Chart Deep Research in LVLMs via Parallel Relative Policy Optimization
Authors: Jiajin Tang
Gaoyang
Wenjie Wang
Sibei Yang
Xing Chen
Venue: ICLR 2026 Poster (2026)
Keywords: Large Vision Language Model
Multimodal Deep Research
Chart Understanding
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: With the rapid advancement of data science, charts have evolved from simple numerical presentation tools to essential instruments for insight discovery and decision-making support. However, current chart data intelligence exhibits significant limitations in deep research capabilities, with existing methods predominantly addressing shallow tasks such as visual recognition or factual question-answering, rather than the complex reasoning and high-level data analysis that deep research requires. This limitation stems from two primary technical bottlenecks: at the training level, existing post-training techniques exhibit deficiencies in handling multi-dimensional reward signal interference and heterogeneous data gradient conflicts, preventing models from achieving balanced development across multiple capability dimensions; at the evaluation level, current methods remain limited to factual retrieval and basic computation, failing to assess end-to-end analytic reasoning and other deep research capabilities. To address the training challenge, we propose PRPO, which performs parallel optimization across reward dimensions and capability partitioning across data types, effectively disentangling conflicts between heterogeneous data and multi-dimensional reward signals while ensuring optimization stability. For the evaluation challenge, we construct MCDR-Bench based on the ``error uniqueness principle," transforming subjective generation assessment into objective error identification through controllable error injection, enabling quantifiable evaluation of deep research capabilities. Experimental validation confirms that the proposed PRPO and MCDR-Bench jointly establish a unified framework that systematically advances chart deep research through enhanced collaborative training and objective evaluation.

Published as a conference paper at ICLR 2026
CHART DEEP RESEARCH IN LVLMS VIA PARALLEL RELATIVE POLICY OPTIMIZATION
Jiajin Tang Gaoyang'; Wenjie Wang", Sibei Yang" Xing Chen',
"ByteDance, "ShanghaiTech University, Sccoool of Computer Science and Engineering, Sun Yat-sen University
ABSTRACT
With the rapid advancement of data science, charts have evolved from simple numerical presentation tools to essential instruments for insight discovery and decision-making support. However, current chart data intelligence exhibits sig- nificant limitations in deep research capabilities, with existing methods predom- inantly addressing shallow tasks such as visual recognition or factual question- answering, rather than the complex reasoning and high-level data analysis that deep research requires. This limitation stems from two primary technical bot- tlenecks: at the training level, existing post-training techniques exhibit deficien- cies in handling multi-dimensional reward signal interference and heterogencous data gradient confficts, preventing models from achieving balanced development across multiple capability dimensions; at the evaluation level, current methods remain limited to factual retrieval and basic computation, failing to assess end-to- end analytic reasoning and other deep research capabilities. To address the train- ing challenge, we propose PRPO, which performs parallel optimization across reward dimensions and capability partitioning across data types, effectively dis- entangling conflicts between heterogeneous data and diltiidimeniional reward signals while ensuring optimization stability. For the evaluation challenge, we construct
based on the "error uniqueness principle," transforming subjective generation assessment into objective error identification through con- trollable error injection, enabling quantifiable evaluation of deep research capa- bilities. Experimental validation confirms that the proposed PRPO and MCDR- Bench jointly establish a unified framework that systematically advances chart deep research through enhanced collaborative training and objective evaluation.
INTRODUCTION
Data-driven technologies and multimodal large models have elevated charts from simple "numerical presentations" to essential tools for discovery and decision -making (Kim et al., 2020; Masry et al., 2024; Hoque et al., 2022). The progress of multimodal large language models (MLLMs) (Bai al., 2025; Achiam et al., 2023; Comanici et al., 2025; Anthropic, 2025b; Grattafiori et al., 2024) has transformed charts into core analytical instruments for pattern discovery, hypothesis testing, and strategic decision support across finance, healthcare, business, and scientific domains (Lee et al., 2025; Shwartz-Ziv & Armon, 2022; Shigarov, 2023).
However, advancing chart deep research the the ability to conduct sophisticated analyt- ical reasoning, pattern synthesis, and strategic insights from visual data-remains fundamental challenge in current AI systems. While charts have evolved into sophisticated analytical instru- ments, existing methods predominantly address shallow tasks such as visual recognition or factual question-answeriing (Masry al., 2022; Wang et al., 2024; Xu et al., 2023), falling short of the complex reasoning and high-level analytical processes that define genuine deep research capabili- ties (Masry et al., 2025; Lin et al., 2025; Mathew al., 2022).
*Work done during an intersship at ByteDance.
I Project lead.
I "oorrsppnniigg author is Sibei Yang.

---

Published as a conference paper at ICLR 2026
GRPO; Grouping with Signal Interference
PRPO: Parallel Policy Optimization
Unpected Optimaation Fath
Eapecied Optimiation Path Beward PSP0 Triectocy
GSPO Ingectocy
Limited Explocation
Near-Optimal Performance
Start
Start
Tugget Bnd
Targei
Bod
Optimization
Optimization
Signal Interfereace
Parallel Advantaggs
Steps
Steps
Subdimetion Subdiraction
GIIN Optimization Demccion
Reward-FRPO Optimizadion Direction
Optimization trajectories of GRPO vs. PRPO. Left: under multi-dimensional rewards, GRPO suffers from signal interference and limited exploration. Right: PRPO decomposes opti- mization across reward dimensions and data types, reducing interference and enabling specialized learning, which yields more effective exploration and near-optimal performance.
Figure 1:
The development of chart deep research capabiliites is systematically constrained by two fundamen- tal bottlenecks. At the training level, existing post-training techniques exhibit deficiencies han- dling the multi-dimensional reward conflicts and heterogeneous data challenges inherent in develop- ing complex analytical reasoning abilities. At the evaluation level, current assessment frameworks remain misaligned with deep research demands, lacking methodologies to evaluate the end-to-end analytic reasoning that defines advanced chart analysis capabilities.
Developing robust chart deep research pabilities requires sophisticated training methodologies that can handle complex multi culli-dimennsonall learning. Chart deep research encompasses diverse analytical tasks such background knowl- edge integration, fact extraction, relationship construction, deep report reasoning, and strategic crrcasting-ccpaaillttie that demand coordinated development across multiple cognitive dimen- sions. However, as illustrated in Figure 1, existing preference-optimization opttmizzaiiiiniiinnnnnni methods such as Group Relative Policy Optimization (GRPO) (Shao et al., 2024) exhibit conftict-oonsrraieed optimization dynamics that hinder the development of these integrated capabilities. We observe two core limita- tions that specifically impede deep research capability development: (1) Multi-dimeensonal reward interference-aggreaaiie aggregating heterogeneous signals leads to mutual cancellation of advantages and in- hibits the exploration necessary for complex reasoning development; (2) Data joint optimization conflicts gradients from different analytical dimensions may dominate cancel each other, pre- venting the balanced capability development essential for deep research competency.
Training Bottleneck for Deep Research Capabilities.
Evaluation Bottleneck for Deep Research Capabilities. Assessing chart deep research capabilities presents unique challenges that existing evaluation frameworks fail to address. Current benchmarks remain focused on surface-level tasks such factual question answering or basic numerical oper- ations (Masry et al., 2022; Wang et al., 2024; Xu et al., 2023; Masry et al., 2025; Lin et al., 2025; Mathew et al., 2022), failing evaluate the end-to-end analytic reasoning. synthesis, and strate- gic insight generation that characterize advanced deep research capabilities. This evaluation gap- a critical barrier to
stemming from high annotation costs and subjective answer diversity- systematically advancing and measuring progress in chart deep research.
To systematically advance chart deep research capabilities, we propose a unified framework ad- dressing both training and evaluation bottlenecks. For training, we introduce Parallel Relative Policy Optimization (PRPO), which enables the coordinated development of analytical capabilities by performing parallel optimization across reward dimensions and capabil- ity partitioning across data types. For evaluation, we construct MCDR-Bench based on the error uniqueness principle, transforming subjective deep rescarch assessment into objective error identi- fication, enabling systematic measurement of analytical reasoning capabilities.
Overall Contributions. (1) We systematically analyze the bottlenecks constraining chart deep research capability development, identifying training challenges from multi-dimensional opti- mization conflicts and evaluation challenges from subjective assessment complexity. (2) We propose PRPO, enabling coordinated development of complex analytical capabilities through parallel opti- mization that mitigates reward interference in multi-dimensional training. (3) We present MCDR-
2

---

Published as a conference paper at ICLR 2026
Bench, providing systematic evaluation of chart deep research capabilities through objective error identification methodology. (4) Together, our unified framework establishes a systematic path- way for ad advancing chart deep research capabilities, addressing both capability development and assessment challenges.
2 RELATED WORK
Chart understanding benchmarks have progressed from simple data extraction to advanced rea- soning. Early benchmarks like PlotQA (Methani et al., 2020) and ChartQA (Masry et al., 2022) focused on factual question-answering and multi-step reasoning. Later work expanded to diverse visual representations through infographic integration (Mathew et al., 2022) and automatic chart summarization (Kantharaj et al., 2022; Tang et al., 2023). State-of-the-ne benchmarks, including ChartBench (Xu et al., 2023), ChartQAro (Masry et al., 2025), and InfoChartQA (Lin al., 2025), improve evaluation quality by introducing diverse question types and reducing annotation bias. Nev- ertheless, most benchmarks remain limited basic QA tasks, lacking evaluation of professional analyst capabilities such as deep insights, causal reasoning, and strategic decision massiion-maiin----0 gaps that motivate our proposed deep research paradigm. Table understanding has followed similar trajectory through multimodal frameworks (Zheng et al., 2024; Mathur et al., 2024; Titiya et al., 2025).
Chart understanding algorithms have evolved from visual alignment to specialized reasoning. Early work explored multimodal adaptation via domain-specife training (Han et al., 2023) and multi-task pattern recognition (Wei et al., 2024), while practical deployment drove efficiency opti- mization with techniques like visual token merging (Zhang et al., 2024a) and mixture-of- chitectures (Xu et al., 2024). Recent methods target complex reasoning through human-like sketch- ing (Huang et al., 2025) and structured chart representations for long-chain reasoning (Jia et al., 2025). Existing algorithms, however, largely focus recognition and QA, leaving systematic mod- eling of professional analyst skills unaddressed.
ar-
RLHF algorithms have advanced from basic alignment to efficient optimization of language models using human feedback. PPO (Ouyang et al., 2022) stabilizes policy updates, while DPO (Rafailov al., 2023) improves efficiency by avoiding explicit partition function computation. Later methods enhance training stability and sample efficiency: GRPO (Shao et al., 2024) removes independent value model training, entropy collapse is addressed by DAPO (Yu al., 2025), replay mechanisms improve sample utilization (Li et al., 2025), and self-explanatory sample generation tackles low success rate scenarios (Zhou al., 2025). Most recently, GSPO (Zheng et al., 2025) introduces sequence-level importance ratios with clipping and reward assignment, improving stability, effi- ciency, and performance for Mixture-of- -fpexetsss models.
While benchmarks and algorithms have become increasingly sophisticated, they still primarily target factual QA and basic chart recognition. Our paradigm innovates by systematically modeling profes- sional analyst capabilities, enabling deep insights, causal reasoning, and strategic decision- decision-making.
3 MCDR-BENCH
Chart Collection. Addressing the core problem of "high chart complexity but shallow understand- ing depth" identified in the Introduction, MCDR-Bench focuses on collecting complex charts pable of supporting deep research during the image collection phase. We carefully curate chart data from professional platforms including Dashboard Design Patterns (Bach et al., 2022), MME- realworld (Zhang et al., 2024b), ChartQAPRO (Masry et al., 2025) and Pew Research (Krogstad al., 2016). To ensure data quality meets the requirements for deep research evaluation, we em- ploy two key filtering criteria: first, we filter out overly simple charts (such as basic bar charts or pie charts with single data series) as these charts cannot demonstrate the true value of charts as "advanced analytical tools"; second, we prioritize complex charts containing multi-element, multi- layered information to ensure they possess the data richness necessary to support deep research tasks. We ultimately selected 1,021 high-quality charts that not only meet the complexity requirements of the visualization layer in form but also possess the intrinsic value to support deep understanding and analysis.
3

