=1$)**. This is because, as defined in our reward ($r = r_a + \\lambda_r \\cdot r_f + \\lambda_t \\cdot r_t$), other rewards (format and length) are scaled by coefficients of 0.5.\n\n---\n\n**Analysis 2: Empirical Evidence Shows This Corner Case Has Negligible Impact**\n\nTo validate our design, we ranked 1,000 random training samples to analyze the correlation between different scoring metrics. We focused on two key aspects: **(1)** the ranking correlation between $S_{difficulty}$ and $H_{image}$ to evaluate potential corner cases, and **(2)** the ranking correlation between multiplicative and the weighted sum. Our correlation metrics included Spearman's Rank Correlation Coefficient (SRCC), Pearson's Linear Correlation Coefficient (PLCC), and Intersection@top-200.\n\nThe results provide insights about our data distribution.\n* **First**, there is a strong positive correlation between $S_{difficulty}$ and $H_{image}$, which suggests the reviewer's proposed corner case is infrequent in our data.\n* **Second**, the two formulations (multiplicative vs. weighted sum) have a high correlation and identify 193 of the same top 200 most complex questions.\n\n| |SRCC| PLCC | Intersect@top 200 |\n|:----:|:-:| :-: | :-: |\n| **$S_{difficulty}$ vs. $H_{image}$** | 0.75 | 0.68 | 156 |\n| **Multiplicative vs. Weighted sum** | 0.94 | 0.92 | 193 |\n\nFinally, we **experimented FAST-GRPO with the weighted-sum formulation ($S_{complexity}=S_{difficulty}+ H_{image}$)**. As shown below, a specific formulation has no significant impact on the model's performance.\n\n| | MathVision | MathVista | MathVerse | Avg. Len. |\n| :--- | :---: | :---: | :---: | :---: |\n| **Multiplicative** | 30.6 | 73.8 | 50.6 | 175.5 |\n| **Weighted Sum** | 29.1 | 73.9 | 50.2 | 183.8 |\n\nIn summary, **our analysis shows that while the corner case is theoretically possible, it is rare in our data distribution, and our method's performance is robust to the specific formulations.** We will incorporate these results and analysis into the revision.\n\n---\n> **W2: Filtering strategy is not laid out well.**\n\nTo filter our initial 500K-question dataset, we applied a rigorous filtering process. First, we deduplicated all samples with duplicate images and removed any questions that overlapped with our evaluation benchmarks. Next, to satisfy the GRPO algorithm's need for verifiable rewards, we standardized the data to include only closed-form questions—such as multiple-choice, numerical, or single-word answers—using regular expressions and custom rules. Finally, we filtered by extrinsic difficulty. We measured our base model's success rate for each question (pass@8) and removed those that were either too easy (pass@8 = 1) or too hard (pass@8 = 0), as these provide a poor learning signal for training. Due to limited space, further specifics will be in the revision.\n\n---\n> **W3, Q2: A graded approach to switching from slow to fast thinking.**\n\nIn response to this feedback, we have designed and conducted experiments to compare our original binary strategy with a **continuous Slow-to-Fast** curriculum. In this new setup, we introduce a linear scheduling for sampling \"Easy\" questions. The probability of sampling an easy question, $P_{easy}$, increases linearly with the training epoch $e$ (from $0$ to total epoches $E=10$), following $P_{easy}(e) = P_{max} \\cdot (e/E)$, where $P_{max}$ is a hyperparameter denotes the max sampling probability of easy questions, set to 0.4. This ensures a gradual transition from focusing on hard and medium samples to incorporating more easy samples as training progresses.\n\nWe evaluated this continuous approach on three benchmarks, with the other settings identical to our main experiments. The results are presented below:\n\n|  | MathVista | MathVision | MathVerse | Avg. Length |\n| :--- | :---: | :---: | :---: | :---: |\n| **Binary** | 73.8 | 30.6 | 50.6 | 175.5 |\n| **Continuous** | 74.4 | 30.9 | 51.0 | 221.2 |\n\nAs shown in the table, the continuous curriculum can **surpass the binary method in accuracy, while with longer responses.** We hypothesize this is because the  $P_{max}$ is not sufficiently high to sample adequate easy questions. We will incorporate results into the revision.