Pith. sign in

REVIEW 3 major objections 5 minor 17 references

An agentic loop that writes TikZ diagrams, invents open-ended accuracy and clarity questions, checks them with a vision-language model on code plus image, and regenerates on failures modestly raises human-rated quality of middle-school math

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-14 15:08 UTC pith:JDI26URA

load-bearing objection Honest exploratory systems paper on a TikZ+QA self-improvement loop for K-12 math diagrams; modest gains, missing controls, still worth a look. the 3 major comments →

arxiv 2607.09839 v1 pith:JDI26URA submitted 2026-07-10 cs.AI cs.CVcs.HC

Exploring Agentic Workflows for Generating High Quality Math Visual Aids

Rizwaan Malik , Ashna Khetan , Isabel Sieh , Samin Khan This is my paper
classification cs.AI cs.CVcs.HC
keywords agentic workflowsmathematical diagramsTikZ generationvision-language modelsquality assurance questionsK-12 educationself-improvement loopseducational AI
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.

Mathematical diagrams are essential in K-12 teaching yet current language models still fail to produce them reliably even from careful descriptions. This paper proposes a closed self-improvement loop: generate TikZ code, invent four open-ended quality-assurance questions on accuracy and clarity, evaluate those questions jointly on the code and the rendered image, then turn unsatisfied answers into feedback for regeneration. Exploratory human checks show that multi-modal evaluation reaches 97 percent agreement, open-ended questions outperform yes/no questions, and average quality scores rise from 3.4 to 3.7 after two regeneration rounds. The results give preliminary evidence that automated evaluation feedback can shrink part of the reliability gap for educational math visuals while also exposing remaining limits in spatial coverage of the generated questions.

Core claim

An agentic workflow that generates a TikZ diagram, auto-creates four open-ended QA pairs focused on accuracy and clarity, evaluates them with a vision-language model on the combined code-and-image representation, and feeds failed answers back for regeneration can iteratively improve the geometric and pedagogical fidelity of AI-produced middle-school mathematics diagrams, producing measurable though modest gains in human quality ratings and high human–model agreement when both code and image are supplied.

What carries the argument

The self-improvement loop that couples LLM-generated open-ended quality-assurance questions with multi-modal (TikZ code + rendered image) vision-language evaluation and feedback-driven regeneration of the diagram.

Load-bearing premise

The four automatically generated open-ended questions will surface the actual geometric, counting, or labeling errors that matter so the feedback can drive the generator toward a correct diagram.

What would settle it

Run a controlled battery of diagrams that contain known count, spacing, or dimension errors through the full loop; if the regenerated outputs still fail the same gold-standard checks (as seen with the balanced hanger and L-shaped polygon) while human quality scores rise only marginally, the claim that the current QA feedback is sufficient is falsified.

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

If this is right

  • Multi-modal evaluation on both TikZ code and rendered image is required for high human–model agreement; either modality alone is substantially weaker.
  • Open-ended questions reduce chance agreement relative to yes/no questions when scoring diagram attributes.
  • Iterative regeneration can raise average human quality scores, yet many diagrams still need further rounds after two cycles.
  • Incomplete coverage of diagram features by the auto-generated questions remains a primary bottleneck to recovering gold-standard diagrams.
  • Stronger spatial-reasoning signals for counts, spacing, and label placement will be needed before such loops can be used at classroom scale.

Where Pith is reading between the lines

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

  • The same code-plus-image QA loop could transfer to other structured educational graphics that use TikZ or SVG intermediates, such as free-body or molecular diagrams.
  • The hanger and L-polygon failures suggest future systems may need an explicit feature-inventory step before free-form question generation.
  • If score gains plateau after two rounds because feedback is incomplete, a hybrid human correction of the QA set could unlock larger jumps.
  • Human Likert scores on usefulness leave open whether regenerated diagrams actually improve student learning—a natural next experiment.

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

3 major / 5 minor

Summary. The paper proposes an agentic self-improvement pipeline for generating K-12 mathematical diagrams from refined textual descriptions. An LLM produces TikZ code and four open-ended QA pairs (accuracy and clarity); a multi-modal evaluator (code + image) answers the questions; a verifier flags unsatisfied criteria; and a feedback extractor drives regeneration until all questions pass or a cycle limit is reached. Two research questions are posed: whether LLMs can generate useful QA questions from quality criteria, and whether VLMs can use those questions to evaluate and iteratively improve diagrams. Exploratory results report human–model agreement rising from 68 % (diagram-only) to 97 % (code + diagram) and modest human quality gains from 3.4 to 3.7 after two regeneration rounds, while 70 % of diagrams remain unsatisfied. Error analysis highlights incomplete QA coverage and weak spatial reasoning.