---

Published as a conference paper at ICLR 2026
Preparation: Chart Image Selection
Human Filerin
Stage Background Acquisition
Stage Fact Extraction
Recognthon
Query
Search
This dosbboard presens corpeceessive
Plyskal stares occonsr for the rejiiity of sales (14 tofus and (822))
satil or commmmr elecmeeies beenee, Hody diccesioon: siles clannnds priduct caogaciess posgnattic
The dan
(5255 5550, thes dedfise stealily lon in Oztober (5U1) H9M0
Stago S: Forccast/Plan
Human Piitering
Stage 4: Deep Research Report
Stage 3: Relationship Construction
TF
Deep
Research
Plan
Topology
Logic
lovrng
araletes and nail time das will cxtcerorm perrs alaring
pofiabilit, with srreghoold is North Amarica snd prodact portfilio by high-alee eletrokks. Howeser shom eignificmt concomaatio googinply and product mis, opportanilis....
2. Pooted Coleggay 5 Chur Syvery
udeninan akysical
A. Pommddre Proilab
proferecces Straegi Plass *fBoest in Advascad Analysice** Thate capoiiitins poolectiv modldingg coloeer segrestation....
Trends
6. Sass Farorranno congunoly
Figure 2: Multi aaetii-geetten annotation process for multimodal chart deep research. The process consists of five stages: (1) Background Acquisition: retrieving domain-specifir knowledge; (2) Fact Ex- traction:
extracting atomic data elements; (3) Relationship Construction: modeling topological and logical connections; (4) Deep Research Report Generation: synthesizing comprehensive re- ports; (5) Forecast/Plan: proposing strategic recommendations. Human filtering ensures quality control throughout the process. The five specialized expert agents are represented by
Our annotation framework employs two-phase design systematically evaluate chart analysis capabilities. Phase generates high-quality deep research reports, while Phase converts sub- jective generation into objective error identification through systematic error injection.
Phase 1: Report Generation. As shown in Figure 2, the generation process follows five intercon- nected stages: (i) Background Acquisition retrieves domain-specifie context enrich chart inter- pretation; (ii) Fact Extraction parses atomic data elements such as values and temporal sequences; (ii) Relationship Construction models intra- and inter-chart dependencies; (iv) Deep Research Re- port synthesizes trends, anomalies, and patterns into coherent analysis; and (v))orecast/Plan derives forward- looking recommendations for decision support. Human review is specifically implemented at the critical report generation and decision decision-making stages, where human experts validate analytical accuracy and strategic soundness.
Phase 2: Error Injection. This phase transforms subjective report generation into objective ror identification by introducing targeted perturbations corresponding to the five capabilities from Phase 1 (knowledge, facts, relationships, reporting, and forecasting). The process yields 3,084 high-difficulty samples with complex charts, enabling robust and fine- -raingraind capability assessment. Complete construction details appear in Appendix E.
Evaluation Paradigm. MCDR-Berr Bench delivers both a comprehensive dataset and an objective eval- uation framework. Through controlled error identification, it enables fine-grained diagnosis of mod- els' analytic strengths and weaknesses across multiple dimensions. Training Implications. How- ever, robust evaluation alone cannot address the fundamental methodological challenges this bench- mark reveals. Cultivating genuine deep research capability requires rethinking training paradigms reconcile heterogeneous objectives, conflicting reward signals, and multi-dimensional learning requirements.
PARALLEL RELATIVE POLICY OPTIMIZATION
4.1 PRELIMINARY
GRPO is a reinforcement learning algorithm designed to optimize large language models (LLMs) by leveraging group-based relative advantages. For each question g. GRPO samples group of
4

---

Published as a conference paper at ICLR 2026
outputs {or from the old policy Told. where P(Q) denotes the distribution over questions and |o:] represents the length of the i-th output sequence. The optimization process combines the probability ratio between the current and old policies with group-based relative advantages. Specifically, the probability ratio (f) quantifies how the current policy wo assigns probability to each token oz, (the 1-th token in the i-th sequence) compared to the old policy, while the advantage A; is computed by normalizing the group-level rewards { [R: [= as follows:
R R
(0,(0) To(or, 9: 0i,ct)
(I)
Told Tola 0zi, 41, 0i,ct)
where R² is the reward assigned to the i-th response, R à Eド=1 R2 is the group mean reward,
and o - Ei Ej= R) is the group standard deviation. This normalization ensures that the advantage calculated relative the group baseline with unit variance, while accounting for the variability within the group. GRPO optimizes the policy model मa by maximizing the following clipped objective, together with KL penalty term:
00.1 Lapp (rap(rr,, (0),
1
1
JGRPO (0) E P(Q.
G
where Leip(r, A) = min (r- A, clip(r,1-ppppppe c,,,++)) A), and is the clipping hyperparameter that constrains the ratio r to ensure stable updates. For notational simplicity, we omit the KL divergence penalty term in this and subsequent formulations.
Achieving strong deep research capability requires models to master multiple complex dimensions simultaneously, including visual recognition, logical consistency, and numerical reasoning. How- ever, this molti-diimnnional nature introduces significant optimization challenges.
First, multi-dimensional reward interference arises when heterogeneous signals are aggregated. Ex- isting methods such as GRPO collapse all reward dimensions into a single scalar, which compresses variability, weakens optimization signals, and diminishes the discriminative power of advantage esti- mation. contrast, our proposed PRPO preserves reward information by processing each dimension independently. thereby retaining signal integrity and enabling stronger optimization guidance (More details please refer to Fiture 4 in Appendx A).
Second, data joint optimization conflicts occur because gradients from heterogeneous tasks interact unevenly: high-magnitude signals from simple tasks dominate training, while weaker but more informative signals from complex tasks are suppressed. This imbalance skews optimization toward certain data types, preventing models from fully leveraging data diversity and realizing balanced capability growth. A detailed visualization comparing GRPO and PRPO, together with extended quantitative analysis, is provided in Appendix C.
4.2 REWARD PARALLEL RELATIVE POLICY OPTIMIZATION
To address the limitations of GRPO in handling multi-diieesional rewards, we propose Reward- PRPO to decomposes the optimization process across different reward dimensions. Rather than aggregating multiple reward signals into a single scalar value, Reward-PRPO treats each reward dimension as an independent optimization objective. This enables the model to learn specialized capabilities while maintaining overall coherence. Specifically, for a given question y and a group of generated outputs {o let [R{ ( i-th response, Reward-PRPO computes dimension speciffc advantages for each reward component:
k= denote the rewards across K different dimensions for the
R
R(0))
A
As == 1,2......4
(k)
where (k) and (A) are the mean and standard deviation for the k-th reward dimension, respectively. This decomposition preserves the distinct optimization signals from each dimension, preventing the signal interference effects that occur in aggregated reward schemes. The Reward- PRPPO objective function is formulated as weighted combination of dimension-specifie policy gradient losses:
5

---

Published as a conference paper at ICLR 2026
GRPO
KL
Reference
Reward |
Scalar Aa desintioon
A
Trained
Aq
Models
Reward 2
Policy Model
Frosen Models
22
aa
Reward K
FC
A
PRPO
Reference Model
Reward
A
4
Reward Parallel
Reward ..* Reward
A
A
Policy Model
A
A2
A
sample from
1 (m0)
{a.... ""
same partition
Partition
Parullel
Reward Parallel
Data
Data
(g' (') Q
M
Im,. (ma3) 0
A.
G
Figure 3: Demonstration of GRPO and our PRPO. PRPO unifies Reward-PRPO and Data-PRPO, partitioning data into capability- groups and decomposing rewards across dimensions. This approach addresses malli-dimensionll reward conflicts and data optimization conflicts, enabling balanced training across complex tasks.
K
04 Leti
JReward-PRPO (0)
(ranprr,, (Te, (r),
(4)
G
0
k=1
where A 2 O with Σx A represents the weight assigned to the k-th reward dimension, and (0) (0) the probability ratio as defined in GRPO. Note that we omit the KI. term here, which follows the same implementation GRPO.
4.3 DATA PARALLEL RELATIVE POLICY OPTIMIZATION
The original GRPO performs grouping at the rollout level within individual samples, where each question y generates group of outputs {or from the old policy Told with unique rollout iden- tifiers rollout.uid,. While this intra-question grouping effectively normalizes rewards relative to multiple attempts at the same task, it fundamentally fails to address optimization conflicts arising from heterogeneous data types with distinct reward characteristics.
To address this fundamental limitation, we propose Data-PRPO, which extends GRPO's rollout- level grouping mechanism capability- partitioning across heterogeneous data types. The core innovation lies in introducing capability-based level identifiers capability _uid that partition training samples according to their underlying cognitive requirements, such as visual understand- ing, logical reasoning, and data analysis. Unlike GRPO's fine- iieegrained rollout_uid uid that distinguishes individual responses within the same question, capability_uie enables coarse- coarse-grained categorization based capability dimensions, creating adaptive sub-distributions (P(Q(m))) JM with homoge- neous reward patterns. Within each capability partition, Data-PRPO computes standardized advantages using partition-specific statistics:
R² R(m)
A(m))
(5)
(m)
where R(m) and (m) represent the empirical mean and standard deviation of rewards within ca- pability partition m. However, this capability-based partitioning faces a critical challenge: samples with extreme advantage values can dominate gradient updates and destabilize optimization. These outliers often indicate incompatibility with their assigned capability partition's 's reward distribution, suggesting that the initial capability- based assignment may not be optimal for all samples. To ad- dress this challenge, PRPa iteratively validates samples to ensure they fall within acceptable confidence bounds:

