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REVIEW 4 major objections 6 minor 73 references

For chart questions, a vision-language model that first decides whether to reason in code or directly from the image outperforms any single fixed reasoning strategy across four benchmarks.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 19:20 UTC pith:URDMQ2CU

load-bearing objection Nice framework idea, but the headline result is a one-point average margin with no error bars and a 3B-scale evaluation that looks broken; worth a serious referee for the framing, not for the numbers as reported. the 4 major comments →

arxiv 2509.09286 v1 pith:URDMQ2CU submitted 2025-09-11 cs.CV

Visual Programmability: A Guide for Code-as-Thought in Chart Understanding

Bohao Tang , Yan Ma , Fei Zhang , Jiadi Su , Ethan Chern , Zhulin Hu , Zhixin Wang , Pengfei Liu
show 1 more author
Ya Zhang
This is my paper
classification cs.CV
keywords chart understandingvision-language modelscode-as-thoughtvisual programmabilityadaptive reasoningreinforcement learningGRPOnumerical hallucination
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper claims that the best way to answer a chart question is not a single reasoning style but a learned choice between two: write code to extract and compute, or reason directly over the image. It introduces Visual Programmability, a property of a chart-question pair that says whether code can faithfully capture what the question needs, and trains a vision-language model to emit a strategy token before answering. The model is trained with reinforcement learning using rewards for answer correctness, for choosing the right strategy, and for extracting the chart's data faithfully. Across four benchmarks the adaptive model averages 62.8% accuracy, ahead of fixed Code-CoT at 61.7% and Standard CoT at 61.2%, and it adjusts code usage from above 60% on structured charts to roughly 10% on complex scientific charts. This matters because it moves chart understanding from building a better single reasoner to teaching a model when each way of reasoning applies.

Core claim

The central claim: Code-as-Thought is powerful but not universal; a fixed code-only specialist reaches 71.6% on structured ChartX charts yet collapses to 18.4% on in-the-wild CharXiv charts. Visual Programmability is a task-dependent property of a chart-question pair: whether the chart's essential information can be faithfully translated into code. The adaptive model emits a strategy token (<CODE> or <DIRECT>) and then reasons along that path, trained with group-relative policy optimization (GRPO) under a reward combining answer accuracy, a decision reward for strategy selection, a data-accuracy reward comparing generated DataFrames to ground-truth tables, and a format reward. The model aver

What carries the argument

The central object is Visual Programmability: a learnable, task-dependent property gauging whether a chart-question pair can be faithfully reasoned about in code, ranging from high (clean bar/line charts with explicit values) to low (scientific plots whose meaning lives in contours and distributions). The framework factorizes the policy as P(y|I,Q)=P(s|I,Q)·P(y|I,Q,s), where s is a strategy token in {<CODE>,<DIRECT>}, and trains the selection policy with Group Relative Policy Optimization (GRPO) under the weighted reward R = w_acc·r_acc + w_decision·r_decision + w_data·r_data + w_format·r_format. The decision reward gives positive signal for choosing the human-annotated correct strategy even

Load-bearing premise

The framework assumes that expert annotators' judgments about whether a chart's information survives translation into code are a reliable guide to which reasoning strategy actually maximizes accuracy; if those human labels are subjective or inconsistent, the decision reward trains the model toward a flawed strategy boundary.

What would settle it

On a held-out set of chart-question pairs, compare each pair's human programmability label with the actual accuracies of the <CODE> and <DIRECT> paths. If the path the human label designates is not systematically the more accurate one, or if independent annotators disagree on the labels, the decision reward is training the model on labels that do not track performance, and removing the decision reward should not hurt accuracy.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Fixed code-only chart systems will keep failing on complex real-world charts no matter how well they code, because the gap is strategic, not skill-based: the model must know when not to code.
  • The decision reward is what prevents mode collapse: without it the model collapses to 0% or 100% code usage and loses performance on low-programmability charts; with it code usage tracks benchmark programmability.
  • The data-accuracy reward reduces numerical hallucination: on ChartX, high-fidelity data extraction (>0.8 reward score) correlates with 85.6% answer accuracy versus 48.4% for low-fidelity (<0.6), and the model unlearns guessing on low-fidelity tasks.
  • The adaptive framework scales to larger models: at 32B it posts the highest average accuracy (61.0%) and the best scores on ChartX and CharXiv; at 3B the adaptive prompt is too cognitively demanding and fixed Code-CoT wins.
  • The adaptive advantage comes where fixed strategies are weak: 44.3% versus 41.9% on CharXiv against fixed code, and 65.6% versus 61.5% on ChartX against standard CoT.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The binary code/direct split is likely a simplification: hybrid reasoning that uses code for data extraction and direct visual reasoning for qualitative pattern interpretation may beat either pure pathway on mid-programmability charts, a direction the paper lists as future work.
  • The annotation bottleneck could be removed: a self-supervised variant that derives programmability labels from whether the code path answered correctly on each instance might learn the same decision boundary without human annotation.
  • The strategy-token plus dual-reward recipe likely transfers to other visual-analytic domains, such as diagrams, maps, and document figures, where symbolic extraction and holistic reading trade off; the paper does not test this extension.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper introduces Visual Programmability, a per-task property indicating whether a chart–question pair is better solved by generating and executing code (Code-as-Thought) or by direct visual reasoning. The authors implement an adaptive framework on Qwen2.5-VL-7B that first emits a strategy token (<CODE> or <DIRECT>) and then follows the corresponding reasoning path. Training uses GRPO with a four-component reward (Eq. 3), including a data-accuracy reward that compares the DataFrame produced by the generated code with a ground-truth CSV, and a decision reward that encourages matching a human-annotated programmability label. Experiments on ChartX, ChartBench, ChartQA, and CharXiv report an average accuracy of 62.8% for the adaptive model versus 61.7% for fixed Code-CoT and 61.2% for fixed Standard CoT (Table 1). Ablations (Tables 5–6) attribute the gains to the decision and data-accuracy rewards. The paper also reports scaling experiments to 3B and 32B models (Table 4) and qualitative case studies.