\n\n---\n> **W4: FAST-GRPO on Larger-scale model.**\n\n**Thank you for the question. As this point is similar to the one raised in comment W1,Q1 by Reviewer NQ6C, we respectfully refer you to our detailed response provided there.**\n\n---\n> **W5: Lack qualitative analysis.**\n\nWe'd like to respectfully point out that we did provide qualitative analyses in the appendix, which are:\n\n* **Case Study of Fast-Slow Thinking (Appendix H, Figure 10):** This section provides a direct, side-by-side comparison of our FAST model against the Base Model and a \"slow-thinking\" model (R1-OneVision) on two distinct problems.\n    * On a simple question (coordinate identification), our model provides a correct and concise 59-token answer, while R1-OneVision exhibits overthinking with a needlessly verbose 349-token response.\n    * On a relatively complex geometry problem, the Base Model fails, and while R1-OneVision is correct, it is again verbose (676 tokens). In contrast, our FAST model adaptively adopts slow thinking, producing a correct and significantly more efficient 375-token solution.\n\n* **Analysis of Naive GRPO Failure (Appendix F, Figure 8):** We show a case where naive GRPO produces a correct final answer but with a logically flawed chain-of-thought, which highlights the overfitting problem that FAST-GRPO can effectively alleviate.\n\n**Due to the rebuttal's restrictions (e.g., no figures), we will provide more qualitative analysis, including case study and failure pattern in the revised version.**\n\n---\n> **Q3: Final gains from dataset curation or FAST-GRPO algorithm.**\n\nFirst, to clarify the point raised from **Table 5 in Section 5.3 Ablations**, the term **Data Sampling** refers specifically to the Slow-to-Fast sampling strategy used during training. This is **distinct from the one-time data filtering** we performed as a preprocessing step to create the 18K training set used across all relevant experiments.\n\nSecond, to precisely isolate and quantify the contribution of our algorithm, we designed the **Naive GRPO** baseline. Specifically, this baseline is trained on the **same 18K curated dataset**, without the core components of our method.\n\nThe results from Table 5 demonstrate a significant performance uplift: Compared to the naive baseline, FAST-GRPO simultaneously boosts accuracy by +3.4 (MathVista), +2.5 (MathVision) points, while also reducing the response length from 243.6 to 175.5 tokens.\n\nIn conclusion, while a well-curated dataset provides a strong foundation, **the FAST-GRPO algorithm itself mainly contributes to improvement in reasoning accuracy and efficiency**.\n\n---\n> **Format Concern: boundaries are not defined in the algorithm**\n\nThe boundary is half of the total epochs. We will revise it in the revision."}, {"review_id": "x8KyLlBag4", "reviewer": "Reviewer_NQ6C", "summary": "The paper introduces FAST-GRPO, a reinforcement-learning framework that explicitly balances “fast” (concise) and “slow” (detailed) reasoning in large vision-language models (LVLMs). It couples four ideas—(i) difficulty estimation, (ii) adaptive length reward, (iii) difficulty-aware KL regularisation, and (iv) a Slow-to-Fast curriculum sampler—to encourage short yet accurate answers. On seven math-heavy vision benchmarks (MathVision, MathVista, MM-Math, etc.), FAST-GRPO lifts average accuracy by 10 + pp while cutting answer length by 32.7 – 67.3 %. Remarkably, it reaches or surpasses strong baselines with only 18 k RL samples and no SFT fine-tuning.", "questions": "Further validating the framework’s scalability to larger models, improving the reliability of the difficulty estimation, and adding cross-task results would greatly enhance the paper’s credibility and practical value.", "limitations": "see above.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1、The authors are first to combine difficulty-aware length rewards, a dynamic KL schedule, and a Slow-to-Fast sampler within GRPO for LVLMs, giving explicit control over “fast vs. slow” reasoning.\n2、On seven public benchmarks, accuracy rises by double digits while answers shorten substantially; ablation studies show each component is necessary.\n\nWeakness:\n1、Experiments stop at 7 B parameters; scalability to ≥ 70 B remains untested (noted in Limitations).