---

Published as a conference paper at ICLR 2026
0 = {i: 1
(6)
where 7 defines the confidence threshold for acceptable advantage values within a partition. When samples exceed this threshold, the algorithm implements fallback mechanism that relegates these outlier samples to individual rollout-level optimization:
rollout_uid; if f
partition(i, t
partitionni,t) otherwise.
This relegation mechanism ensures that outlier samples are optimized individually, preventing them from distorting the reward statistics of their capability partitions while preserving partition-based optimization benefits for samples that fit well within their assigned capability partitions. The itera- tive validation process terminates when no outliers are found (Oi)) = 0) or the maximum iteration
limit is reached, yielding the final validated partition {9m Mari
m==1
Upon establishing the validated data partition, Data-PRPO computes the GRPO objective function as a weighted aggregation across homogeneous partitions:
Muni
lod Leti((rs,e (r),e(0), A A(m))
Datu-PRrO
Σ m=1
Am Eg PiQ(m)) ma((119))
19ml
Los
icf
where Am 2 0 with EM Am 1 and A(T)) represents the advantage computed within partition In using partition-specitue statistics. Through this sapability-basee partitioning and iterative valida- tion framework, Data-PRPO successfully resolves optimization conflicts multi-type data training, enabling balanced development across different capability dimensions.
4.4 PARALLEL RELATIVE POLICY OPTIMIZATION
Building upon Reward-PRPO and Data-PRPO, we present Overall PRPO that unifies both ap- proaches to simultaneously address multi-dimensional reward conflicts and data joint optimization conflicts.
PRPO first partitions training samples into capability based groups using Data-PRPO, then decom- poses rewards across multiple dimensions within each partition following Reward-PRPO. For sam- ples in capability partition and reward dimension k the advantage is computed as:
(()) R(km))
(k.m
(k)m)
where (kkmm) and (k,m)) are the mean and standard deviation for the k-th reward dimension within capability partition m. The unified objective function combines both parallelization strategies:
Misi
K
lou
(rip ((r,,((),, A (him))
JJRPO
Am
|m
0
m===
(10)
This comprehensive framework effectively prevents signal interference between reward dimensions while mitigating optimization conflicts from heterogeneous data types, enabling balanced capability development across complex multi-task scenarios.
5 EXPERIMENTS
5.1 SETTINGS
-CDhh Evaluation. We compare against both commercial and open-source models to demonstrate the effectiveness of our approach. For commercial models, we test GPT-4o (Hurst al., 2024), GPT-4.1 (OpenAI, 2025), Claude-3.7 Sonnet(Anthropic, 2025b), and Gemini-2.5- Pro(Comantes et al., 2025) using their respective APIs. For open-source models, we evaluate CharGGemma33B(Mary al., 2024), -1-n.55-VL-----nstueeee et al., 2025), ChartInstruct-
7

---

Published as a conference paper at ICLR 2026
Table Performance comparison on MCDR-Bente across different splits. We evaluate both GRPO and our PRPO under two prompt settings: direct answer generation and chain-of-thouge reasoning (Think). The Think setting encourages models to provide sep-bb--tter reasoning before generating final answers, which is particularly important for complex chart analysis tasks.
Model
BG
FE
RL
DR
F/P
Overall
Mean
GPT-4o
27.17
21.89
41.01
47.45
60.00
35.83
38.89
GPT-4.1
34.68
19.50
72.25
77.11
79.22
50.87
55.61
Claude-3.7 Sonnet
68.78
57.27
89,45
85.02
86.97
74.96
77.08
Gemini-2.5-PP
81.21
87.31
91.44
93.78
92.98
89.29
89.34
CharGemma-33
7.53
5,02
7.51
9.25
14.29
8.14
8,29
Qwen2.5-VVL33--Innsee Insttructt
1.88
0,81
3,06
10.83
12.58
4.96
5.69
Mhartinstruc-LLLamaa
3.38
5.84
6.69
5.54
5,09
5.24
LLaVA-Next-7B
10.73
7.81
23.08
20.66
27.29
16.96
17.76
Intern VL2.5-BB
21.09
20.77
37.27
32.67
47.12
30.64
31.59
Llama-3 1..-111--Viiiii
28.06
33.02
36.02
36.41
39.44
34.40
34.56
Bwenn255vL-7B--nstreee
23.35
39.43
51.04
37.59
45.63
40.01
39.51
w/ GRPO
41.24
51.69
75.38
66.14
77.40
61.71
62.26
w/ PRPO
50.65
61.38
81.78
72.83
84.01
69.62
69.90
+9.41
+9.69
+6.40
+6.69
+6.61
+7.91
+7.64
GRPO Think
43.13
48.77
77.75
70.28
81.02
63.00
63.99
PRPO Think
62.90
65.23
88.87
80.91
87.21
76.26
76.89
+19.77
+16.46
+11.12
+ -0.63
+6.19
+1.26
+12.90
Table 2: Performance comparison on ChartQAPRO across different splits.
Model
Factoid
MCQ
Conv.
FactChk
Hypo.
Overall
Mean
GPT-4o
35.76
46.72
34.75
45.49
28.91
37.67
38.33
Claude-3.5 Sonnet
51.40
44.53
55.60
45.48
43.58
46.57
Gemini-Flan Flash--.0
43.43
60.28
40.25
67.62
24.47
46.85
47.15
ChartGemma-3B
6.86
0.0
16.00
1.22
6.53
6.84
6.12
TinyChart-3B
8.52
7.00
17.46
33.19
16.06
13.25
16.45
ChartInstruct-LLammaa
7.09
0.0
3.77
0.0
6.91
4.88
3.55
LLaVA-Next-7B
15.35
35.98
21.09
41.80
17.79
21.97
25.83
InternVL2.55853
35.21
25.70
32.26
$3.27
29.61
35.67
35,29
Llama 3.-11 Visioo
12.34
2.33
0.19
27.18
10.93
11.09
10.68
Qwen2.5-VL-77-Insse
27.49
37.85
55,22
46.72
44.40
36.31
41.33
w/ ChartReasoner-SFT
37.94
w/ Caar
39.97
w/ PRPO
36,24
50.47
49,65
53.28
53.69
42.95
47.69
+8.75
+ +12.62
-5.59
+6.56
+9.29
+6.64
+6.36
LLama2-7B(Han et al., 2023), LLaVA-Next-7B (Liu et al., 2024), VnternV....58BBCC
et al., 2024), and 1-aaa-3.2-1BB- 1---ma-----1B-isiiooooe Vision(Grattafion et al., 2024). We maintain consistency with the de- fault hyperparameters and prompt methods provided by each model. To demonstrate the effective- ness of our PRPO, specifically fine-tune Ween2.5-vL-7B-Imme
using different optimization
strategies: baseline GRPO and our proposed PRPO.
ChartQAPRO Evaluation. We further validate approach ChartQAPRO(Massy al., 2025), a specialized benchmark for chart question answering. The model list includes commer- cial models GPT-4o(Hurst et al., 2024), Claude-3.5 AnthrooAn 2025a), and Gemini-Flash- 2.0(Comanici et al., 2025), as well as open-source models ChanGemma-33. TinyChart-3B(haal al., 2024a). ChartInstruct-LLamm22
LLaVA-Next-7BB Intem Llama-3.2-1111 Vision
and ChartReasoner (Jia et al., 2025).
5.2 MCDR-BENCH RESULTS
Table presents comprehensive evaluation results MCDR-Benn across five capability dimen- sions: Background knowledge (BG), Relationship construction (RL), Factual information extraction (FF), Deep Research Report (DR), and Forecast/Plan (F/P). These dimensions correspond to the five
8

---

Published as a conference paper at ICLR 2026
Table 3: Ablation results of differ-
Table 4: Reward Ablation Results on geometry3k.
ent algorithms on MCDR-Benche
Method
Accuracy (%)
Response Length +
Method
Performance (%)
Format Reward
36.17
328
Baseline
40.01
Accuracy Reward
44.46
350
GRPO
61.71
Accuracy Format
43.74
274
Reward-PRPO
64.30
Format -> Accuracy
44.79
303
Data-PRPO
63.55
GRPO
42.02
356
PRPO
69.62
PRPO
48.75
319
stages of our PRPO framework, where we systematically inject targeted errors to transform subjec- tive generation tasks into objective error detection tasks.
Closed-Souree Models. Among commercial models, Gemini-2.5-Pro achieves the strongest per- formance with an 89.34% mean score, particularly excelling in relationship construction at 91.44% and deep research 93.78%. Claude-3.7 follows with 77.08% mean performance, while significant gaps exist with GPT-4. at 55.61 % and GPT-4o at 38.89%.
Open-Source Models. Open-source models generally underperform their commercial counterparts. Llama-3.2-1 1B-Vision Vision achieves the highest mean score of 34.56% followed by Intern VI.2.5-8B at 31.59%. Smaller models such as ChartGemma-33 at 8.29% and struggle across all dimensions, highlighting the critical importance of model scale for complex chart reasoning tasks.
--nt---sttt 5.69%
PRPO Effectiveness. Our PRPO algorithm demonstrates substantial improvements over the base- line GRPO approach. For direct answer generation, PRPO achieves 69. 69.90% mean performance ver- sus GRPO's 62.26%, representing a 7.64% improvement, with notable gains in background knowl- edge of 9.41 % and factual extraction of 9 9.69%. The improvement becomes more pronounced in the Think setting, where PRPO reaches 76.89% versus GRPO's 63.99%, achieving 12.90% improve- ment, with background knowledge showing the largest gain of 19.77%. This demonstrates PRPO's effectiveness in optimizing complex reasoning tasks that require coordinated multi-dimensional ca- pabilities. Notably, PRPO with the Think setting at 76.89% approaches Claude-3.1 3.7's performance at 77.08%, effectively bridging the gap between open-source and commercial models through rein- forcement learning optimization.
5.3 CHARTQAPRO RESULTS
Table presents evaluation results on ChartQAPRO (Masry et al., 2025), an external benchmark for chart question answering across five task types: Factoid questions, Multiple Choice Questions (MCQ), Conversational reasoning (Conv.), Fact Checking (FactChk), and Hypothetical scenarios (Hypo.). This evaluation demonstrates the generalizability of our PRPO algorithm beyond our pro- posed MCDR Bench.
Baseline Models. Among closed-source models, Gemini-Flash- achieves the best performance with 47.15% mean score, followed by Claude-3.5 Sonnet at 46.57% and GPT-4o at 38.33%. Open- source models generally underperform, with Intern VL2.5-8B leading at 35.29% and the baseline Qwen2.5-VL-7B. - achieving 41.33% mean performance.
Generalization. Our PRPO algorithm demonstrates consistent effectiveness on this external bench- mark, achieving 47.69% mean performance compared to the baseline's 41.33%, representing 6.36% improvement. The improvement particularly notable MCQ with a 12.62% gain and hypothetical scenarios with 9.29% gain, suggesting that PRPO's parallel optimization strategy effectively handles diverse reasoning requirements across different task types. These results, consis- tent with MCDR-Benn findings, validate both the feasibility of our objective error discrimination evaluation paradigm which transforms difficult-to-assess open generation tasks into approximately objective assessments with unique answers- and the effectiveness of our PRPO algorithm through controlled comparisons and superior performance relative to contemporary work.
5.4 ABLATION STUDY