Significance. Reliable generation of pedagogically sound math diagrams remains a genuine bottleneck for AI-assisted curriculum tools. The multi-modal evaluation design (code + image) and the explicit shift from yes/no to open-ended QA are concrete, reusable contributions; the 97 % human agreement figure is a useful empirical finding. The work is exploratory and the absolute quality lift is small, yet it supplies a clear problem framing, a public code repository, and a diagnostic error analysis that can guide subsequent systems. If the causal role of the feedback loop can be established and the QA coverage gaps closed, the approach would be of practical value to educational-technology research.

major comments (3)
  1. §5.2 / Table 2: The central claim that the agentic loop improves diagram quality rests on a 0.3-point human-score rise (3.4 → 3.7). No control that regenerates the same description without QA-derived feedback is reported. Because 70 % of diagrams remain unsatisfied after both regeneration rounds, the modest lift could be an artifact of extra independent sampling rather than of the extracted feedback. A pure re-sample baseline (or an ablation that withholds the Feedback Extractor) is required to establish causality.
  2. §5.3 (hanger and L-polygon examples): The error analysis shows that the generated QA questions frequently miss the true failure modes (uneven box spacing; incorrect side-length values). Consequently the feedback signal cannot steer the generator toward the gold standard. The paper’s own examples therefore undermine the assumption that four automatically generated open-ended questions supply sufficiently complete and actionable feedback—the weakest link in the self-improvement claim.
  3. §5 (final paragraph) and Tables 1–2: Exact model identities, prompt templates, evaluation sample sizes, and inter-annotator agreement statistics are not preserved. Without these metadata the reported percentages and average scores cannot be reproduced or compared with later work. At minimum the authors should state the number of diagrams scored, the number of annotators, and the models used for generation and evaluation.
minor comments (5)
  1. Abstract and §1 cite a 73.9 % success rate from [5]; the same figure is not re-measured on the authors’ own diagram set, making the baseline gap hard to quantify.
  2. Figure 2 is referenced as the workflow diagram but is never described in sufficient detail for a reader to reconstruct the data flow among Generator, QA Generator, Evaluator, Verifier and Feedback Extractor.
  3. §4.1: The decision to drop the “appropriateness” and “miscellaneous” categories is reasonable, yet the final prompt that elicits the four accuracy/clarity questions is never shown.
  4. Appendix Figure 9 caption claims “6 hexagons, 0 trapezoids” while the accompanying text discusses an overlapping-hexagon failure; the caption appears inconsistent with the intended illustration.
  5. References [8]–[16] are recent and relevant, but the related-work discussion of AutomaTikZ and MathVerse could more explicitly contrast evaluation protocols rather than merely listing them.

Circularity Check

0 steps flagged

No circularity: empirical agentic-workflow evaluation measured against external human judges, not a derivation that collapses into its own inputs.

full rationale

This is an exploratory systems paper, not a first-principles derivation. The load-bearing claims are empirical: (i) human agreement with the multi-modal QA evaluator rises to 97% when both TikZ code and image are supplied (Table 1), and (ii) human-rated diagram quality on a 1–5 scale moves modestly from 3.4 to 3.7 across two regeneration rounds (Table 2). Neither quantity is defined in terms of the other, fitted from the target outcome, or forced by a self-citation uniqueness theorem. The pipeline (TikZ generation → open-ended accuracy/clarity QA pairs → VLM/LLM evaluation → feedback extraction → regeneration) is a proposed procedure whose success is checked by independent human annotators scoring diagrams against the original description and K-12 pedagogical usefulness. Self-citations (e.g., Malik et al. 2025) appear only as background motivation that LLMs still struggle with diagrams; they do not underwrite the measured gains. There are no fitted constants later re-labeled as predictions, no ansatz smuggled via prior author work, and no renaming of a known empirical pattern. Limitations noted by the authors (incomplete QA coverage, weak spatial reasoning, missing re-sample baseline) are correctness/causality concerns, not circularity. Score 0 is therefore the honest finding.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 1 invented entities

The work is an empirical systems paper; it rests on a handful of design choices rather than mathematical axioms. The free parameters are the fixed number of QA items, the two retained quality categories, and the regeneration budget. No new physical or mathematical entities are postulated.

