---
title: "SHAPE — paper by Zhao et al. (2026) — summary and ideas"
description: "On this basis they build SHAPE, a linear-algebra benchmark that pairs questions with students of different knowledge… 45 references."
authors: ["Sihang Zhao", "Kangrui Yu", "Youliang Yuan", "Pinjia He", "Hongyi Wen"]
year: 2026
venue: "Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)"
source: "https://aclanthology.org/2026.acl-long.529/"
doi: "10.18653/v1/2026.acl-long.529"
licence: "CC BY 4.0 (ACL Anthology)"
licence_url: "https://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/zhao-2026-shape-unifying-safety-helpfulness-pedagogy/"
---
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# SHAPE: Unifying Safety, Helpfulness and Pedagogy for Educational LLMs

**Authors:** Sihang Zhao, Kangrui Yu, [Youliang Yuan](https://md.research.elamur.ai/free/en/authors/youliang-yuan/), [Pinjia He](https://md.research.elamur.ai/free/en/authors/pinjia-he/) and Hongyi Wen · **Year:** 2026 · **Venue:** [Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)](https://md.research.elamur.ai/free/en/venues/acl/) ([ACL 2026](https://md.research.elamur.ai/free/en/venues/acl/2026/)) · **Publisher:** [Association for Computational Linguistics](https://md.research.elamur.ai/free/en/publishers/association-for-computational-linguistics/) · **Licence:** [CC BY 4.0 (ACL Anthology)](https://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://aclanthology.org/2026.acl-long.529/) · [PDF](https://aclanthology.org/2026.acl-long.529.pdf) · [DOI 10.18653/v1/2026.acl-long.529](https://doi.org/10.18653/v1/2026.acl-long.529) · [OpenAlex](https://openalex.org/W7166827188)

**Citations:** 2 citations (OpenAlex, 2026-10-14)

## Summary
The paper looks at a weakness of LLM tutors that the authors call "pedagogical jailbreaks." In these attacks, students write prompts designed to extract final solutions when the tutor should be guiding them step by step. The authors formalize safe, helpful and pedagogical behavior using a knowledge-mastery graph, a directed acyclic graph of prerequisite concepts. Under this definition, a direct answer is acceptable only when the student has mastered every concept the query depends on. Otherwise the tutor should scaffold, targeting the missing prerequisites closest to what the student already knows.

On this basis they build SHAPE, a linear-algebra benchmark that pairs questions with students of different knowledge backgrounds. They test it against open and closed models, including tutoring prompts and pedagogically tuned systems. Most of these models either give in to simple jailbreaks or become unhelpful in order to stay safe.

The proposed training-free pipeline works in three steps:
- It infers the prerequisites a query needs.
- It finds the student's mastery gaps.
- It gates between an instructing mode and a problem-solving mode.

This pipeline greatly improves safety under two jailbreak settings while keeping helpfulness close to ceiling. The authors conclude that pedagogy needs architectural support, not just prompting.

## Key points
- SHAPE contains 9,087 student-question pairs in linear algebra. The authors constructed the concept graph using the publicly available headings for topics and sections listed on Math Academy's Linear Algebra course page.
- The models evaluated include:
  - Qwen, plus closed-source OpenAI, Gemini and Anthropic models running with educational system prompts or study mode.
  - Approximations of LearnLM and ChatGPT Study Mode prompts.
  - Pedagogical fine-tuned and chain-of-thought systems such as SocraticLM.
- Mastery is modeled as binary and static. Concept extraction is approximated by a few-shot GPT-5 evaluator.
- The graph-augmented gating pipeline is training-free. It routes each response between scaffolding and direct help based on the query-induced prerequisite subgraph.
- Code and data are available at github.com/MAPS-research/SHaPE.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Chinese University of Hong Kong](https://md.research.elamur.ai/free/en/universities/chinese-university-of-hong-kong/) — University, Hong Kong, China · 126 works · 14,073 citations
- [Chinese University of Hong Kong, Shenzhen](https://md.research.elamur.ai/free/en/universities/chinese-university-of-hong-kong-shenzhen/) — University, Shenzhen, China · 47 works · 2,596 citations
- [New York University Shanghai](https://md.research.elamur.ai/free/en/universities/new-york-university-shanghai/) — University, Shanghai, China · 8 works · 523 citations

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🧭 Topics (2): [🧠 Language models & pretraining](https://md.research.elamur.ai/free/en/topics/language-models/) · 3,320 works · [🛡️ Bias, fairness & safety](https://md.research.elamur.ai/free/en/topics/bias-fairness-safety/) · 517 works

## Cite

Cite as: Sihang Zhao, Kangrui Yu, Youliang Yuan, Pinjia He and Hongyi Wen. 2026. SHAPE: Unifying Safety, Helpfulness and Pedagogy for Educational LLMs. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@inproceedings{zhao2026shape,
  title = {{SHAPE: Unifying Safety, Helpfulness and Pedagogy for Educational LLMs}},
  author = {Sihang Zhao, Kangrui Yu, Youliang Yuan, Pinjia He and Hongyi Wen},
  booktitle = {Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.acl-long.529},
  url = {https://doi.org/10.18653/v1/2026.acl-long.529}
}
```

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*Updated 31 October 2026*