---

Published as a conference paper at ICLR 2026
Table 5: Data Ablation Results.
We conduct comprehensive ablation experiments to demonstrate the effectiveness our proposed algorithm.
Data
Score
Levell
34.89
Overall. Table 3 presents the ablation results for the components of our PRPO. The improvement from the baseline model's 40.01% % GRPO's 61.71% validates the fundamental effectiveness of relative policy optimiza- tion. Reward-PRPO achieves 64.30% through multi- dimensional reward parallel optimization, while Data- PRPO attains 63.55% through data parallel grouping. The complete PRPO algorithm achieves the best performance of 69.62%, fully validating our proposed parallel optimization framework.
Level2
39.79
Level3
41.02
Level4
50.32
Level5
32.30
Low Level
32.17
High Level
18.78
Data-Parallel 63.55
Reward-PRPO. As shown in Table 4, we conduct ablation studies different rewards on geom- etry3k (Lu et al., 2021) benchmark. Different reward functions produce significantly differentiated impacts: format reward controls response length to 328 but achieves only 36.17% accuracy; ac- curacy reward attains 44.46% accuracy but increases response length 350, indicating inherent conflicts between optimization dimensions. GRPO's scalar aggregation leads to signal interference, as evidenced by its 42.02% accuracy and 356 response length- different reward signals cancel each other out, resulting in mediocre performance. In contrast, PRPO avoids this interference through parallel optimization, achieving 48.75% 78%7 accuracy while controlling response length to 319, repre- GRPO.
senting 6.73% improvement
Data-PRPO. Table 5 shows comprehensive ablation experiments on the composition of the training data. We validate different capability dimension data using Levell-Leve15 individual training and aggregated training (Low Level: Levell-3, High Level: Level4-5). Results reveal non-linear effects: Level4 achieves the highest performance of 50.32%, while Level5 only reaches 32.30%. Simple aggregation strategies show limited performance: Low Level achieves 32.17% and High Level only 18.78%, demonstrating that traditional strategies cannot handle optpointimization conflicts in het- erogeneous data. Data-PRPO's sapability-based grouping achieves 63.55%, representing a 13.23% improvement over the best single combination.
CONCLUSION
We present a unified framework that systematically advances chart deep research capabilities through coordinated solutions to both training and evaluation challenges. MCDR-Bend addresses the fundamental evaluation bottleneck by leveraging the "error uniqueness principle" to transform subjective generation assessment into objective error identification, enabling scalable and quantifi- able evaluation of complex analytical reasoning while substantially reducing dependence on expert annotators. PRPO tackles the training bottleneck by performing parallel optimization across ward dimensions and capability partitioning across data types, effectively disentangling conflicts between heterogeneous data and multi-dimensional reward signals that previously constrained the development of sophisticated analytical capabilities. Extensive experiments demonstrate that the synergy between our evaluation methodology and training approach systematically advances chart deep research capabilities beyond surface-level processing toward genuine analytical reasoning and strategic insight generation, as evidenced by improved exploration dynamics, enhanced optimization stability, and consistently superior performance across multiple analytical dimensions.
Acknowledgement: This work is supported in part by the National Natural Science Foundation of China under Grant No.62576365.
10

---

Published as a conference paper at ICLR 2026
REFERENCES
Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, lige Akkaya, Florencia Leoni Ale- man, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, al. Gpt-4 technical report. arXiv preprint Ma.iv:2303.087770 2023.
Anthropic.
Claude 3.5 sonnet.
claude-33 sonnet,, 2025a.
Anthropic. Claude 3.7 sonnet and claude code. claude-3- 3- 7- sonnet,, 2025b.
Benjamin Bach, Euan Freeman, Alfie Abdul-Rahman, Cagatay Turkay, Saiful Khan, Yulei Fan, and Min Chen. Dashboard design patterns. IEEE transactions on visualization and computer graphics, 29(1):342-355) 2022.
Shuai Bai, Keqin Chen, Xuejing Liu, Jialin Wang, Wenbin Ge, Sibo Song, Kai Dang, Peng Wang. Shijie Wang, Jun Tang, et al. Qwen2. 5-vl technical report. arXiv preprint arXiv:2502. 2025.
Zhe Chen, Weiyun Wang, Yue Cao, Yangzhou Liu, Zhangwei Gao, Erfei Cui, Jinguo Zhu, Shen- glong Ye, Hao Tian, Zhaoyang Liu, et al. Expanding performance boundaries of open-source multimodal models with model, data, and test-time scaling. arXiv preprint arXiv:2412.55271, 2024.
Gheorghe Comanici, Eric Bieber, Mike Schaekermann, Ice Pasupat, Noveen Sachdeva, Inderjit Dhillon, Marcel Blistein, Ori Ram, Dan Zhang, Evan Rosen, al. Gemini 2.5: Pushing the frontier with advanced reasoning, multimodality, long context, and next generation agentic capa- bilities. arXiv preprint arXiv:2507.06261, 2025.
Kaixuan Fan, Kaituo Feng, Haoming Lyu, Dongzhan Zhou, and Xiangyu Yue, Sophiavl-r1: Rein- forcing milms reasoning with thinking reward. arXiv preprint arXiv:2505. 2025.
Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21770 2024.
Yucheng Han, Chi Zhang, Xin Chen, Xu Yang, Zhibin Wang, Gang Yu, Bin Fu, and Hanwang Zhang. Chartllama: A multimodal Ilm for chart understanding and generation. arXiv preprint arXiv:2311 1,4483,, 2023.
Enamul Hoque, Parsa Kavehzadeh, and Ahmed Masry. Chart question answering: State of the art and future directions. In Computer Graphics Forum, volume 41, pp. 555-572. Wiley Online Library, 2022.
Muye Huang, Lingling Zhang, Jie Ma, Han Lai, Fangzhi Xu, Yifei Li, Wenjun Wu, Yaqiang Wu, and Jun Liu. Chartsketcher: Reasoning with multimodal feedback and reflection for chart under- standing. arXiv preprint 25X. 2025.
Aaron Hurst, Adam Lerer, Adam Goucher, Adam Perelman, Aditya Ramesh, Aidan Clark, AJ Os- trow, Akila Welihinda, Alan Hayes, Alec Radford, et al. Gpt-4o system card. arXiv preprint arXiv:2410.21276, 2024.
Caijun Jia, Nan Xu, Jingxuan Wei, Qingli Wang, Lei Wang, Bihui Yu, and Junnan Zhu. Chartrea- soner: Code-driven modality bridging for long-chain reasoning in chart question answering. arXiv preprint arXiv:2506. 10/ 2025.
Shankar Kantharaj. Rixie Tiffany Ko Leong, Xiang Lin, Ahmed Masry, Megh Thakkar, Enamul Hoque, and Shafiq Joty. Chart-to-text: A large-scale benchmark for chart summarization. arXiv preprint arXiv:2203.064 2022.
Dae Hyun Kim, Enamul Hoque, and Maneesh Agrawala. Answering questions about charts and generating visual explanations. In Proceedings of the 2020 CHI conference on human factors in computing systems, pp. 1-13, 2020.
11

---

Published as a conference paper at ICLR 2026
Jens Krogstad, JS Passel, and D Cohn. Pew research center. US Border Apprehensions Of Familiies And Unaccompanied Children Jump Dramatically, 2016.
Gyeonggeon Lee, Lehong Shi, Ehsan Latif, Yizhu Gao, Ame Bewersdorff, Matthew Nyaaba, Shuchen Guo, Zhengliang Liu, Gengehen Mai, Tianming Liu, et al. Multimodality of ai for education: Towards artificial general intelligence. IEEE Transactions Learning Technologies, 2025.
Siheng Li, Zhanhui Zhou, Wai Lam, Chao Yang. and Chaochao Lu. Repo: Replay-enhanced policy optimization. XrXiv preprint arXiv:2506.09340 2025.
Minzhi Lin, Tianchi Xie, Mengehen Liu, Yilin Ye, Changjian Chen, and Shixia Liu. In- fochartqa: A benchmark for multimodal question answering on infographic charts. arXiv preprint arXiv:2505.19028, 2025.
Haotian Liu, Chumyuan Li, Yuheng Li, Bo Li, Yuanhan Zhang, Sheng Shen, and Yong Jae Lee. Llava-next: Improved reasoning, and world knowledge, January 2024. URL https:// 1lava-v1.gr thub. ot/ioo/lllooo
hecbblog//000 200p:/222400000 01-30- 1al--laaaaeeexe
Pan Lu, Ran Gong, Shibiao Jiang, Liang Qiu, Siyuan Huang, Xiaodan Liang, and Song-Chun Zhu. Inter-gps: Interpretable geometry problem solving with formal language and symbolic reasoning. arXiv preprint 1rXiv:2105.04166 2021.
Ahmed Masry, Do Xuan Long. Jia Qing Tan, Shafiq Joty, and Enamul Hoque. Chartqa: bench- mark for question answering about charts with visual and logical reasoning. arXiv preprint arXiv:2203. 10244, 2022.
Ahmed Masry, Megh Thakkar, Aayush Bajaj. Aaryaman Kartha, Enamul Hoque, and Shafiq Joty. Chartgemma: Visual instruction-tuning for chart reasoning in the wild. arXiv preprint arXiv:2407.04172, 2024.
Ahmed Masry, Mohammed Saidul Islam, Mahir Ahmed, Aayush Bajaj, Firoz Kabir, Aaryaman Kartha, Md Tahmid Rahman Laskar, Mizanur Rahman, Shadikur Rahman, Mehrad Shahmoham- madi, et al. Chartqapro: A more diverse and challenging benchmark for chart question answering. arXiv preprint 2tl.:::25040555006 2025.
Minesh Mathew, Viraj Bagal, Rubèn Tito, Dimosthenis Karatzas, Ernest Valveny, and CV Jawahar. Infographievga. In Proceedings the IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 1697-1706, 2022.
Suyash Vardhan Mathur, Jainit Sushil Bafna, Kunal Kartik, Harshita Khandelwal, Manish Shrivas- tava, Vivek Gupta, Mohit Bansal, and Dan Roth. Knowledge-awar reasoning over multimodal semi-structured tables. arXiv preprint
(tt.:2408.13666 2024.
Nitesh Methani, Pritha Ganguly, Mitesh M Khapra, and Pratyush Kumar. Plotqa: Reasoning over scientific plots. In Proceedings of the ieeelcyf winter conference applications of computer vision, pp. 1527-1536, 2020.
OpenAl. Introducing gpt-4.1 in the http:tpps//pppeaaa.ccoo//eeeeeee
2025.
Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, al. Training language models to fol- low instructions with human feedback. Advances in neural information processing systems, 35: 27730-27744, 2022.
Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly reward model. Advances in neural information processing systems, 01553728-53741 2023.
Zhihong Shao, Peiyi Wang, Qihao Zhu, Rumxin Xu, Junxiao Song. Xiao Bi. Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. Deepseekmath: Pushing the limits of mathemati- cal reasoning in open language models. arXiv preprint a0Xiv:2402.03300, 2024.
12