Significance. If the empirical claims held up, the paper would make a useful contribution: the idea of learning when to use symbolic code vs. direct perception is intuitive, and the data-accuracy reward is a concrete mechanism for grounding code-based reasoning in chart facts. The authors ship substantial experimental infrastructure, detailed prompts, hyperparameters, and an open-source implementation, which are strengths. The central weakness is that the reported evidence does not support the headline claim of 'consistently outperforming' rigid strategies: the margins in Table 1 are about one point, there are no error bars, seeds, or significance tests, and the adaptive model is not the best on ChartQA. The selective code-usage behavior (e.g., 76% on ChartX vs. 10% on CharXiv, Table 2) is also, by construction, a direct consequence of the decision reward in Eq. (3), not an emergent discovery; the paper frames it as learned adaptive behavior without validating that human programmability labels correlate with the accuracy-optimal strategy. These issues are fixable with additional analysis and qualified claims, so the paper merits major revision rather than rejection.

major comments (4)
  1. [§5.2, Table 1] The abstract and §5.2 claim that the adaptive model 'consistently outperforms' rigid strategies. The evidence in Table 1 is too weak to support this: the average advantage over fixed Code-CoT is 1.1 points (62.8 vs. 61.7), and on ChartQA the adaptive model (86.4) is lower than both fixed Code-CoT (86.7) and Standard CoT (86.6). No standard deviations, number of seeds, confidence intervals, or significance tests are reported anywhere. Given benchmark sizes of roughly 1,100–2,400 samples per dataset, a 1-point gap can easily arise from evaluation noise. Please report variance across at least 3–5 seeds (or a bootstrap CI) and use a paired test for the per-benchmark comparisons; alternatively, temper the claim to 'competitive or slightly better on average.'
  2. [§5.4, Table 4] Table 4 contains unexplained anomalies that suggest an unstable evaluation pipeline. On the 3B base model, the Adaptive strategy scores 1.0% on ChartX, 0.7% on ChartBench, and 0.3% on ChartQA, while Standard CoT scores 48.0%, 39.2%, and 13.8% respectively. A factor-of-~50 drop for merely adding a strategy-selection prefix is not a 'performance gap'; it indicates either a parsing failure (e.g., the base model did not emit the expected special token for most samples) or a broken evaluation harness for that condition. Similarly, RL-trained Standard CoT collapses from a 31.9% average to 20.4% after training, with ChartQA dropping from 13.8% to 41.8% (the reader should confirm this is not a typo: the table shows an increase at ChartQA but large decreases elsewhere). The paper acknowledges the 3B result is 'nuanced' but does not diagnose these pathologies. Please report the cause or remove the
  3. [§4.3.2, Eq. (3); §5.2, Table 2] The decision reward r_decision explicitly rewards the model for choosing the human-annotated strategy: 'It gives a full reward for a correct answer via the correct strategy, a partial reward for a wrong answer but using the correct strategy, and zero reward for using the wrong strategy.' Therefore the code-usage percentages in Table 2 (76% on ChartX, 10% on CharXiv) are a direct consequence of fitting the annotation labels, not an emergent property of the model learning to reason about programmability. The paper repeatedly frames these percentages as evidence of learned adaptivity. To support that framing, Appendix D must demonstrate that the human labels are reliable and correlate with actual optimal strategy. Currently it provides no inter-annotator agreement statistics, no second-annotator validation, and no evidence that the annotated strategy is the one that maximizes accuracy on th
  4. [Appendix D, Appendix F] The annotation framework is load-bearing for the decision reward, as the paper itself acknowledges in Appendix F ('A key challenge is reducing the reliance on annotated training data for programmability.') The criteria in Appendix D are subjective: annotators are asked whether 'a code-based representation preserves the essential information' and to perform a 'mental compilation,' with no quantitative measures of reliability. Since the central result depends on the decision reward steering the policy, the paper must at minimum report agreement (e.g., Cohen's kappa) on a held-out annotation set and, ideally, validate labels against accuracy-based oracle selection on a small subsample. Without that, the reader cannot distinguish 'the model learned human annotators' preferences' from 'the model learned the accuracy-optimal strategy.'
minor comments (6)
  1. [Table 5 caption and header] The ablation rows use 'w/or decision' and 'w/or data' in the table header; this is a typo for 'w/o' (without). Please correct.
  2. [§5.2, Table 1 note] The note says 'All values are accuracy (%).' but the table also includes an 'Average' column; consider clarifying that the average is the unweighted mean across the four benchmarks, and state whether the benchmarks have equal weight despite different sample sizes.
  3. [§5.4, Table 4] For the 3B base model, the Adaptive row is visually remarkable but never discussed after the table. Either provide an explanation (e.g., failure to emit <CODE>/<DIRECT> tokens) or remove the row; as written, it raises more questions than it answers.
  4. [§4.3.2 and Algorithm 1] The Data Accuracy Reward formula in Algorithm 1 uses a row completeness score that is 1 only if the row counts exactly match (r_row = 1[len(DF_pred) == len(DF_gt)]). This is very brittle; consider using a soft or proportional row-match score, and state whether this strictness affected training.
  5. [Appendix A, Table 8] The appendix says the specialist was trained on 'the ChartX validation set' and evaluated on 'a stratified sample from the official test set.' Please clarify the relationship between the training/validation split and the test split to rule out test-set contamination.
  6. [General] Several appendix cross-references are incomplete, e.g., 'Prompt E' is referred to without distinguishing the three different prompts. Consider labeling them Prompt E.1, E.2, E.3.