free parameters (3)
  • number_of_QA_questions = 4
    Fixed at four (two accuracy, two clarity) after earlier category experiments; the choice directly controls feedback granularity.
  • max_regeneration_cycles = 2 (reported)
    Hard stop after a small number of loops (results shown for two); determines when an imperfect diagram is accepted.
  • quality_categories = accuracy + clarity
    Reduced to ‘accuracy’ and ‘clarity’ after ‘appropriateness’ and ‘miscellaneous’ proved uninformative; an ad-hoc modeling decision.
axioms (3)
  • domain assumption Open-ended questions plus a separate verifier yield more reliable diagram feedback than yes/no questions.
    Stated in §4.1 after Cohen’s κ = 0.11 for yes/no; treated as given for the rest of the pipeline.
  • domain assumption Evaluating both TikZ code and rendered image is strictly superior to either modality alone.
    Supported by Table 1 (68 % → 97 % agreement) and used as the final evaluation design.
  • domain assumption Human 1–5 ratings of pedagogical usefulness are a valid external ground truth for diagram quality.
    Used throughout §5.2; three annotators, no further validation reported.
invented entities (1)
  • agentic self-improvement loop for math diagrams no independent evidence
    purpose: Coordinates generator, QA writer, multi-modal evaluator, verifier and feedback extractor into a closed regeneration cycle.
    The concrete orchestration and the four-question open-ended protocol are introduced by the paper; no independent external evidence of the full loop exists prior to this work.

pith-pipeline@v1.1.0-grok45 · 13413 in / 2625 out tokens · 26910 ms · 2026-07-14T15:08:15.989376+00:00 · methodology

0 comments
read the original abstract

Mathematical diagrams play a crucial role in K 12 education, both as problem components and as scaffolding for student comprehension. However, current AI tools, including Large Language Models (LLMs), struggle to reliably generate accurate and pedagogically sound visual diagrams, even when provided with detailed descriptions. A significant gap therefore remains in the reliable generation of diagrams for middle school mathematics. To address this, we introduce an agentic workflow that enables LLM agents to evaluate the quality of generated visuals and use this feedback to iteratively improve their outputs. This self improvement loop aims to enhance the accuracy and educational appropriateness of AI generated diagrams. Our research investigates two questions. First, can LLMs accurately generate quality assurance questions for a visual aid given specific criteria for visual quality? Second, given valid quality assurance questions, can Vision Language Models effectively evaluate generated K 12 visual aids and use the resulting feedback to improve them iteratively? We conduct an exploratory evaluation of our agentic workflow and identify key areas for improvement, including stronger spatial reasoning and more comprehensive coverage of diagram features in the generated quality assurance questions. Our results provide preliminary evidence that this approach can improve the reliability and educational value of AI generated mathematical diagrams.

Figures

Figures reproduced from arXiv: 2607.09839 by Ashna Khetan, Isabel Sieh, Rizwaan Malik, Samin Khan.

Figure 1
Figure 1. Figure 1: Sample benchmark diagram from Illustrative Mathematics. This is the associated [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Workflow Diagram for Auto-Evaluation Process [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Balanced Hanger (Gold Standard) 7 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Initial AI Generated Diagram of Balanced Hanger [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Regenerated AI Diagram of Balanced Hanger [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 3
Figure 3. Figure 3: • QA Question "Describe the TikZ commands used to ensure the hanger bar appears horizontal and balanced. Does the code explicitly specify equal vertical distances from the support to each end of the bar?" • Gold Standard Answer (if code correct) "The code should define . . . such that the y-coordinate is constant across its length. There should be symmetry in y-values . . . ." • LLM Answer "No; the horizon… view at source ↗
Figure 6
Figure 6. Figure 6: AI Generated Diagram of L-shaped Polygon [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: L-shaped Polygon (Gold Standard) • Gold Standard Diagram: The gold standard ( [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Initial Generation: 1 hexagon 7.2 Code All code can be found at https://github.com/ashnakhetan/self-improve-math-diagrams 12 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Updated Generation: 6 hexagons, 0 trapezoids [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

17 extracted references · 1 canonical work pages

  1. [1]

    Abraham Arcavi. 2003. The role of visual representations in the learning of mathematics. Educational Studies in Mathematics52, 3 (2003), 215–241.https://doi.org/10.1023/ A:1023284510913

    2003

  2. [2]

    Lawrence Zitnick, and Devi Parikh

    Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C. Lawrence Zitnick, and Devi Parikh. 2015. VQA: Visual question answering. In 10 Proceedings of the IEEE International Conference on Computer Vision. 2425–2433. https://doi.org/10.1109/ICCV.2015.279

    doi:10.1109/iccv.2015.279 2015

  3. [3]

    Rizwaan Malik, Dorna Abdi, Rose Wang, and Dorottya Demszky. 2025. Scaffolding middle-school mathematics curricula with large language models.British Journal of Educational Technology56, 3 (2025), 1363–1386. https://doi.org/10.1111/bjet. 13571

    doi:10.1111/bjet 2025

  4. [4]

    Palak Roy, Helen Poet, Ruth Staunton, Katherine Aston, and David Thomas. 2024. ChatGPT in Lesson Preparation: A Teacher Choices Trial. Education Endowment Foundation and National Foundation for Educational Research.https://www.nfer.ac. uk/publications/chatgpt-in-lesson-preparation-a-teacher-choices-trial/

    2024

  5. [5]