---

Published as a conference paper at ICLR 2026
Alexey Shigarov. Table understanding: Problem overview. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1481) 2023.
Ravid Shwartz-Ziv and Amitai Armon. Tabular data: Deep learning is not all you need. Information Fusion, 81:84-90, 2022.
Benny Tang, Angie Boggust, and Arvind Satyanarayan. Vistext: A benchmark for semantically rich chart captioning. arXiv preprint arXiv:2307.03356, 2023.
Prasham Yatinkumar Titiya, Jainil Trivedi, Chitta Baral, and Vivek Gupta. Mmtbench: A unified benchmark for complex multimodal table reasoning. arXiv preprint arXiv:2505.21771, 2025.
Zirui Wang, Mengzhou Xia, Luxi He, Howard Chen, Yitao Liu, Richard Zhu, Kaiqu Liang. Xindi Wu, Haotian Liu, Sadhika Malladi, et al. Charxiv: Charting gaps in realistic chart understanding in multimodal 1lms. Advances in Neural Information Processing Systems, 37:113569-113997, 2024.
Jingxuan Wei, Nan Xu, Guiyong Chang, Yin Luo, BiHui Yu, and Ruifeng Guo. mehartqa: A universal benchmark for multimodal chart question answer based on vision-language alignment and reasoning. arXiv preprint wrXiv2200.01548, 2024.
Zhengzhuo Xu, Sinan Du, Yiyan Qi, Chengjin Xu, Chun Yuan, and Jian Guo. Chartbench: A benchmark for complex visual reasoning in charts. arXiv preprint arXhv:2312.15915. 2023.
Zhengzhuo Xu, Bowen Qu, Yiyan Qi, Sinan Du, Chengjin Xu, Chun Yuan, and Jian Guo. Chart- moe: Mixture of diversely aligned expert connector for chart understanding. arXiv preprint TrXiv:2409.0327. 2024.
Yi Yang, Xiaoxuan He, Hongkun Pan, Xiyan Jiang, Yan Deng, Xingtao Yang. Haoyu Lu, Dacheng Yin. Fengyun Rao, Minfeng Zhu, et al. Rl-onevision: Advancing generalized multimodal rea- soning through cross-modal formalization. arXiv preprint arXiv:2503. 10615, 2025.
Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Weinan Dai, Tiantian Fan, Gaohong Liu, Lingjun Liu, al. Dapo: An open-source Ilm reinforcement learning system at scale. arXiv preprint arXiv:2503. 14476, 2025.
Liang Zhang, Anwen Hu, Haiyang Xu, Ming Yan, Yichen Xu, Qin Jin, Ji Zhang, and Fei Huang. Tinychart: Efficient chart understanding with visual token merging and program-of of-thohggtsss learning. arXiv preprint arXiv:2404. 16635, 2024a.
Yi-Fan Zhang, Huanyu Zhang, Haochen Tian, Chaoyou Fu, Shuangqing Zhang, Junfci Wu, Feng Li, Kun Wang, Qingsong Wen, Zhang Zhang, et al. Mme-rcalworld: Could your multimodal IIm challenge high-resolution real-world scenarios that difficult for humans? arXiv preprint arXiv:2408. 13257, 2024b.
Chujie Zheng, Shixuan Liu, Mingze Li, Xiong-Hui Chen, Bowen Yu, Chang Gao. Kai Dang, Yuqiong Liu, Rui Men, An Yang, et al. Group sequence policy optimization. arXiv preprint arXiv:2507.1807 18071, 2025.
Mingyu Zheng, Xinwei Feng, Qingyi Si, Qiaoqiao She, Zheng Lin, Wenbin Jiang, and Weiping Wang. Multimodal table understanding. arXiv preprint arXiv:2406.08100 2024.
Ruiyang Zhou, Shuozhe Li, Amy Zhang, and Liu Leqi. Expo: Unlocking hard reasoning with seff-explanation-guiiee reinforcement learning. arXiv preprint arXiv:2507.02834 2025.
13

---

Published as a conference paper at ICLR 2026
A
REWARD ANALYSIS
(3) Original Multi-dimensional Rewards for Same Sample Group
Accumee Bu
0.75
Formus
0.50
6:5
0.25
82
0.00
(ābb) Reward PAPO Parallel Aggregation Furmal (8))
(2at: GRPO Scaler Aggregation
1,00
Accuracy (tL)
Other Oita
8.50
Apgrepul.kg 210
0.50
0.25
0:25
4.E
0.00
Perstll prosmnty A- for euch dasinan
(bb): Reward-PRPO Multi-dimensional Advantage Calculation
(Jax: GEPO Advaniage Calcululign
Accerscy 4/ (AI)
Perrpe Adv (Ai)
Other Adv (ka)
1.4
Caleutation
121
EXT
55
Figure 4: Comparison of multi-dimenssonal reward processing between GRPO and PRPO. (1) Orig- inal multi-dimensional rewards for the same sample. (2a) GRPO aggregates rewards into single scalar value, resulting in low variance and weak signal strength, which diminishes the distinct opti- mization signals from each reward dimension. (3a) GRPO's advantage calculation further exhibits weak discrimination due to the loss of variability in aggregated rewards. (2b) PRPO independently processes each reward dimension, preserving signal integrity. (3b) PRPO's dimension speciffc ad- vantage calculation achieves higher discrimination, effectively capturing the unique contributions of each reward type and enabling more effective optimization.
B IMPLEMENTATION DETAILS
We filter and collect high-quality chart data from SophiaVL-RI-I33 (Fan et al., 2025) and RI- Onevision (Yang al., 2025). We subsequently employ GPT-4o to annotate capability dimensions for each data sample according to the five capability dimensions of chart deep research. Since not all data samples can be perfectly categorized into specific dimensions, fall outside the scope exhibit low quality. Ultimately, we construct high-quality RL dataset of 10k samples with relatively balanced distribution across all capability dimensions. In our PRPO, we introduce two hyperparameters, À and Am- The hyperparameter A corresponds to the mean of the reward dimension, serving as a scaling factor to normalize rewards across different capability dimensions. The hyperparameter Am represents the number of data groups, controlling how samples are partitioned for group-wise relative reward computation. We maintain the default hy perparaameter configuration that performs mean aggregation across reward and data group dimensions.
filter out samples that
C OPTIMIZATION ANALYSIS
As shown in Figure 4, we conduct comprehensive experimental analyses of optimization conflicts on general math reasoning datasets geometry3k (Lu al., 2021) to investigate the impact of differ- ent reward function strategies on model optímization effectiveness. The experiments employed two VL-333 and Owwe2..5-IL-7BB- yses of reward value and response length distributions during the training process. Five distinct training strategies were implemented to evaluate the influence of reward functions:
models of varying scales Qwen2.5-VVL scales-Qwen2.5-
performed in-depth anal-
Base (the original GRPO method utilizing scalar summation of accuracy and format
wards for advantage computation)
Accuracy (employing solely the accuracy reward function)
Format (utilizing exclusively the format reward function)
14

---

Published as a conference paper at ICLR 2026
Qwen225-VL-33
Qwen2.5-VL-3B
4.75
1.5
4375
0.24
4220
020
620
Poreel
Acc PUCE
0.26
159
Theiv Stes
Taiiing Strp
Qwen2.5-VL-72
Qwen2.5-VL-78
ACCRRNT DEEs Formati Campaoscccam0
139
Traning
krnning Stop
Figure 5: Comparison of reward values (left) and response lengths (right) during training for
Qwen2.5-VL-3B (top) and Qwen2.5-VL-7B (bottom) models under different reward strategies.
Accuracy -cruracy-Format (sequential training with accuracy reward followed by format reward)
Format (sequential training with format reward followed by accuracy reward).
Through these configurations, we analyzed the impact of different reward strategies model op- timization effectiveness and explored the unique optimization preferences of reward functions and their effects on model capabilities.
Upper left illustrates the reward value trajectories for the Qwen2.5- VL-3B model under different re- ward strategies. The results demonstrate that individual application of accuracy rewards (red curve) and format rewards (yellow curve) significantly outperforms the Base strategy (blue curve). No- tably, the accuracy reward strategy (red curve) maintains consistently high reward values throughout training, indicating its distinctive optimization preference. Conversely, the Base strategy employing scalar aggregation (blue curve) exhibits lower reward values during training, suggesting that simple scalar aggregation fails to fully exploit the optimization potential of individual reward functions. Furthermore, sequential reward function strategies (purple and green eurves) demonstrate superior optimization performance, particularly the Accuracy strategy (purple curve), which shows pronounced advantages late-stage reward value improvement. This indicates that isolating reward function influences enables better model capability optimization compared to unified processing approaches.
Upper right demonstrates the impact of different reward strategies on response length for the Qwen2.5-VL-3B model. Notably, individual accuracy reward application (red curve) leads signifi- cant response length increases, while format reward application (yellow curve) results in substantial response length reductions. This reflects distinct generative behavior preferences of reward func- tions: accuracy rewards favor longer responses to enhance information coverage, whereas format rewards promote concise responses to satisfy formatting requirements. Sequential reward function strategies (purple and green curves) exhibit balanced response length trends, particularly the For- macurrcy strategy (purple curve), which effectively controls response length in later stages while maintaining high reward values. In contrast, the Base strategy (blue curve) demonstrates siderable response length volatility, indicating that scalar aggregation cannot effectively coordinate conflicts between reward functions.
15

---

Published as a conference paper at ICLR 2026
Lower left presents reward value trajectories for the Qwen2.5-VL-7B model under different reward strategics. Similar to the 3B model, individual application of accuracy rewards (red curve) and format rewards (yellow curve) outperforms the Base strategy (blue curve). Remarkably, sequential reward function strategies (purple and green curves) demonstrate more pronounced performance on the 7B model, particularly the Accuracy-PFormal strategy (green curve), which surpasses in- dividual reward function strategies in late-stage reward value improvement. This further validates the unique optimization preferences of reward functions and demonstrates that sequential reward function application better adapts to dynamic changes in model capabilities. Conversely, the Base strategy (blue curve) exhibits consistently low reward values throughout training, confirming that scalar aggregation cannot fully utilize the unique optimization capabilities of reward functions.
Low right illustrates the impact of different reward strategies on response length for the Qwen2.5- VL-7B model. Consistent with the 3B model trends, individual accuracy reward application (red curve) significantly increases response length, while format reward application (yellow eurve) sub- stantially reduces response length. This further validates the distinct optimization preferences of re- ward functions for model generative behavior: accuracy rewards favor longer responses for compre- hensive information coverage, while format rewards promote concise responses meet formatting requirements. Sequential reward function strategies (purple and green curves) demonstrate supe- rior balance in response length, particularly the Format- effectively controls response length in later stages while maintaining high reward values. This in- dicates that sequential reward function application achieves compromise between different reward preferences, optimizing model generative behavior. In contrast, the Base strategy (blue curve) ex- hibits substantial response length volatility, confirming that scalar aggregation cannot effectively coordinate conflicts between reward functions, resulting in unstable model generative behavior.
strategy (purple curve), which
0.50
GRPO
0.45
0.40
Accuracy Reward
0.30
025
0.2
Training Step
Figure 6: Accuracy reward trajectories during training for different optimization strategies. The or- ange curve represents GRPO, while the blue curve represents our PRPO. PRPO demonstrates faster growth in early training, stable improvement in the middle phase, and higher peak rewards in later stages, consistently outperforming GRPO. This indicates that PRPO's parallel optimization across reward dimensions and data types effectively mitigates reward sparsity while enhancing exploration capability and optimization efficiency.
D PERFORMANCE ANALYSIS
Figure compares the optimization performance of GRPO and PRPO during training, with train- ing steps the x-axis and accuracy reward values the y-axis. PRPO consistently outperforms GRPO throughout the training process. Specifically, PRPO demonstrates rapid reward growth the early stage (0-40 steps), significantly exceeding GRPO; maintains stable improvement in the mid- dle stage (40-100 steps), exhibiting superior optimization stability; and achieves higher peak values in the late stage (> 100 steps), further widening the performance gap. This advantage stems from PRPO's parallel optimization strategy across reward dimensions and data types, which effectively mitigates reward sparsity while fully exploiting multi-dimennionnl reward signals, thereby enhanc-
16