\n2、Evaluation focuses on math/diagram reasoning; generalisation to open-domain VQA, captioning, or dialogue is uncertain.", "was_revised": true, "final_justification": "Thanks for the detailed rebuttal and additional experimental detail. All my concerns have been resolved.", "rebuttal": "We’d like to thank the reviewer for acknowledging the novelty and effectiveness of our proposed approach. We address your raised points as follows.\n\n> **W1,Q1: Experiments stop at 7B parameters, scalability on larger models remains untested.**\n\nWe agree with your point that validating the scalability of our approach on larger models is important. \n\nWhile we noted the computational constraints in our original manuscript's limitations section, to directly address your concern, we **train FAST-GRPO on Qwen-2.5-VL-32B with the same training dataset. Due to time and compute constraints, we stopped training after three epochs (1200 GPU hours), resulting in a likely sub-optimal checkpoint.** We compare our method against several strong baselines on 6 benchmarks including the newly introduced MM K12 benchmark proposed in MM-Eureka [1], a comprehensive reasoning benchmark of 2,000 problems spanning math, physics, chemistry, and biology. The results are presented below:\n\n| Model           | MathVision (Acc/Len) | MathVista (Acc/Len) | MathVerse (Acc/Len) | WeMath (Acc/Len) | MM-K12 (Acc/Len) | MM-Vet (Acc/Len) | Avg Acc | Avg Len |\n|-----------------|----------------------|----------------------|----------------------|------------------|------------------|------------------|---------|---------|\n| Qwen-2.5-VL-32B | 38.4 / 651           | 71.7 / 331           | 49.9 / 550           | 69.1 / 515       | 66.8 / 840     | 71.1 / 312       | 61.1    | 533.2   |\n| Vision-R1-32B   | 39.1 / 976           | 76.4 / 410           | 60.9 / 818           | 74.2 / 637       | 64.8 / 1039      | 72.2 / 384       | 64.6    | 710.6   |\n| MM-Eureka-32B   | 34.4 / 639           | 74.8 / 352           | 56.5 / 560           | 73.4 / 524       | 72.2 / 857     | 73.4 / 344       | 64.1    | 546.0   |\n| **FAST-32B**    | 37.2 / 531           | 75.4 / 268           | 57.6 / 430           | 74.4 / 420       | 68.4 / 629    | 72.6 / 254       | **64.3**    | **422.1**   |\n\nThese new experimental results demonstrate the effectiveness and scalability of our approach:\n\n1.  **Comparable or Superior Reasoning Accuracy:** Compared to strong \"slow-thinking\" models like Vision-R1-32B and MM-Eureka-32B, FAST-32B achieves comparable or even better average accuracy across various reasoning and VQA benchmarks.\n2.  **Significant Efficiency Gains:** The average response length of FAST-32B (422.1 tokens) is nearly 40% shorter than that of Vision-R1-32B (710.6 tokens) and 22% shorter than that of MM-Eureka-32B (546.0 tokens), achieving a balance for both performance and efficiency.\n\n-----\n\n> **Q2: Improving the reliability of the difficulty estimation.**\n\nThank you for your question regarding the reliability of our difficulty estimation. Our difficulty estimation framework is composed of two complementary components to ensure its reliability:\n\n1.  **Extrinsic Difficulty:** This metric is derived from the model's performance (*pass@k* on a given problem). As this metric is derived directly from the model's actual performance, it accurately reflects the model's empirical problem-solving ability.\n2.  **Intrinsic Difficulty:** This metric captures the inherent visual complexity of an image using GLCM and ViT entropy. The reliability of our intrinsic metric is validated from two perspectives:\n      * The GLCM component is established to have strong human alignment ($SRCC=0.75, PLCC=0.77$)[2].\n      * As detailed in Section 5.4 Validation of Image Complexity, our human annotation study confirmed that our combined image complexity metric has a moderate and statistically significant correlation with human judgments ($SRCC=0.49, PLCC=0.50$).\n\nBy combining these two metrics, our approach provides a comprehensive and reliable estimation of problem difficulty.\n\n-----\n\n> **W2,Q3: Evaluation focues on math/diagram reasoning; Generalisation to open-domain VQA, captioning or dialogue is uncertain.