Circularity Check

1 steps flagged

Partial circularity: the reported adaptive strategy-selection behavior is directly entailed by the decision reward and the human-annotated Visual Programmability labels; the benchmark accuracy comparison itself is independent.

specific steps
  1. fitted input called prediction [Section 4.3.2 (Equation 3, r_decision); Section 5.2 (Table 2); Appendix D.1]
    "This reward explicitly incentivizes selecting the correct strategy based on the chart’s pre-annotated Visual Programmability. It gives a full reward for a correct answer via the correct strategy, a partial reward for a wrong answer but using the correct strategy (to encourage exploration), and zero reward for using the wrong strategy. ... We built our methodology around a single, functional question for annotators:"Does a code-based representation preserve the essential information required to correctly answer this question?""

    The decision reward r_decision is defined directly over the human-annotated VP label: positive reward is given only when the model's <CODE>/<DIRECT> selection matches the label, and zero reward is given for the 'wrong strategy.' Maximizing this reward fits the policy's selection distribution to the annotation prior. Section 5.2 then presents Table 2's code-usage rates (76.0% on ChartX, 10.1% on CharXiv) as evidence that the model 'learns to apply code frequently on high-programmability charts and sparingly on low-programmability ones.' These rates are the training target read back out, not an independent discovery of an optimal strategy. The headline accuracy comparison remains an external benchmark result, so the circularity is partial, but the 'adaptive behavior' claim reduces by constru

full rationale

One clear reduction-by-construction exists: the strategy-selection percentages used to demonstrate adaptive behavior are entailed by r_decision, which rewards exactly the human-annotated VP label. This matches the fitted-input-called-prediction pattern. The central accuracy claim (62.8% vs 61.7% / 61.2%) does not itself reduce to the reward: it is measured on external benchmarks and depends on the accuracy reward, data reward, and model capability. No load-bearing self-citation or imported uniqueness theorem is present. Appendix F explicitly acknowledges reliance on annotated programmability data, confirming the decision boundary is imported from annotations rather than derived. Accordingly, the paper is partially circular in its adaptive-behavior evidence but retains independent content in its benchmark comparison, giving a score of 5.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 1 invented entities

The central claim rests on human-annotated programmability labels, which are subjective and unvalidated. The reward weights and data-accuracy reward components are fitted to the validation data, and several thresholds are hand-chosen. These parameters and assumptions are load-bearing for the claimed adaptive behavior.

free parameters (3)
  • Reward weights (w_acc, w_decision, w_data, w_format) = 0.8, 0.3, 0.15, 0.05
    Tuned on a validation set (Section 5.1) to maximize average accuracy; these weights directly shape the learned selection policy.
  • Data accuracy reward component weights (0.2, 0.1, 0.7) = 0.2, 0.1, 0.7
    Hand-chosen in Algorithm 1 to combine column, row, and value fidelity; no sensitivity analysis is provided.
  • Fuzzy match threshold and value tolerance = match_score > 50; relative tolerance 1e-2
    Hand-chosen in Appendix C to define column matching and numerical comparison; affects the data accuracy reward.
axioms (4)
  • domain assumption Human annotations of Visual Programmability are a reliable ground truth for the optimal reasoning strategy.
    The decision reward (Eq. 3) rewards choosing the annotated strategy; if annotations are inconsistent or misaligned with accuracy, the learned policy is biased.
  • domain assumption The code used to generate a chart from ChartMimic is the ground-truth data for the Data Accuracy Reward.
    r_data compares the model's DataFrame to a CSV parsed from the generation code; this assumes the generation code exactly reflects the chart's visual data.
  • ad hoc to paper GRPO without KL penalty (beta=0) is a stable optimization setup.
    Section 4.3.1 sets beta=0 with no comparison to beta>0; this could affect training stability and final policy.
  • domain assumption The strategy token (<CODE>/<DIRECT>) faithfully indicates the reasoning path actually used.
    The factorization in Eq. 1 assumes the choice of token determines the generation path; if the model emits a token but generates the other path, the code usage analysis is invalid.
invented entities (1)
  • Visual Programmability independent evidence
    purpose: A learnable property that labels chart-question pairs as suitable for code-based or direct visual reasoning; used as the target for the decision reward.
    The paper provides measurable code-usage percentages across benchmarks as an observable handle, but the property is defined by human annotation rather than an external ground truth.

pith-pipeline@v1.3.0-alltime-deepseek · 18581 in / 11126 out tokens · 115837 ms · 2026-08-04T19:20:52.329841+00:00 · methodology

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Cite this review

Pith. "Pith review of Visual Programmability: A Guide for Code-as-Thought in Chart Understanding." pith.science (2026). https://pith.science/paper/URDMQ2CU

@misc{pith2026250909286,
  author       = {Pith},
  title        = {Pith review of: Visual Programmability: A Guide for Code-as-Thought in Chart Understanding},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/URDMQ2CU}},
  note         = {Machine review of arXiv:2509.09286}
}
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read the original abstract