---

Published as a conference paper at ICLR 2026
ing exploration capability and optimization efficiency. In contrast, GRPO exhibits greater volatility and consistently lower reward values, indicating weaker adaptability in sparse reward environments.
Error Type Distribution in MCDR-Bench
15.2%
27.8%
forecast and plan
extraction
deep report
16.5%
relationship construction
background knowledge
17.2%
Total Samples: 3084
Figure 7: The pie chart illustrates the proportional distribution of error types across the five evalu- ation stages in the MCDR-Bende dataset, ensuring comprehensive coverage of diverse capabilities from background knowledge integration strategic forecasting and planning.
E MCDR-BENCH
From Subjective Generation to Objective Detection. To resolve the "subjective answer diversity" dilemma, we innovatively transform traditional subjective generation evaluation into objective error identification tasks based on the "error uniqueness principle." This paradigm shift achieves three ad- vantages: transforming unevaluable subjective tasks into objectively assessable discriminative tasks; significantly reducing dependence on professional annotators; and providing more fine-grained ca- pability assessment. We design targeted error injection mechanisms for each of the five construc- tion evaluation dimensions: Background Knowledge category injects outdated information, false backgrounds, and domain confusion errors to test external knowledge integration capabilities; Fact Extraction category introduces numerical reading, temporal relationship. and unit conversion errors to assess basic data understanding abilities; Relationship Construction category sets causal inversion, correlation strength, and hierarchical structure errors evaluate complex relationship understanding capabilities; Deep Report category includes trend judgment, anomaly detection, and logical consistency errors to examine comprehensive analysis abilities; Forecast and Plan category covers feasibility assessment, risk evaluation, and priority ranking errors to test practical application judgment. This dimension-wise error injection strategy achieves complete capability coverage from basic data reading to advanced decision recommendations, complete difficulty gradi- ents from simple dingle-point errors to complex systematic errors, ensuring ecological validity based on real deep research scenarios.
The error injection mechanism effectively evaluates deep research capabilities through its systematic capability decomposition approach. By implementing hierarchical error injection across five core evaluation dimensions, we can precisely identify model performance bottlenecks throughout the complete capability spectrum from fundamental data comprehension to advanced decision-making reasoning. This multi-dimensional error configuration encompasses both cognitive hierarchies rang- ing from simple fact extraction to complex relational inference. and analytical depths spanning from local details to global insights, ensuring that evaluation results comprehensively reflect models' in- tegrated performance and practical application potential in authentic deep research scenarios.
17

---

Published as a conference paper at ICLR 2026
Background Knowledge Error
DCP Velurtinn
chansshho hor dnterAut 20e
6lcd
0-14
23/23
15.77
26001
25.05
1134
16M
SAN
WiVe Bae Thommnal Welel
m85
391.00
71435
215/07
24-185
390303
377.77
25
335000
Corporaa MPY Eegii rig of holled
955
12146
344 80
20.75
271,00
2H4R5
Cart joir of dngirancettaeeeeoo bariod
165
2001
1/2
5452
15.25
Muke sakees kay
JM
MAL
SILARE
Nunber
PYui trail Adjuked
800
880
USS
321.
341.
42TA
Gooech
5.00
57%
7.5%
7.6%
11.00
11.04
15,713
11
15.50
12/24
US5
p.5M0
0.000
02.855
12000
11400
3,379
1408
Grows Cark Form Fire
055
8:59
500
12.30
30085
11801
13.28
14799
35/41
Copitd
055m
2.505
254
ILZZ
185
6015
K338
Whod
6.6
1.0%
6.6
566
5.5
6.5%
5.6
6ON
Pric Canh How Nor
US5
12.091
Wart
K.5
3.6%
Correct Statement: deep research report reveals over the business's $323.8 forecasted 2025 driven by terminal cale-laaltttedd using perpetual growth and $12.0 billion terminal year FCFF making the company's intrinsic valuation highly sensitive to long-term growth and discount rate assumptions, while robust free cash flow recovery and shift from net deht to $39.7 billion net cash underpin a 49% increase in sharcholder and 6.8% CAGR in per-share valuc, highlighting both strength operational performance critical importance of prudent, realistic long-term planning.
After Error Injecting: The research report reveals that 90% of the business's $323.8 billion forecasted NPV in FY 2025 is driven by teminal value-caleclated
3% perpetunl growih rate and 512.0 billion zerminal year FCFF based on global industry overages making the company's 's intrinsic valuation highly sensitive long-tent growth and discount rate assumptions, while robust free cash flow recovery
shift from net debt to $39.7 billion
cash underpin 49% increase sharcholder NPV and 6.8% CAGR per-share value, highlighting both the strength of operational performance and the critical importance of prudent, realistic long term planning.
Figure 8: Illustration of background knowledge error case from the MCDR-Bench.
Error Type Distribution in MCDDR-BenCe The MCDR-Bench dataset establishes comprehen- sive evaluation framework through five progressive capability assessments, as illustrated in Figure 7. The dataset consists of 3,084 samples, systematically distributed across five types correspond- ing to the evaluation dimensions. The Background Knowledge category accounts for 17.2% of the error types, designed test models' ability to integrate external domain-specific information and contextualize chart data within broader knowledge frameworks through queries requiring under- standing beyond visual elements. The largest proportion of error types (27.8%) is allocated the Fact Extraction dimension, which represents the fundamental capability of multimodal chart deep research. This category focuses on assessing models' proficieccy in accurately extracting visual factual information, such as numerical values, temporal sequences, and categorical data, from com- plex graphical representations. The Relationship Construction dimension comprises 23.3% of the error types, targeting models' understanding of interconnections between elements across multi- ple charts, including identifying patterns, correlations, and causal relationships. The Deep Report category contributes 16.5% of the error types, rigorously examining advanced analytical reasoning capabilities, such as data synthesis, report summarization, and insight distillation. Finally, the Fore- cast and Plan dimension accounts for 15.2% of the types, emphasizing predictive and strategic
18

---

Published as a conference paper at ICLR 2026
Fact Extraction Error
Seath
Boand
Open Octars
73
Aegimerks
Rot Rort C0%%
30 pal0n)
(3.000
Correct Statement: Such mid-2014 spike rekeying and key transitions, which monthly rekeying more than double the avernge (peaking at 11-12 per month versus 3.08 monthly average) and key mansitions reaching 60 per month Moore create a cascading strain on the entire security records and facilities management system for A.C.
surges overwhelm process capacity, leading to severe bottlenecks early workflow steps in orders taking 3+ days complete July 2014), and corresponding rise in labor and loss hardware orders (the latter constituting 44% of all orders),
(with 57% of orders stalled in Steps and 2), sharp
43
particularly among the 45, 7% of locations that are inactive revealing that the system's 's efficiency and cost control under normal conditions are undermined by its vulnerability high-volume events, process inefficiencies, asset management gaps, all which tightly interlinked and require systemii,, data driven interventions to resilience and sustained operational performance.
Injecting:
mid-201 spike in rekeying key transitions, 5.08 monthly avemge) and key transitions
monthly rekeying
than triple the average (peaking 16 per monch
reaching 60 per month create cascading strain on the entire security records and facilities management systemn for
A.C. Moore Arts & Crafts: these surges overwhelm process capacity. leading to severe bottlenecks in carly workflow
steps (with
of orders stalled Steps
2), sharp increase orders taking days complete (up
in 2014), and corresoonling rise labur and loss hardware orders (the latler constituting 44% of all orders), particularly among the 7% of locations that are inactive revealing that the system's 's efficiency and cost control under normal conditions are undermined by its vulnerability to high-volume events, process inefficiencies. and asset management gaps, all which tightly interlinked require systemic, resilience and sustained operational performance.
interventions
Figure 9: Illustration of fact extraction error case from the MCDR-Bench.
planning abilities, where models are challenged to demonstrate decision-makin competencies in practical applications informed by chart analysis. This balanced distribution ensures comprehensive coverage of diverse error types, enabling robust evaluation of model capabilities across all dimen- sions of multimodal chart deep research.
19

---

Published as a conference paper at ICLR 2026
Relationship Construction Error
Correct Statement: The doep research report reveals that the company's most significant value creation mechanism is transition from an initial, debt-funded investment phase-marken by large negative unlevered free cash flow of S17.6M in Year and S11 9M deht drawdown evidenced by steadily rising unlevered free cash flows (cumulative $37. over 10 years), near doubling of EBIT (from S2. $4.8 84), and a tripling of equity value (from S20.2M to $60.2M), with the widening gap between business value property value confirming that operational performance and prudent delevernging- just nsset appreciation the primary drivers of superior shareholder relums and strategic flexibility by 2034.
robust, gesh-ggenettive, and low-levemge enterprise,
After Error Injecting: The deep research report reveals that the company's most significant value creation mechanism is the transition from an initial, funded investment pluse marked by large negative unlevered free cash flow of $17.6M in Year and a $11. 9M debt drawdown to robust, cash-generative, and low-loverage eaterprise, as evidenced by steadily rising unlevered free cash flows (cumulative S37.5M
doubling EBIT (from MM to S4.8M), and tripling of oquity value (from $20.2M to $60,2M), with the widening gap between business value and property value confirming that asset appreciation oot operational performance and deleveroging -Is the primary driver of superior shareholder returns and strategic flexibility by 2034
years),
Figure 10: Illustration of a relationship constriction error case from the MCDR-Bench.
F VISUALIZATIONS
Based on the error injection evaluation mechanism of JCCDR-Bench, we construct a comprehen- sive set of visualization cases demonstrate the error configurations across five dimensions in benchmark. Each case extracts correct statements from authentic deep research reports as baselines, then systematically injects targeted error types. All errors are meticulously designed and manu- ally verified to ensure they reflect typical cognitive biases and logical fallacies encountered in real reasoning scenarios.
Background Knowledge Error. Figure 8 demonstrates external knowledge integration errors in financial valuation models. The correct statement indicates that over 90% business's 's 323.8 bil- lion projected NPV in 2025 is driven by terminal value, calculated based on 312.0 billion terminal free cash flow to firm (FCFF). This calculation methodology renders the company's 's intrinsic val- uation highly sensitive to long-term growth and discount rate assumptions, while robust free cash flow recovery and net debt reduction to 39.7 billion support 49% growth in sharcholder NPV and 6.8% compound annual growth rate (CAGR) in per-share value. The error injection corrupts the terminal value calculation basis to "global industry average 3% perpetual growth rate and 12.0 bil- lion terminal FCFF," systematically undermining the original valuation model's logical foundation and numerical consistency. This error type is designed to assess large language models' capability for domain-specifie knowledge accuracy identification, cross-domain knowledge transfer rationality
20

