---
id: magic-circle-programming-languages/03-recognition-in-2026-geometry-is-cheap-topology
title: 'Magic circle programming languages: 3. Recognition in 2026: geometry is cheap,
  topology is hard, VLMs judge badly'
report: https://ai.hiina.space/reports/magic-circle-programming-languages.md
section: 3
version: 1
updated: '2026-10-27'
author: Hiina
---

Index of everything on this site: https://ai.hiina.space/index.md

# Magic circle programming languages: 3. Recognition in 2026: geometry is cheap, topology is hard, VLMs judge badly

- Section 3 of 13 of the report "Magic circle programming languages" by Hiina (v1, updated 2026-10-27)
- Report overview and contents: https://ai.hiina.space/reports/magic-circle-programming-languages.md
- Previous: https://ai.hiina.space/reports/magic-circle-programming-languages/02-every-existing-system-solves-one-half-of.md
- Next: https://ai.hiina.space/reports/magic-circle-programming-languages/04-five-designs-five-computational-models.md

## 3. Recognition in 2026: geometry is cheap, topology is hard, VLMs judge badly

Per-stroke quality metrics (circle-fit residuals, closure gaps, template distances) were worked out in earlier prototyping, so this section covers only what sits above them: whole-diagram structure, calibration, and where models fail.

**Structure-level accuracy lags symbol-level accuracy everywhere.** Arrow R-CNN, which adds an arrow head-and-tail keypoint head to Faster R-CNN, raised whole-diagram recognition on a scanned flowchart dataset from 37.7% to 78.6% and recognised more than 68% of diagrams across four datasets combined, while symbol recall on FC_A reached 98.3%, in under 100 ms per diagram ([Springer](https://link.springer.com/article/10.1007/s10032-020-00361-1)). Its weak point is arrows: overlapping arrow boxes confuse head attribution. A 2025 pipeline that feeds a fine-tuned detector's graph to GPT-4o reports arrow-related detection mAP of 0.235 against 0.653 for other classes ([arXiv 2505.07864](https://arxiv.org/html/2505.07864v1)). In handwritten maths, a structural recogniser reaches 80.52, 83.63 and 74.14% expression rate on CROHME 2016, 2019 and 2023 with generated annotations, and 56.29, 54.63 and 52.82% without them ([arXiv 2508.19773](https://arxiv.org/pdf/2508.19773)). DECIMER, trained only on up to 152 million synthetic renders, reads 73.25% of 5,088 real hand-drawn molecules exactly, where earlier tools score 0.57 to 26.98%, and quadrupling the synthetic set from 38 million added under 3 points ([PMC11227129](https://pmc.ncbi.nlm.nih.gov/articles/PMC11227129)). **A fixed grammar plus synthetic renders with jitter is the transferable recipe**, and in a circle language the quality model doubles as the augmentation model.

**LADDER is the closest precedent for a declarative circle grammar.** Hammond and Davis describe shapes hierarchically from primitives (line, arc, ellipse, spiral and others) under a long predefined constraint list, about 44 named constraints across two lists with no stated total, plus draw order, rotation invariance and a beautifier that moves points as little as possible to satisfy constraints ([LADDER](https://groups.csail.mit.edu/mug/pubs/Hammond2005Ladder.pdf)). Its soft constraints were never implemented and it reports no accuracy figures. Turning each constraint into a normalised residual gives a quality score straight out of parsing, and the beautifier's total displacement is a second, calibratable precision signal.

**Vision-language models fail exactly where circles need them.** On FlowLearn's simulated flowcharts, 2024-era models counted nodes correctly 0.52 (Claude-3-Opus) and 0.58 (GPT-4V) of the time on a 100-sample subset, and in Mermaid generation Claude-3-Opus reached node F1 of about 0.94 but link F1 of only 0.30 ([FlowLearn](https://arxiv.org/html/2407.05183v2)). On SketchJudge, which asks 16 multimodal models to diagnose errors in 1,015 hand-drawn student diagrams, the best (GPT-5) scored 78.42% accuracy against 83.33% for three non-expert human raters on a 160-answer subset, a gap of about five points, with error-type F1 of 61.13 against 66.42 ([SketchJudge](https://arxiv.org/html/2601.06944)). The Visual Aesthetic Benchmark found the best of 20 frontier models identified both the best and worst image in only 26.5% of tasks against 68.9% for experts, and that scalar scores agree poorly with direct comparisons; its domain is fine art, photography and illustration, not drawings ([arXiv 2605.12684](https://arxiv.org/abs/2605.12684)). No study found for this report calibrates a VLM on drawing neatness. **Counting, link topology and judging neatness are three things a magic circle needs and three things VLMs do worst**, and their latency rules them out of a VR loop anyway.

**Calibrate quality with pairwise human judgments, and grade rather than gate.** The aesthetic benchmark's finding that ranking beats scoring, and the CHAED precedent of regressing hand-designed geometric features on 33 raters' handwriting scores ([IJCAI 2015](https://www.ijcai.org/Abstract/15/356)), both point to fitting existing geometric residuals to "which of these two is neater?" judgments. For converting a continuous error into tiers, osu! shrinks nested judgement windows linearly with difficulty (300 = 80 − 6·OD ms) and weights tiers non-uniformly at 100%, 33.33% and 16.67% ([osu! wiki](https://osu.ppy.sh/wiki/en/Gameplay/Judgement/osu%21)). Ido's kanji auto-scorer keeps stroke order, stroke count and shape deductions separate and stores penalty tables as data ([JSiSE 2019](https://www.jsise.org/taikai/2019/program/contents/pdf/F5-1.pdf)). For VR, the evidence is thin: a Würzburg project call notes that arm ergonomics curve intended-straight mid-air strokes ([Würzburg HCI](https://hci.uni-wuerzburg.de/topics/20250722-sketch-stroke-correction/)), and no controller noise or latency-tolerance numbers were found, so per-device and per-player baselines must be measured. Accessibility is a design input, not an afterthought: a 2022 adaptation of the VR game Spellcasters let clinicians customise gestures per stroke-rehabilitation patient ([eScholarship](https://escholarship.org/uc/item/0nf117zh)).

---

Text licensed CC BY 4.0 (attribution: Hiina, ai.hiina.space). Source: https://github.com/hiinaspace/ai-hiina-space