Chart understanding presents a critical test to the reasoning capabilities of Vision-Language Models (VLMs). Prior approaches face critical limitations: some rely on external tools, making them brittle and constrained by a predefined toolkit, while others fine-tune specialist models that often adopt a single reasoning strategy, such as text-based chain-of-thought (CoT). The intermediate steps of text-based reasoning are difficult to verify, which complicates the use of reinforcement-learning signals that reward factual accuracy. To address this, we propose a Code-as-Thought (CaT) approach to represent the visual information of a chart in a verifiable, symbolic format. Our key insight is that this strategy must be adaptive: a fixed, code-only implementation consistently fails on complex charts where symbolic representation is unsuitable. This finding leads us to introduce Visual Programmability: a learnable property that determines if a chart-question pair is better solved with code or direct visual analysis. We implement this concept in an adaptive framework where a VLM learns to choose between the CaT pathway and a direct visual reasoning pathway. The selection policy of the model is trained with reinforcement learning using a novel dual-reward system. This system combines a data-accuracy reward to ground the model in facts and prevent numerical hallucination, with a decision reward that teaches the model when to use each strategy, preventing it from defaulting to a single reasoning mode. Experiments demonstrate strong and robust performance across diverse chart-understanding benchmarks. Our work shows that VLMs can be taught not only to reason but also how to reason, dynamically selecting the optimal reasoning pathway for each task.

Figures

Figures reproduced from arXiv: 2509.09286 by Bohao Tang, Ethan Chern, Fei Zhang, Jiadi Su, Pengfei Liu, Yan Ma, Ya Zhang, Zhixin Wang, Zhulin Hu.

Figure 1
Figure 1. Figure 1: Adaptive Reasoning vs. Fixed Strategies for Chart Understanding. Prevailing approaches [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance of Fixed Strategies Highlights a Critical Trade-off. While the Code-as￾Thought (CaT) strategy excels on structured charts (ChartX), its performance collapses on complex, ’in-the-wild’ charts (CharXiv). All values are accuracy (%). The results reveal a sharp dichotomy in generalization performance. As shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of our adaptive reasoning framework. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cases of Visual Programmability for different charts and tasks. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of the Data Accuracy Reward calculation. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Training dynamics on ChartX, illustrating the effect of the Data Accuracy Reward ( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Failure of a Rigid Code-Based Strategy on a CharXiv Example. The model is tasked with analyzing the original chart (a) from the CharXiv dataset. It generates Python code (indicated in the red box) to extract the data, but this code hallucinates an incorrect data structure. Chart (b) is the visualization produced by executing the model’s flawed code. The model then faithfully reasons over its own erroneous … view at source ↗
Figure 8
Figure 8. Figure 8: Case Study 1: High-Programmability Chart from ChartX. [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Case Study 2: Low-Programmability Chart from CharXiv. [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

73 extracted references · 34 linked inside Pith

  1. [1]

    Gpt-4 technical report.arXiv preprint arXiv:2303.08774, 2023

    Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report.arXiv preprint arXiv:2303.08774, 2023

    Pith/arXiv arXiv 2023

  2. [2]

    Self-imagine: Effective unimodal reasoning with multimodal models using self-imagination.arXiv preprint arXiv:2401.08025, 2024

    Syeda Nahida Akter, Aman Madaan, Sangwu Lee, Yiming Yang, and Eric Nyberg. Self-imagine: Effective unimodal reasoning with multimodal models using self-imagination.arXiv preprint arXiv:2401.08025, 2024

    Pith/arXiv arXiv 2024

  3. [3]

    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:2502.13923, 2025

    Pith/arXiv arXiv 2025

  4. [4]

    Conditional computa- tion in neural networks for faster models.arXiv preprint arXiv:1511.06297, 2015

    Emmanuel Bengio, Pierre-Luc Bacon, Joelle Pineau, and Doina Precup. Conditional computa- tion in neural networks for faster models.arXiv preprint arXiv:1511.06297, 2015

    Pith/arXiv arXiv 2015

  5. [5]

    Language models are few-shot learners.Advances in neural information processing systems, 33:1877–1901, 2020

    Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners.Advances in neural information processing systems, 33:1877–1901, 2020

    1901

  6. [6]

    Genome: gen- erative neuro-symbolic visual reasoning by growing and reusing modules.arXiv preprint arXiv:2311.04901, 2023

    Zhenfang Chen, Rui Sun, Wenjun Liu, Yining Hong, and Chuang Gan. Genome: gen- erative neuro-symbolic visual reasoning by growing and reusing modules.arXiv preprint arXiv:2311.04901, 2023

    Pith/arXiv arXiv 2023

  7. [7]

    Chartreader: A unified framework for chart derendering and comprehension without heuristic rules

    Zhi-Qi Cheng, Qi Dai, and Alexander G Hauptmann. Chartreader: A unified framework for chart derendering and comprehension without heuristic rules. InProceedings of the IEEE/CVF International Conference on Computer Vision, pages 22202–22213, 2023

    2023

  8. [8]

    Gemini 2.5: Pushing the frontier with advanced reasoning, multimodality, long context, and next generation agentic capabilities.arXiv preprint arXiv:2507.06261, 2025

    Gheorghe Comanici, Eric Bieber, Mike Schaekermann, Ice Pasupat, Noveen Sachdeva, Inderjit Dhillon, Marcel Blistein, Ori Ram, Dan Zhang, Evan Rosen, et al. Gemini 2.5: Pushing the frontier with advanced reasoning, multimodality, long context, and next generation agentic capabilities.arXiv preprint arXiv:2507.06261, 2025

    Pith/arXiv arXiv 2025

  9. [9]

    Instructblip: Towards general-purpose vision-language models with instruction tuning.Advances in neural information processing systems, 36:49250–49267, 2023

    Wenliang Dai, Junnan Li, Dongxu Li, Anthony Tiong, Junqi Zhao, Weisheng Wang, Boyang Li, Pascale N Fung, and Steven Hoi. Instructblip: Towards general-purpose vision-language models with instruction tuning.Advances in neural information processing systems, 36:49250–49267, 2023