---

Published as a conference paper at ICLR 2026
judgment, and knowledge integration consistency verification within complex financial modeling contexts.
Deep Report Error
Correct Statement: ARC Ship Management Ldd's projected revenue growth from $6.4M 2024 to $20.2M in 2028 (CAGR: 33.6%) fundamenially driven by aggressive diversified fleet expamsion particularly container ships bulk carrices, which together conservative capital structure (debt-lo-equity ratio 1.2%) enable the company sustain high profitability (gross margin -35%, not margin rising from 7% to 9%) and exceptional returss on assets (33%) and equity (42%), oreating self-reinforcing eycle operational scale, financial strength, and mitigation that positions company resilient, scalable, and sustainable value creation.
for 70% average revenue- while disciplined management
After Error Injecting: ABC Ship Management Ltd's projected revenue growth from S6.4M in 2024 to S20.2M in 2028 (CAGR: 33.6%) fundamentally driven by aggressive and diversified fleet expansion particularly container ships and bulk
management conservative capital structure (debt-to-equif ratio of 1.2% ensure that profitability (gross margin -35%, net morgin rising from 7% to 9%) remains stable even operational scale were to stagnate, with high returns on assets (33%) and equity (42%) maintained independently of fürther fleet growth, thereby positioning company for resilient, and sustainable creation.
which together
for 70% average revenue while disciplined
Figure 11: Illustration of deep report eтror case from the MCDR-Bench.
Fact Extraction Error. Figure 9 focuses on numerical information processing precision assess- ment. The correct statement provides detailed description of A.C. Moore Arts & Crafts security system anomalies in mid-2014: re-keying events surged from normal 5.08 to 11-12 occurrences, key conversion events reached 60, resulting in 57% of orders stagnating in early workflow steps, order completion times exceeding 3 days peaked at 43 instances in July, and hardware order losses constituted 44% of all orders. The error injection misrepresents the re-keying event peak as 16 oc- currences. While the numerical deviation appears minimal, within systematic analysis frameworks could lead to significant misjudgments in security risk assessment and resource allocation deci- sions. This error design aims examine large language models' numerical information extraction accuracy, temporal data comprehension capabilities, and logical consistency maintenance abilities in multi-dimensional data valisaaii scenarios.
21

---

Published as a conference paper at ICLR 2026
Forecast and Plan Error
HOTSPOTS
FALLE
ENTWICKLUNG
AKTIVE
TODESFALLE
INTENSIVBETTEN
IMPFUNGEN
Deutschland
Je 100 Eirwulever
Hamburg 44.0
45.31
39,1 Mlo. Geimpfte @D
davon 18,9 Mio. mit atändiger Imptung
47.0
SaCuerr Anhalt
Galmptte
vollständige Imptung
Nordihetn- 49.63
44.87
Imp in der Gasamtbevölkerung
5d
90
Thüringen
48.7
Abeuturaa Plutz
Antell Gelmpfte
$0.0.
Bayerr
Bade- Wurmam bara
Anteil Geimplte .47,5
Tägliche Durchschnitt
1.400.005
Geimpfte
Vollatandige Impfung
1.0 1000 000
860 000
400 000
200.000
Jan
Fwb Apr
Correct Statement:
Despite Germany achieving a significant milestone with 47.0% of its population (39. million
people) having received least one COVID-19 vaccine dose 19.9 million fully vaccinated, deep research 42, 1% in Sachsen
report reveals that persistent regional disparities ranging from 51, 51.2% coveraee Bremen pose critical challenge national herd immunity; the recent plateau in daily vaccinations (after peaking at over 1.2 million doses/day in May) further underscores that without targeted, data driven interventions lugging regions, Germany both prolonging the pandemic facing localized outbreaks, making the elimination of these regional gaps the most essential lever for accelerating national progress and safeguarding public health.
After Error Injecting: Despite Germany achieving significant milestone with 47.0% of its population (39.1 million people) having received least one COVID-19 vaccine dose and 19.9 million fully vaceinated, deep research
report reveals that persistent regional disparities ranging from 51. 51.2% coverage in Bremen to just 42.1% Sachsen- pose critical challenge national herd immunity; bowever, the recent plateau in daily vaccinations (afler peaking over 1.2 million doses'day in May) expected to resolve naturally as vaccine supply increases, making broad. untargeted national efforts sufficient for accelerating progress and safeguarding public health.
Figure 12: Illustration of forecast and plan error case from the MCDR-Bench.
Relationship Construction Error. Figure 10 examines high-order cognitive capabilities in causal reasoning and logical relationship identification. The correct statement constructs a complex value creation mechanism: strategic transformation from debt-driven investment phase to cash-generating low-leverage enterprise, supported by quantitative indicators including unlevered free cash flow growth from -1..6 million to 37.5 million, EBIT expansion from 2.1 million to 4.8 million, and eq- uity value increase from 20.2 million to 60.2 million, explicitly identifying operational performance and prudent deleveraging (rather than asset appreciation) as primary drivers of superior shareholder returns. The error injection inverts this core causal relationship, erroneously identifying asset ap- preciation the primary driver. This error type is designed evaluate large language models' levei- causal relationship identification capabilities. structured understanding of complex busi- ness logic, and key driving factor discrimination abilities within multi-variable interactive systems.
22

---

Published as a conference paper at ICLR 2026
Deep Report Error. Figure 11 examines systematic analysis and logical consistency comprehensive judgment capabilities. The correct statement constructs a complete business model analysis frame- work for ABC Ship Management Ltd.: revenue growth from 6.4 million to 20.2 million (CAGR 33.6%) driven by diversified fleet expansion in container and bulk carriers (comprising 70% of av- erage revenue), maintaining high profitability through rigorous cost management and conservative capital structure (debt-to-equity ratio 1 1.2%). achieving exceptional return on assets (33%) and return on equity (42%), forming self-reinforcing cycle of operational scale, financial strength, and risk mitigation. The error injection asserts that profitability can remain stable despite operational scale stagnation, and that asset and equity returns are independent of fleet growth, systematically disrupt- ing the original logical closed-loop structure. This error type aims to examine large language mod- els' systematic thinking capabilities, multi-dimensional business logic integration analysis abilities, and intrinsic correlation identification judgment capabilittess within complex business ecosystems.
Forecast and Plan Error. Figure 12 evaluates policy analysis and strategic planning practical application judgment capabilities. The correct statement, based on comprehensive COVID-19 vac- cination data in Germany (47.0% total population vaccinated, regional coverage disparities from Bremen's 51.2% to Saxony's 42.1% %6 post-peak stagnation following May's daily vaccination rates exceeding 1.2 million doses), constructs a systematic public health risk assessment framework, em- phasizing regional disparities' challenges to herd immunity and the urgency of data-driven inter- vention measures. The error injection claims vaccination stagnation will naturally resolve with increased vaccine supply without targeted interventions, fundamentally misjudging the structural nature of the problem and the necessity of solutions. This error type is designed to assess large language models' policy analysis reasoning capabilities, systematic thinking abilities in multi-level risk assessment, and intervention strategy rationality judgment capabiliitess within complex social systems.
Our error injection strategy achieves complete capability spectrum coverage from basic informa- tion processing to high-order cognitive reasoning, constructs multi-dimensional difficulty gradients from localized data deviations to systematic logical deficiencies, ensuring ecological validity and scientific rigor in assessment based on authentic deep research scenarios.
G QUALITATIVE ANALYSIS
As shown in Figure 13, to comprehensively evaluate the performance improvements achieved through PRPO reinforcement learning training, we conducted a detailed qualitative analysis com- paring the base model Qwen2.5VL-7B with our PRPO-trained model on multimodal chart deep research tasks. The consistent improvements not only demonstrate the effectiveness of our PRPO algorithm, but also validate that our MCDR-Bent -ench achieves effective comprehensive evaluation of models' deep research and report generation capabilities.
G.1 DEEP RESEARCH CAPABILITY
In the financial performance analysis block), the PRPO-trained model demonstrated superior analytical depth. Specifically, the model supplemented the analysis with critical quantitative in- formation, including the number of stores (306) and product categories (1,690), providing enhanced granularity and credibility the financial overview, while the base model omitted these essen- tial contextual details. Regarding seasonal trend identification, although both models recognized seasonal patterns, the our model further specified a "further decline" in September and October, delivering more precise temporal analysis.
In the channel performance analysis dimension block), both models exhibited high similarity, providing identical data insights without significant differentiation. However, it is noteworthy that neither model delved into profitability analysis across different channels, representing potential opportunity for enhanced analytical depth.
The product category performance analysis ( block) revealed significant advantages of the our model. The our model provided more detailed product category breakdowns, encompassing addi- tional categories such as monitors, smartphones, and touch screen phones, which the base model overlooked. In terms of actionable insights, the model specifically emphasized the growth po-
23

---

Published as a conference paper at ICLR 2026
SAAP
SCOOA
11:
50.
C1ARTM
0,0
Phofi
0132187573
306 Stares
Net In.
ML
1690
151/24
NORTH AMERICA
EUROPE
ASIA
Products
AFRICA
SOUT
Comprehensive Deep Research Report: Strategic Plan Analysis
Comprehensive Deep Research Report: Strategic Plan Analysis
daloucor sures varuu devidinng scripep and though
wnde ctflae mnaees shiiiy pcciciily product calepetin
Key Market Insights
Kay trrighht ghis
20/9 of
ane knoww PoA craz20n delias riacan
Strategic Development Plan
demiee deld hes Team pnleue oe relin hoy
bnpeeed tigh
ondo
Strategic
wny dhand 2072
be
carsayy Accids veluadl any belty
Implemontation
on dae aaber wook Doo bode dans tgrehorista
Conciuatin
Conclusion
BASE
OURS
Figure 13: Qualitative Results.
tential of emerging categories like smartphones and accessories, offering forward-looking market opportunity identification, while the base model focused solely on top-performing traditional cate- gories.
Geographic market distribution analysis block) further highlighted the our model's advantages in data granularity. The model provided specific country-level sales figures (e.g., UK: $89.39M,
24