**\n\nWhile our initial focus was on enhancing visual reasoning across math, science, VQA, and figure understanding, we agree that demonstrating broader generalization capability strengthens the value of our work.\n\nFirst, we would like to clarify that, as GRPO typically requires verifiable reward signals, our training dataset did not include open-domain VQA samples. Despite this, our method was evaluated on the MM-Vet benchmark, an open-domain VQA benchmark, where FAST-7B shows gains over the base model (71.2% vs. 67.1%).\n\nSecond, to address your concerns, we have conducted a comprehensive set of **experiments on 5 additional benchmarks**, which cover diverse tasks including open-domain VQA, hallucination analysis, low-level visual perception, and scientific reasoning. The additional benchmarks are:\n\n  * **Bingo Score [3]:** An open-domain VQA benchmark designed for holistic hallucination analysis.\n  * **MMHal Benchmark [4]:** An open domain VQA benchmark, evaluating both hallucination and informativeness to calculate an overall socre.\n  * **MMVP [5]:** A diagnostic benchmark that evaluates low-level visual perception capability of LVLMs.\n  * **MMEval-Pro [6]:** A comprehensive calibrated evaluation benchmark, adapted from sources including MathVista, MMMU, ScienceQA and manually crafted questions.\n  * **MM K12 [1]:** A Human-annotated multimodal scientific reasoning benchmark across math, physics, chemistry and biology.\n\nWe compare FAST-3B and FAST-7B against strong slow-thinking baselines, with the results below:\n\n| Model            | Bingo ↑ | MMHALU ↑ | MMVP ↑ | MMEval-Pro ↑ | MM K12 ↑ |\n|------------------|:-------:|:--------:|:------:|:------------:|:--------:|\n| Qwen2.5-VL-3B    |  3.64   |  3.33    |  36.0  |   67.8       |   —      |\n| LLM-R1-3B        |  3.58   |  2.78    |  28.7  |   66.9       |   —      |\n| Curr-REFT-3B     |  3.52   |  2.27    |  24.0  |   60.2       |   —      |\n| **FAST-3B**      |  **3.60**   |  **3.10**    |  **37.2**  |   **67.1**       |  **55.1**    |\n| Qwen2.5-VL-7B    |  3.70   |  3.50    |  47.3  |   76.0       |  53.6    |\n| Vision-R1-7B     |  3.62   |  3.10    |  44.0  |   72.2       |   —      |\n| R1-OneVision-7B  |  3.65   |  3.20    |  43.0  |   69.4       |  39.8    |\n| OpenVLThinker-7B |  3.45   |  3.00    |  46.5  |   71.5       |  60.6    |\n| MM-Eureka-7B     |  3.69   |  3.20    |  46.7  |   74.8       |  64.5    |\n| **FAST-7B**      |  **3.72**   |  **3.40**  |  **47.0**  |   **75.0**       |  **62.2**    |\n\nThese results on new benchmarks demonstrate that:\n\n1.  **Our method has strong generalization capabilities in scientific reasoning.** The performance of FAST on MM K12, which covers physics, chemistry, and biology, shows that our method generalizes well beyond math to other scientific domains, outperforming strong baselines.\n2.  **Our method outperforms slow-thinking LVLMs in open-domain VQA tasks.** On the hallucination benchmarks (Bingo Score and MMHALU), visual perception, and general VQA and benchmarks (MMVP and MMEval-Pro), slow-thinking LVLMs tend to significantly degrade, while our FAST models achieve higher scores. **This observation corroborates the findings of Liu et al. [7], who noted that lengthy reasoning chains in slow-thinking models can amplify visual hallucinations**.\n\n\n[1] Meng, Fanqing, et al. \"Mm-eureka: Exploring the frontiers of multimodal reasoning with rule-based reinforcement learning.\" arXiv:2503.\n\n[2] Zhang, Jinjin, et al. \"Diffusion-4k: Ultra-high-resolution image synthesis with latent diffusion models.\" CVPR. 2025.\n\n[3] Cui, Chenhang, et al. \"Holistic analysis of hallucination in gpt-4v (ision): Bias and interference challenges.\" arXiv preprint arXiv:2311.03287 (2023).\n\n[4] Sun, Zhiqing, et al. \"Aligning Large Multimodal Models with Factually Augmented RLHF.\" ACL. 2024.\n\n[5] Tong, Shengbang, et al. \"Eyes wide shut? exploring the visual shortcomings of multimodal llms.\" CVPR. 2024.\n\n[6] Huang, Jinsheng, et al. \"MMEVALPRO: Calibrating Multimodal Benchmarks Towards Trustworthy and Efficient Evaluation.\" NAACL, 2025\n\n[7] Liu, Chengzhi, et al. \"More Thinking, Less Seeing? Assessing Amplified Hallucination in Multimodal Reasoning Models.\" arXiv:2505."}]