    2023

  10. [10]

    Msg-chart: Multimodal scene graph for chartqa

    Yue Dai, Soyeon Caren Han, and Wei Liu. Msg-chart: Multimodal scene graph for chartqa. InProceedings of the 33rd ACM International Conference on Information and Knowledge Management, pages 3709–3713, 2024. 12

    2024

  11. [11]

    Pal: Program-aided language models

    Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. Pal: Program-aided language models. InInternational Conference on Machine Learning, pages 10764–10799. PMLR, 2023

    2023

  12. [12]

    Adaptive computation time for recurrent neural networks.arXiv preprint arXiv:1603.08983, 2016

    Alex Graves. Adaptive computation time for recurrent neural networks.arXiv preprint arXiv:1603.08983, 2016

    Pith/arXiv arXiv 2016

  13. [13]

    Visual programming: Compositional visual reasoning without training

    Tanmay Gupta and Aniruddha Kembhavi. Visual programming: Compositional visual reasoning without training. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 14953–14962, 2023

    2023

  14. [14]

    Chartllama: A multimodal llm for chart understanding and generation.arXiv preprint arXiv:2311.16483, 2023

    Yucheng Han, Chi Zhang, Xin Chen, Xu Yang, Zhibin Wang, Gang Yu, Bin Fu, and Hanwang Zhang. Chartllama: A multimodal llm for chart understanding and generation.arXiv preprint arXiv:2311.16483, 2023

    Pith/arXiv arXiv 2023

  15. [15]

    From pixels to insights: A survey on automatic chart understanding in the era of large foundation models.IEEE Transactions on Knowledge and Data Engineering, 2024

    Kung-Hsiang Huang, Hou Pong Chan, Yi R Fung, Haoyi Qiu, Mingyang Zhou, Shafiq Joty, Shih-Fu Chang, and Heng Ji. From pixels to insights: A survey on automatic chart understanding in the era of large foundation models.IEEE Transactions on Knowledge and Data Engineering, 2024

    2024

  16. [16]

    Vprochart: Answering chart question through visual perception alignment agent and programmatic solution reasoning

    Muye Huang, Lingling Zhang, Han Lai, Wenjun Wu, Xinyu Zhang, and Jun Liu. Vprochart: Answering chart question through visual perception alignment agent and programmatic solution reasoning. InProceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 3689–3696, 2025

    2025

  17. [17]

    Chartsketcher: Reasoning with multimodal feedback and reflection for chart understanding.arXiv preprint arXiv:2505.19076, 2025

    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 understanding.arXiv preprint arXiv:2505.19076, 2025

    Pith/arXiv arXiv 2025

  18. [18]

    Mohammed Saidul Islam, Raian Rahman, Ahmed Masry, Md Tahmid Rahman Laskar, Mir Tafseer Nayeem, and Enamul Hoque. Are large vision language models up to the challenge of chart comprehension and reasoning? an extensive investigation into the capabilities and limitations of lvlms.arXiv preprint arXiv:2406.00257, 2024

    Pith/arXiv arXiv 2024

  19. [19]

    Mixtral of experts.arXiv preprint arXiv:2401.04088, 2024

    Albert Q Jiang, Alexandre Sablayrolles, Antoine Roux, Arthur Mensch, Blanche Savary, Chris Bamford, Devendra Singh Chaplot, Diego de las Casas, Emma Bou Hanna, Florian Bressand, et al. Mixtral of experts.arXiv preprint arXiv:2401.04088, 2024

    Pith/arXiv arXiv 2024

  20. [20]

    macmillan, 2011

    Daniel Kahneman.Thinking, fast and slow. macmillan, 2011

    2011

  21. [21]

    Pix2struct: Screenshot parsing as pretraining for visual language understanding

    Kenton Lee, Mandar Joshi, Iulia Raluca Turc, Hexiang Hu, Fangyu Liu, Julian Martin Eisensch- los, Urvashi Khandelwal, Peter Shaw, Ming-Wei Chang, and Kristina Toutanova. Pix2struct: Screenshot parsing as pretraining for visual language understanding. InInternational Confer- ence on Machine Learning, pages 18893–18912. PMLR, 2023

    2023

  22. [22]

    Blip-2: Bootstrapping language-image pre-training with frozen image encoders and large language models

    Junnan Li, Dongxu Li, Silvio Savarese, and Steven Hoi. Blip-2: Bootstrapping language-image pre-training with frozen image encoders and large language models. InInternational conference on machine learning, pages 19730–19742. PMLR, 2023

    2023

  23. [23]

    Blip: Bootstrapping language- image pre-training for unified vision-language understanding and generation

    Junnan Li, Dongxu Li, Caiming Xiong, and Steven Hoi. Blip: Bootstrapping language- image pre-training for unified vision-language understanding and generation. InInternational conference on machine learning, pages 12888–12900. PMLR, 2022

    2022

  24. [24]

    Let’s verify step by step

    Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. InThe Twelfth International Conference on Learning Representations, 2023

    2023

  25. [25]

    Deplot: One-shot visual language reasoning by plot-to-table translation.arXiv preprint arXiv:2212.10505, 2022

    Fangyu Liu, Julian Martin Eisenschlos, Francesco Piccinno, Syrine Krichene, Chenxi Pang, Kenton Lee, Mandar Joshi, Wenhu Chen, Nigel Collier, and Yasemin Altun. Deplot: One-shot visual language reasoning by plot-to-table translation.arXiv preprint arXiv:2212.10505, 2022

    Pith/arXiv arXiv 2022

  26. [26]

    Visual instruction tuning.Advances in neural information processing systems, 36:34892–34916, 2023