---

Published as a conference paper at ICLR 2026
Genmany: $71.06M), while the base model lacked such precise geographic segmentation. In strate- gic recommendations, the our model explicitly identified expansion opportunities in emerging mar- kets, whereas the base model failed to elaborate specific strategies for these markets.
Promotional strategy effectiveness evaluation block) demonstrated the our model's more com- prehensive promotional campaign coverage. The our model included analysis of additional pro- motional activities, such the "European Summer Sale" ($65.28M) and "European Winter Sale" (S44.05M), which were omitted in the base model. Regarding actionable recommendations, the our model proposed refined seasonal promotional strategies based on regional success patterns, while the base model provided no specific optimization suggestions.
G.2 FORECAST AND PLAN
In the future forecasting and strategic decision-making section block), both models exhibited varying depths across multiple strategic dimensions. For digital transformation, while the base model focused on website optimization and e-commerce partnerships, the our model introduced "personalized recommendation systems," reflecting more advanced technological approach. In store optimization, the base model emphasized operational metries like inventory turnover, whereas the our model prioritized customer experience enhancement.
our model demonstrated superior comprehensiveness in product portfolio strategy by incorporating emerging categories like smartphones and accessories, while the base model focused solely on tra- ditional high-margin products. For geographic expansion, the ours enhanced the base framework by integrating specific promotional strategies such as European seasonal sales campaigns, making expansion plans more actionable and data-driven.
Regarding profitability enhancement, the our model added promotional optimization dimensions, emphasizing "No Discount" strategies and seasonal campaign refinements, demonstrating a more dynamic approach compared to base model's focus on cost management and supply chain op- timization. In customer engagement, the model incorporated multi-channel strategies ensuring consistent experiences across all touch points, while the base model provided only general loyalty program suggestions.
Comprehensive analysis revealed that our PRPO-trained model consistently provided more detailed data support, stronger linguistic expressions, and more specific actionable recommendations. These results demonstrate that PRPO reinforcement learning training significantly enhanced model per- formance in complex multimodal chart deep research tasks, particularly in data integration, insight depth, and the action ability of strategic recommendations for report analysis and generation.
H ETHICS STATEMENT
While our research advances multimodal chart deep research capabilities, we acknowledge poten- tial risks including the possibility of automated systems making erroneous analytical conclusions that could mislead decision-making processes. We emphasize that our methods should be used as analytical assistance tools rather than replacements for human expertise, particularly high-stakes domains such as healthcare or finance.
This work utilized large language models for writing assistance and language polishing. All techni- cal contributions, experimental results, and scientific insights remain solely the work of the authors.
25


Reviews:
[{"review_id": "MvQyqcmqA5", "reviewer": "Reviewer_BU6V", "summary": "Chart deep research, which bridges visual chart understanding and Large Language Model (LLM)-driven deep research capabilities, is a complex task that lies at the intersection of pattern discovery, hypothesis testing, and strategic decision support (lines 41-43). Unfortunately, the investigation of chart deep research has been hindered by 1) a lack of a proper evaluation benchmark and framework and 2) the inability of existing post-training techniques to simultaneously handle multiple reward dimensions and heterogeneous data. This work thus releases MCDR-Bench, a high-quality chart benchmark that consists of complex charts with multi-element, multi-layered information. MCDR-Bench supports both subjective and objective evaluation by assessing the report generation and error identification abilities, respectively. In addition, the authors propose Parallel Relative Policy Optimization (PRPO), a novel Reinforcement Learning framework that is capable of mitigating multi-dimensional reward interference (line 201) and data joint optimization conflicts (line 208). PRPO treats each reward dimension as an \"independent optimization objective\" (Reward) and employs capability-based partitioning during the rollout grouping process (Data). Results on MCDR-Bench, as well as other datasets, show that the proposed method significantly outperforms existing approaches in chart deep research.", "questions": "Please refer to the weaknesses above.", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "- MCDR-Bench is an impactful dataset that can fill an important research gap in academia: a lack of a proper benchmark to evaluate deep research capabilities. Not only does it allow researchers to systematically evaluate the chart understanding ability of multimodal LLMs, but it also contributes to assessing LLMs' deep research report generation capabilities.\n\n- The proposed RL training framework for chart deep research is technically sound. The authors pinpoint two key limitations of GRPO that render it inapplicable to the chart deep research domain, and successfully address them, as demonstrated in impressive empirical results.\n\n- In general, the paper was easy to follow. Multiple visual aids were provided to accompany the technical material. Although the dataset was not provided as part of the submission, the authors included sufficient details in the Appendix to give a sense of what the dataset looks like.", "weaknesses": "- If the authors could verify that PRPO can be used in a model-agnostic manner by training models other than Qwen2.5 with PRPO, it would make the paper even stronger.\n\n- While PRPO greatly advances the optimization algorithm of GRPO, it still relies on the combination of accuracy + format reward. Do the authors anticipate that PRPO could benefit further from more refined reward shaping? For instance, what would happen if we add more vision-centric rewards, such as those proposed in [1,2] to PRPO? (Considering that this is also a multimodal task.)\n\n[1] Visual-RFT: Visual Reinforcement Fine-Tuning\n\n[2] VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Model\n\n- Slight tweak on the above question, do the authors think that PRPO could be generalized to improve the performance on other multimodal tasks?\n\n- Considering that open-sourcing and reproducibility are highly prioritized in today's research landscape (and even more so in datasets & benchmarks papers), I would have appreciated it if the authors had made the benchmark accessible as part of submission (either as an anonymized link or supplementary materials).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "tForLgHyN3", "reviewer": "Reviewer_jssn", "summary": "The authors introduce a unified framework that improves chart research by solving training and evaluation challenges. They present MCDR-Bench, which removes evaluation bottlenecks using an error uniqueness principle that turns subjective assessments into objective error identification, enabling scalable evaluation and reducing reliance on experts. Secondly, authors introduce PRPO, which addresses training bottlenecks by parallel optimization across reward dimensions and capability partitioning across data types, which reduces conflicts between different data and multi-dimensional rewards that have limited progress. Experiments show the combination of their evaluation method and training approach advances chart research beyond surface-level work toward real analytical reasoning and strategic insights, as shown by better exploration, more stable optimization, and stronger performance across multiple analytical dimensions.", "questions": "How does PRPO do against improved GRPO versions?", "limitations": "", "rating": 8, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- Well written paper.\n- Comprehensive evaluations", "weaknesses": "- Related works can be improved", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "mRp0QO2tlW", "reviewer": "Reviewer_GFfR", "summary": "This paper focuses on the chart understanding task of Large Vision-Language Models (LVLMs), aiming to break through the limitation that existing models can only perform simple fact extraction and endow them with complex analytical reasoning capabilities required for \"deep research\". To address the two core issues—training instability caused by multi-dimensional reward conflicts and heterogeneous data, and the lack of an evaluation benchmark suitable for deep analytical reasoning—the study proposes the novel MCDR-Bench benchmark (which transforms subjective chart analysis into an objective error identification task through controlled error injection across five capability dimensions) and the PRPO (Parallel Relative Policy Optimization) training algorithm (extended from GRPO, which mitigates signal interference and gradient conflicts through parallel optimization across reward dimensions and data partitioning by capability type). Additionally, extensive experiments are conducted to verify the effectiveness of the proposed methods.", "questions": "1. Could you explain why, in Table 3, the average response length of GRPO after scalar optimization of rewards is longer than that corresponding to format rewards and accuracy rewards, while PRPO can make the response length fall between the two?\n2. In Table 5, why is there such a large score gap when Level 4 and Level 5 are trained separately? How can this phenomenon be explained?\n3. Transforming the task into error detection will encourage the model to be good at \"discovering injected errors\", but will the model rely on subtle traces during the error injection process rather than genuine deep understanding?\n4. Could you elaborate on the differences between the PRPO method proposed in this paper and the corresponding methods presented in References 1 and 3? \n\n[1]  Nguyen, T., Khan, N., Tran, K., Phan, N., & Khalil, I. (2025). PRPO: Paragraph-level Policy Optimization for Vision-Language Deepfake Detection. arXiv preprint arXiv:2509.26272. \n\n[2]  Yu, Q., Zhang, Z., Zhu, R., Yuan, Y., Zuo, X., Yue, Y., ... & Wang, M. (2025). Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476. \n\n[3]  Zhao, Y., Huang, J., Hu, J., Wang, X., Mao, Y., Zhang, D., ... & Chen, Y. (2025, April). Swift: a scalable lightweight infrastructure for fine-tuning. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 39, No. 28, pp. 29733-29735).", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. The problem and benchmark proposed in the paper are of great significance for the research on deep chart question answering and analytical reasoning.\n\n2. The paper conducts sufficient experiments to verify the effectiveness of the proposed methods.\n\n3. The paper elaborates on the proposed methods in detail.\n\n4. The paper provides code for verifying the experimental results, and this practice is commendable.", "weaknesses": "1. The organizational structure of the paper is suboptimal.\n\n2. Hyperparameter sensitivity: The paper mentions hyperparameters λ_k and λ_m but fails to discuss the sensitivity of the results to their settings, lacking a robustness analysis.\n\n3. There is no detailed comparison of the time and resource consumption of different methods.\n\n4. The comparison with baseline methods of the same type is mainly limited to GRPO. However, there are more recent state-of-the-art (SOTA) methods available, such as DAPO.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kRDGIvMF8W", "reviewer": "Reviewer_ehoV", "summary": "This paper addresses the challenge of enabling \"deep research\" capabilities in large vision-language models for chart understanding, moving beyond simple factual question answering to complex analytical reasoning. The authors identify a training bottleneck and an evaluation bottleneck. To tackle these, the paper makes two main contributions. First, it introduces Parallel Relative Policy Optimization (PRPO), an algorithm that extends Group Relative Policy Optimization (GRPO) by parallelizing optimization across different reward dimensions (Reward-PRPO) and partitioning data by capability type (Data-PRPO). Second, it proposes a new benchmark, MCDR-Bench, which evaluates deep research capabilities by transforming subjective report generation tasks into objective error-identification tasks based on a novel \"error uniqueness principle.\" The experiments show that PRPO significantly outperforms the GRPO baseline on MCDR-Bench.", "questions": "Please see weaknesses.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The motivation and premise of this paper are well-considered. The design of MCDR-Bench also holds certain significance.", "weaknesses": "I have the following concerns, and if the authors can address them, I will raise the rating.\n1. The PRPO algorithm appears to introduce significant computational overhead, both in terms of training time and token consumption, due to the parallel reward calculations and the iterative data partitioning process. However, the paper provides no experimental data or theoretical analysis on this front. While the performance gains are impressive, a discussion of the trade-off between performance and computational cost is essential for understanding the practical utility of the method.\n2. A central motivation for PRPO is to resolve conflicts between optimization objectives. However, the proposed solution—a weighted sum of losses with fixed hyperparameters $\\lambda_k$ and $\\lambda_m$—does not fully address this issue. Firstly, manually tuning the $M_{final} + K$ hyperparameters is impractical. The paper states that a default mean aggregation is used(4), which implies uniform weighting. This is unlikely to be optimal and sidesteps the challenge of balancing different objectives. A static, linear combination of losses, as in Equation 4 ($J(\\theta) = \\sum_{k=1}^{K}\\lambda_{k} \\mathcal{L}_k$)(5), does not fundamentally resolve gradient conflicts. During optimization, the gradients from different objectives $\\mathcal{L}_k$ can still point in conflicting directions, leading to destructive interference. This problem has been extensively studied in the field of multi-objective optimization (MOO). The authors should consider and discuss more principled MOO approaches (e.g., [1]) instead of relying on fixed weights.\n3. The core innovation of MCDR-Bench is transforming subjective evaluation into objective error identification via synthetic error injection. While this is a clever evaluation paradigm, the paper does not sufficiently discuss whether these synthetically injected errors are truly representative of the typical failure modes of state-of-the-art LVLMs in real-world scenarios. The paper asserts that the errors are designed to mirror \"typical cognitive biases and logical fallacies\", but there's a risk that the model is simply being trained to detect a specific, synthetic class of errors, which may not perfectly correlate with its ability to produce accurate and logically coherent analysis on its own.\n\n[1] Ozan Sener and Vladlen Koltun. Multi-task learning as multi-objective optimization. Advances in neural information processing systems, 31, 2018.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)