Author rebuttal:

Meta-review: **Summary**

This paper introduces FAST-GRPO, a reinforcement learning (RL) framework built on GRPO to address the inefficiency of slow-thinking large vision-language models (LVLMs)—which generate verbose outputs across all tasks with marginal accuracy gains. The core design dynamically adapts reasoning depth via: (1) two complementary difficulty metrics (extrinsic, based on model pass@k performance; intrinsic, based on image complexity via GLCM and ViT entropy); (2) adaptive length-based rewards that encourage conciseness for easy questions and detail for hard ones; (3) difficulty-aware KL divergence to regulate policy updates; and (4) a "Slow-to-Fast" curriculum that prioritizes hard questions early and shifts to easy ones later. Initially evaluated on 7 reasoning benchmarks (mostly math-focused), the framework achieves ~10% relative accuracy improvement over base models and 32.7–67.3% token reduction vs. slow-thinking approaches. Post-rebuttal, the authors expanded evaluations to 5 additional benchmarks (e.g., MM-K12 for science reasoning, Bingo for open-domain VQA) and a 32B-parameter model, confirming broader generalizability and scalability.

**Strengths**

1. The work is the first to integrate difficulty-aware rewards, dynamic KL regularization, and a Slow-to-Fast sampler within GRPO for LVLMs, directly addressing a critical gap in adaptive reasoning, namely, balancing accuracy and efficiency. Reviewers noted this fills a key gap in LVLM reasoning literature.

2. Across initial and expanded benchmarks, FAST-GRPO consistently delivers double-digit accuracy gains (vs. base models) while drastically reducing token usage (22–40% fewer tokens vs. slow-thinking baselines like Vision-R1 and MM-Eureka). Ablation studies confirm the necessity of each component (e.g., difficulty metrics, adaptive rewards), reinforcing the framework’s robustness. The dual-metric (extrinsic-intrinsic) difficulty framework is well-validated: extrinsic metrics reflect empirical model performance (pass@k), while intrinsic metrics (GLCM/ViT entropy) align with human judgments (SRCC=0.49, PLCC=0.50). This ensures reliable guidance for fast/slow thinking toggling.

3. Post-rebuttal experiments address early narrow-task limitations, showing effectiveness across science domains (physics, chemistry, biology via MM-K12) and open-domain VQA (Bingo). A 32B-parameter variant of FAST-GRPO matches or outperforms strong baselines (e.g., MM-Eureka-32B) with shorter responses, demonstrating scalability beyond 7B models.

**Weaknesses**

1. Initial Narrow Evaluation Scope. The original submission focused 6/7 benchmarks on math reasoning, raising concerns about generalizability to non-math domains. While resolved via post-rebuttal experiments (e.g., MM-K12, Bingo), the initial design prioritized math, limiting early insight into cross-domain applicability.