    Haotian Liu, Chunyuan Li, Qingyang Wu, and Yong Jae Lee. Visual instruction tuning.Advances in neural information processing systems, 36:34892–34916, 2023. 13

    2023

  27. [27]

    One rl to see them all: Visual triple unified reinforce- ment learning.arXiv preprint arXiv:2505.18129, 2025

    Yan Ma, Linge Du, Xuyang Shen, Shaoxiang Chen, Pengfei Li, Qibing Ren, Lizhuang Ma, Yuchao Dai, Pengfei Liu, and Junjie Yan. One rl to see them all: Visual triple unified reinforce- ment learning.arXiv preprint arXiv:2505.18129, 2025

    Pith/arXiv arXiv 2025

  28. [28]

    Unichart: A universal vision-language pretrained model for chart comprehension and reasoning.arXiv preprint arXiv:2305.14761, 2023

    Ahmed Masry, Parsa Kavehzadeh, Xuan Long Do, Enamul Hoque, and Shafiq Joty. Unichart: A universal vision-language pretrained model for chart comprehension and reasoning.arXiv preprint arXiv:2305.14761, 2023

    Pith/arXiv arXiv 2023

  29. [29]

    Chartqa: A benchmark for question answering about charts with visual and logical reasoning.arXiv preprint arXiv:2203.10244, 2022

    Ahmed Masry, Do Xuan Long, Jia Qing Tan, Shafiq Joty, and Enamul Hoque. Chartqa: A benchmark for question answering about charts with visual and logical reasoning.arXiv preprint arXiv:2203.10244, 2022

    Pith/arXiv arXiv 2022

  30. [30]

    Chartgemma: Visual instruction-tuning for chart reasoning in the wild.arXiv preprint arXiv:2407.04172, 2024

    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

    Pith/arXiv arXiv 2024

  31. [31]

    Mm-eureka: Exploring the frontiers of multimodal reasoning with rule-based reinforcement learning.arXiv preprint arXiv:2503.07365, 2025

    Fanqing Meng, Lingxiao Du, Zongkai Liu, Zhixiang Zhou, Quanfeng Lu, Daocheng Fu, Tiancheng Han, Botian Shi, Wenhai Wang, Junjun He, et al. Mm-eureka: Exploring the frontiers of multimodal reasoning with rule-based reinforcement learning.arXiv preprint arXiv:2503.07365, 2025

    Pith/arXiv arXiv 2025

  32. [32]

    Chartassisstant: A universal chart multimodal language model via chart-to-table pre-training and multitask instruction tuning.arXiv preprint arXiv:2401.02384, 2024

    Fanqing Meng, Wenqi Shao, Quanfeng Lu, Peng Gao, Kaipeng Zhang, Yu Qiao, and Ping Luo. Chartassisstant: A universal chart multimodal language model via chart-to-table pre-training and multitask instruction tuning.arXiv preprint arXiv:2401.02384, 2024

    Pith/arXiv arXiv 2024

  33. [33]

    Plotqa: Reasoning over scientific plots

    Nitesh Methani, Pritha Ganguly, Mitesh M Khapra, and Pratyush Kumar. Plotqa: Reasoning over scientific plots. InProceedings of the ieee/cvf winter conference on applications of computer vision, pages 1527–1536, 2020

    2020

  34. [34]

    Point-rft: Improving multimodal reasoning with visually grounded reinforcement finetuning.arXiv preprint arXiv:2505.19702, 2025

    Minheng Ni, Zhengyuan Yang, Linjie Li, Chung-Ching Lin, Kevin Lin, Wangmeng Zuo, and Lijuan Wang. Point-rft: Improving multimodal reasoning with visually grounded reinforcement finetuning.arXiv preprint arXiv:2505.19702, 2025

    Pith/arXiv arXiv 2025

  35. [35]

    Gpt-5 system card

    OpenAI. Gpt-5 system card. Technical report, OpenAI, 2025. PDF available; Accessed: 2025-08-11

    2025

  36. [36]

    Training language models to follow instructions with human feedback.Advances in neural information processing systems, 35:27730–27744, 2022

    Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. Training language models to follow instructions with human feedback.Advances in neural information processing systems, 35:27730–27744, 2022

    2022

  37. [37]

    Adamml: Adaptive multi-modal learning for efficient video recognition

    Rameswar Panda, Chun-Fu Richard Chen, Quanfu Fan, Ximeng Sun, Kate Saenko, Aude Oliva, and Rogerio Feris. Adamml: Adaptive multi-modal learning for efficient video recognition. In Proceedings of the IEEE/CVF international conference on computer vision, pages 7576–7585, 2021

    2021

  38. [38]

    Talm: Tool augmented language models.arXiv preprint arXiv:2205.12255, 2022

    Aaron Parisi, Yao Zhao, and Noah Fiedel. Talm: Tool augmented language models.arXiv preprint arXiv:2205.12255, 2022

    Pith/arXiv arXiv 2022

  39. [39]

    Gorilla: Large language model connected with massive apis.Advances in Neural Information Processing Systems, 37:126544–126565, 2024

    Shishir G Patil, Tianjun Zhang, Xin Wang, and Joseph E Gonzalez. Gorilla: Large language model connected with massive apis.Advances in Neural Information Processing Systems, 37:126544–126565, 2024

    2024

  40. [40]

    Learning transferable visual models from natural language supervision

    Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. InInternational conference on machine learning, pages 8748–8763. PmLR, 2021

    2021

  41. [41]

    Direct preference optimization: Your language model is secretly a reward model

    Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. Direct preference optimization: Your language model is secretly a reward model. Advances in neural information processing systems, 36:53728–53741, 2023

    2023

  42. [42]