    Rijul Jain, Wode Ni, and Joshua Sunshine. 2023. Generating domain-specific programs for diagram authoring with large language models. InCompanion Proceedings of the 2023 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity. ACM, 70–71. https://doi.org/10.1145/ 3618305.3623612

    arXiv 2023

  6. [6]

    Jonas Belouadi, Anne Lauscher, and Steffen Eger. 2024. AutomaTikZ: Text-guided syn- thesis of scientific vector graphics with TikZ. InProceedings of the Twelfth International Conference on Learning Representations.https://arxiv.org/abs/2310.00367

    Pith/arXiv arXiv 2024

  7. [7]

    Ishani Mondal, Zongxia Li, Yufang Hou, Anandhavelu Natarajan, Aparna Garimella, Sambaran Bandyopadhyay, and Jordan Boyd-Graber. 2024. SciDoc2Diagrammer-MAF: Towards generation of scientific diagrams from documents guided by multi-aspect feedback refinement. InFindings of the Association for Computational Linguistics: EMNLP 2024.https://aclanthology.org/20...

    2024

  8. [8]

    https://arxiv.org/abs/2411.05423

    JeongwooLee, KwangsukPark, andJihyeonPark.2024.VISTA:Visualintegratedsystem for tailored automation in math problem generation using LLM.arXiv:2411.05423. https://arxiv.org/abs/2411.05423

    Pith/arXiv arXiv 2024

  9. [9]

    Renrui Zhang, Dongzhi Jiang, Yichi Zhang, Haokun Lin, Ziyu Guo, Pengshuo Qiu, Aojun Zhou, Pan Lu, Kai-Wei Chang, Peng Gao, and Hongsheng Li. 2024. MathVerse: Does your multi-modal LLM truly see the diagrams in visual math problems? In European Conference on Computer Vision.https://arxiv.org/abs/2403.14624

    Pith/arXiv arXiv 2024

  10. [10]

    Heffernan, and Kyle Lo

    Sami Baral, Li Lucy, Ryan Knight, Alice Ng, Luca Soldaini, Neil T. Heffernan, and Kyle Lo. 2025. DrawEduMath: Evaluating vision language models with expert-annotated students’ hand-drawn math images. InProceedings of the 2025 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies.https://acla...

    2025

  11. [11]

    Jon Lundstrom, James Urban, Luc Thomes, and Daniel Bojar. 2023. GlycoDraw: A Python implementation for generating high-quality glycan figures.Glycobiology33, 11 (2023), 927–934.https://doi.org/10.1093/glycob/cwad063

    work page doi:10.1093/glycob/cwad063 2023

  12. [12]

    Shengran Hu, Cong Lu, and Jeff Clune. 2025. Automated design of agentic systems. InProceedings of the Twelfth International Conference on Learning Representations. https://arxiv.org/abs/2408.08435

    Pith/arXiv arXiv 2025

  13. [13]

    Shreeyash Gowaikar, Srinivasan Iyengar, Sameer Segal, and Shivkumar Kalyanaraman

  14. [14]

    InAAAI Workshop on AI to Accelerate Science and Engineering

    An agentic approach to automatic creation of P&ID diagrams from natural language descriptions. InAAAI Workshop on AI to Accelerate Science and Engineering. https://arxiv.org/abs/2412.12898

    Pith/arXiv arXiv

  15. [15]

    Sirui Hong, Yizhang Lin, Bang Liu, Bangbang Liu, Binhao Wu, Ceyao Zhang, Chenxing Wei, Danyang Li, Jiaqi Chen, Jiayi Zhang, Jinlin Wang, Li Zhang, Lingyao Zhang, Min Yang, Mingchen Zhuge, Taicheng Guo, Tuo Zhou, Wei Tao, Xiangru Tang, Xiangtao Lu, Xiawu Zheng, Xinbing Liang, Yaying Fei, Yuheng Cheng, Zhibin Gou, Zongze Xu, and Chenglin Wu. 2024. Data Inte...

    Pith/arXiv arXiv 2024

  16. [16]

    Qian Wan, Jiannan Li, Huanchen Wang, and Zhicong Lu. 2025. Polymind: Parallel visual diagramming with large language models to support prewriting through microtasks. arXiv:2502.09577.https://arxiv.org/abs/2502.09577

    Pith/arXiv arXiv 2025

  17. [17]

    dos Santos

    Melanie Swan, Takashi Kido, Eric Roland, and Renato P. dos Santos. 2023. Math agents: Computational infrastructure, mathematical embedding, and genomics. arXiv:2307.02502.https://arxiv.org/abs/2307.02502 7 Appendix 7.1 TikZ Code and Visual Diagrams When code was evaluated for the following diagram, it appeared that the diagram had all six hexagons, but up...

    Pith/arXiv arXiv 2023