2. Despite adding a 32B model, the framework’s performance on ≥70B-parameter LVLMs remains untested. The authors acknowledge this as a limitation, and it persists as a minor gap for real-world deployment in largest-scale systems.

3. The original Slow-to-Fast curriculum used a binary epoch split. Post-rebuttal continuous curriculum experiments showed marginal accuracy gains but longer token usage, with authors noting suboptimal hyperparameters (e.g., insufficient \(P_{max}\) for easy questions). Further refinement of curriculum scheduling could enhance efficiency.

4. The initial submission lacked systematic error breakdown and comparative case studies. While authors added detailed failure mode analysis (e.g., visual perception vs. reasoning errors) and side-by-side model comparisons post-rebuttal, one reviewer noted residual gaps in qualitative insights (e.g., more diverse task-specific examples).

**Discussions during Rebuttal Period**

During rebuttal, reviewers raised four critical concerns, all addressed by the authors with concrete experiments and analysis.

1. Generalizability to non-math domains. A reviewer noted 6/7 initial benchmarks focused on math. Authors responded by adding 5 benchmarks (MM-K12 for science, Bingo for open VQA, MMHal for hallucination analysis) and showed FAST-GRPO outperforms baselines in physics (+8.4% vs. base), chemistry (+7.0%), and biology (+8.8%), confirming cross-domain applicability. This was weighted heavily as it resolved a key limitation of the initial submission.

2. Model scale limitations (7B Only), Reviewers asked for larger model testing. Authors trained FAST-GRPO on a 32B model (Qwen-2.5-VL-32B) and showed it matches MM-Eureka-32B’s accuracy with 22% fewer tokens. This addressed scalability concerns, though ultra-large models (≥70B) remain untested—a minor gap outweighed by 32B results.

3. Method details (Complexity Score, Curriculum, Qualitative Analysis) are unclear. A reviewer questioned the multiplicative complexity score (theoretical edge case) and binary curriculum. Authors showed: (a) The reward design avoids conflicting signals (zero penalty for incorrect hard/easy questions), and weighted sum formulations yield identical results; (b) Continuous curriculum improves accuracy but increases tokens (attributed to hyperparameter tuning); (c) Expanded qualitative analysis (error breakdown, 3 failure modes, side-by-side model comparisons) filled initial gaps. These clarifications resolved technical doubts.

4. Dataset filtering clarity. A reviewer asked for details on reducing 500K to 18K questions. Authors explained the process (deduplication, benchmark overlap removal, closed-form question standardization, pass@8 filtering for extreme difficulty), addressing transparency concerns.

Overall, most reviewers (high confidence, e.g., A2xT, jkkr) confirmed their concerns were resolved. The authors’ proactive addition of experiments and technical clarifications demonstrated commitment to strengthening the work.

**Decision Justification**

The paper’s core claim is that adaptive reasoning depth guided by question difficulty, which enables LVLMs to balance accuracy and efficiency. Key findings include: (1) Extrinsic and intrinsic difficulty metrics reliably categorize question complexity; (2) Adaptive rewards and dynamic KL divergence reduce overthinking (verbose outputs) for easy questions and enhance depth for hard ones; (3) FAST-GRPO outperforms base GRPO and slow-thinking baselines across math, science, and open-domain VQA; (4) Scalability to 32B models confirms the framework’s applicability beyond small LVLMs.

The paper provides novel solution to a high-impact problem in LVLM reasoning: inefficient, one-size-fits-all reasoning. Unlike prior work that prioritizes either accuracy (slow-thinking) or efficiency (fast-thinking), FAST-GRPO provides a principled, RL-based method to unify both, addressing a practical pain point for deploying LVLMs in token-constrained environments (e.g., edge devices, real-time applications). Post-rebuttal experiments (new benchmarks, 32B model) strengthen the validity of its claims, while ablation studies and difficulty metric validation ensure technical rigor. Despite untested ultra-large model scalability and residual qualitative gaps, this paper  makes a valuable contribution to LVLM RL and adaptive reasoning.
Decision: Accept (spotlight)