    Dynamic routing between capsules

    Sara Sabour, Nicholas Frosst, and Geoffrey E Hinton. Dynamic routing between capsules. Advances in neural information processing systems, 30, 2017. 14

    2017

  43. [43]

    Toolformer: Language models can teach themselves to use tools.Advances in Neural Information Processing Systems, 36:68539– 68551, 2023

    Timo Schick, Jane Dwivedi-Yu, Roberto Dessì, Roberta Raileanu, Maria Lomeli, Eric Hambro, Luke Zettlemoyer, Nicola Cancedda, and Thomas Scialom. Toolformer: Language models can teach themselves to use tools.Advances in Neural Information Processing Systems, 36:68539– 68551, 2023

    2023

  44. [44]

    Deepseekmath: Pushing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024

    Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models.arXiv preprint arXiv:2402.03300, 2024

    Pith/arXiv arXiv 2024

  45. [45]

    Reflexion: Language agents with verbal reinforcement learning.Advances in Neural Information Processing Systems, 36:8634–8652, 2023

    Noah Shinn, Federico Cassano, Ashwin Gopinath, Karthik Narasimhan, and Shunyu Yao. Reflexion: Language agents with verbal reinforcement learning.Advances in Neural Information Processing Systems, 36:8634–8652, 2023

    2023

  46. [46]

    Openthinkimg: Learning to think with images via visual tool reinforcement learning.arXiv preprint arXiv:2505.08617, 2025

    Zhaochen Su, Linjie Li, Mingyang Song, Yunzhuo Hao, Zhengyuan Yang, Jun Zhang, Guanjie Chen, Jiawei Gu, Juntao Li, Xiaoye Qu, et al. Openthinkimg: Learning to think with images via visual tool reinforcement learning.arXiv preprint arXiv:2505.08617, 2025

    Pith/arXiv arXiv 2025

  47. [47]

    Modular visual question answering via code generation.arXiv preprint arXiv:2306.05392, 2023

    Sanjay Subramanian, Medhini Narasimhan, Kushal Khangaonkar, Kevin Yang, Arsha Nagrani, Cordelia Schmid, Andy Zeng, Trevor Darrell, and Dan Klein. Modular visual question answering via code generation.arXiv preprint arXiv:2306.05392, 2023

    Pith/arXiv arXiv 2023

  48. [48]

    Vipergpt: Visual inference via python execution for reasoning

    Dídac Surís, Sachit Menon, and Carl V ondrick. Vipergpt: Visual inference via python execution for reasoning. InProceedings of the IEEE/CVF international conference on computer vision, pages 11888–11898, 2023

    2023

  49. [49]

    Llama: Open and efficient foundation language models.arXiv preprint arXiv:2302.13971, 2023

    Hugo Touvron, Thibaut Lavril, Gautier Izacard, Xavier Martinet, Marie-Anne Lachaux, Timo- thée Lacroix, Baptiste Rozière, Naman Goyal, Eric Hambro, Faisal Azhar, et al. Llama: Open and efficient foundation language models.arXiv preprint arXiv:2302.13971, 2023

    Pith/arXiv arXiv 2023

  50. [50]

    Multimodal transformer for unaligned multimodal language sequences

    Yao-Hung Hubert Tsai, Shaojie Bai, Paul Pu Liang, J Zico Kolter, Louis-Philippe Morency, and Ruslan Salakhutdinov. Multimodal transformer for unaligned multimodal language sequences. InProceedings of the conference. Association for computational linguistics. Meeting, volume 2019, page 6558, 2019

    2019

  51. [51]

    Self-consistency improves chain of thought reasoning in language models.arXiv preprint arXiv:2203.11171, 2022

    Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models.arXiv preprint arXiv:2203.11171, 2022

    Pith/arXiv arXiv 2022

  52. [52]

    Charxiv: Charting gaps in realistic chart understanding in multimodal llms.Advances in Neural Information Processing Systems, 37:113569–113697, 2024

    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 llms.Advances in Neural Information Processing Systems, 37:113569–113697, 2024

    2024

  53. [53]

    Chain-of-thought prompting elicits reasoning in large language models

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824–24837, 2022

    2022

  54. [54]

    Simple statistical gradient-following algorithms for connectionist reinforce- ment learning.Machine learning, 8(3):229–256, 1992

    Ronald J Williams. Simple statistical gradient-following algorithms for connectionist reinforce- ment learning.Machine learning, 8(3):229–256, 1992

    1992

  55. [55]

    Chartx & chartvlm: A versatile benchmark and foundation model for complicated chart reasoning.arXiv preprint arXiv:2402.12185, 2024

    Renqiu Xia, Bo Zhang, Hancheng Ye, Xiangchao Yan, Qi Liu, Hongbin Zhou, Zijun Chen, Peng Ye, Min Dou, Botian Shi, et al. Chartx & chartvlm: A versatile benchmark and foundation model for complicated chart reasoning.arXiv preprint arXiv:2402.12185, 2024

    Pith/arXiv arXiv 2024

  56. [56]

    Deebert: Dynamic early exiting for accelerating bert inference.arXiv preprint arXiv:2004.12993, 2020

    Ji Xin, Raphael Tang, Jaejun Lee, Yaoliang Yu, and Jimmy Lin. Deebert: Dynamic early exiting for accelerating bert inference.arXiv preprint arXiv:2004.12993, 2020

    Pith/arXiv arXiv 2004

  57. [57]

    Language-vision planner and executor for text-to-visual reasoning.arXiv preprint arXiv:2506.07778, 2025

    Yichang Xu, Gaowen Liu, Ramana Rao Kompella, Sihao Hu, Tiansheng Huang, Fatih Ilhan, Selim Furkan Tekin, Zachary Yahn, and Ling Liu. Language-vision planner and executor for text-to-visual reasoning.arXiv preprint arXiv:2506.07778, 2025

    arXiv 2025

  58. [58]

    Chartbench: A benchmark for complex visual reasoning in charts.arXiv preprint arXiv:2312.15915, 2023

    Zhengzhuo Xu, Sinan Du, Yiyan Qi, Chengjin Xu, Chun Yuan, and Jian Guo. Chartbench: A benchmark for complex visual reasoning in charts.arXiv preprint arXiv:2312.15915, 2023. 15

    Pith/arXiv arXiv 2023

  59. [59]

    Chartmoe: Mixture of diversely aligned expert connector for chart understanding.arXiv preprint arXiv:2409.03277, 2024

    Zhengzhuo Xu, Bowen Qu, Yiyan Qi, Sinan Du, Chengjin Xu, Chun Yuan, and Jian Guo. Chartmoe: Mixture of diversely aligned expert connector for chart understanding.arXiv preprint arXiv:2409.03277, 2024

    Pith/arXiv arXiv 2024

  60. [60]

    Chartmimic: Evaluating lmm’s cross-modal reasoning capability via chart-to-code generation.arXiv preprint arXiv:2406.09961, 2024

    Cheng Yang, Chufan Shi, Yaxin Liu, Bo Shui, Junjie Wang, Mohan Jing, Linran Xu, Xinyu Zhu, Siheng Li, Yuxiang Zhang, et al. Chartmimic: Evaluating lmm’s cross-modal reasoning capability via chart-to-code generation.arXiv preprint arXiv:2406.09961, 2024

    Pith/arXiv arXiv 2024

  61. [61]

    Tree of thoughts: Deliberate problem solving with large language models.Ad- vances in neural information processing systems, 36:11809–11822, 2023

    Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models.Ad- vances in neural information processing systems, 36:11809–11822, 2023

    2023

  62. [62]

    React: Synergizing reasoning and acting in language models

    Shunyu Yao, Jeffrey Zhao, Dian Yu, Nan Du, Izhak Shafran, Karthik Narasimhan, and Yuan Cao. React: Synergizing reasoning and acting in language models. InInternational Conference on Learning Representations (ICLR), 2023

    2023

  63. [63]

    Text2chart31: Instruction tuning for chart generation with automatic feedback.arXiv preprint arXiv:2410.04064, 2024

    Fatemeh Pesaran Zadeh, Juyeon Kim, Jin-Hwa Kim, and Gunhee Kim. Text2chart31: Instruction tuning for chart generation with automatic feedback.arXiv preprint arXiv:2410.04064, 2024

    Pith/arXiv arXiv 2024

  64. [64]

    Thyme: Think beyond images, 2025

    Yi-Fan Zhang, Xingyu Lu, Shukang Yin, Chaoyou Fu, Wei Chen, Xiao Hu, Bin Wen, Kaiyu Jiang, Changyi Liu, Tianke Zhang, Haonan Fan, Kaibing Chen, Jiankang Chen, Haojie Ding, Kaiyu Tang, Zhang Zhang, Liang Wang, Fan Yang, Tingting Gao, and Guorui Zhou. Thyme: Think beyond images, 2025

    2025

  65. [65]

    Mul- timodal chain-of-thought reasoning in language models.arXiv preprint arXiv:2302.00923, 2023

    Zhuosheng Zhang, Aston Zhang, Mu Li, Hai Zhao, George Karypis, and Alex Smola. Mul- timodal chain-of-thought reasoning in language models.arXiv preprint arXiv:2302.00923, 2023

    Pith/arXiv arXiv 2023

  66. [66]

    Pyvision: Agentic vision with dynamic tooling.arXiv preprint arXiv:2507.07998, 2025

    Shitian Zhao, Haoquan Zhang, Shaoheng Lin, Ming Li, Qilong Wu, Kaipeng Zhang, and Chen Wei. Pyvision: Agentic vision with dynamic tooling.arXiv preprint arXiv:2507.07998, 2025

    Pith/arXiv arXiv 2025

  67. [67]

    Chartcoder: Advancing multimodal large language model for chart-to-code generation.arXiv preprint arXiv:2501.06598, 2025

    Xuanle Zhao, Xianzhen Luo, Qi Shi, Chi Chen, Shuo Wang, Zhiyuan Liu, and Maosong Sun. Chartcoder: Advancing multimodal large language model for chart-to-code generation.arXiv preprint arXiv:2501.06598, 2025

    Pith/arXiv arXiv 2025

  68. [68]

    in-the- wild

    Yaowei Zheng, Junting Lu, Shenzhi Wang, Zhangchi Feng, Dongdong Kuang, and Yuwen Xiong. Easyr1: An efficient, scalable, multi-modality rl training framework. https://github. com/hiyouga/EasyR1, 2025. GitHub repository. 16 A Detailed Analysis of Fixed-Strategy Experiments Experimental Setting.To create our specialist model, we fine-tuned Qwen2.5-VL-7B usin...

    2025

  69. [69]

    Answers must come from chart observation and code understanding

  70. [70]

    Provide exactly one brief, precise response with **no additional details**

  71. [71]

    Avoid multiple choice, yes/no, or lengthy descriptive formats

  72. [72]

    Emphasize questions requiring data interpretation expertise

  73. [73]

    question

    Keep answers short (numbers, percentages, names, dates, or brief terms) ### Question Categories #### **Numerical Operations** - **Counting Tasks**: Enumerate items, groups, or elements with properties - **Basic Mathematics**: Addition, subtraction, multiplication, division - **Descriptive Statistics**: Average, median, mode, range, maximum, minimum - **Ra...

    2022