---
title: "STCOR: A Trilevel Syllogism-Driven Reasoning Framework (2026)"
description: "They define a problem class called Textual Constrained Optimization (TCO). 44 references."
authors: ["Keying Yang", "Hao Wang", "Chengtao Jian", "Kai Yang"]
year: 2026
venue: "Proceedings of the 13th Workshop on Argument Mining and Reasoning"
source: "https://aclanthology.org/2026.argmining-1.1/"
doi: "10.18653/v1/2026.argmining-1.1"
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/yang-2026-stcor-trilevel-syllogism-driven-reasoning/"
---
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# STCOR: A Trilevel Syllogism-Driven Reasoning Framework

**Authors:** Keying Yang, [Hao Wang](https://md.research.elamur.ai/free/en/authors/hao-wang/), Chengtao Jian and [Kai Yang](https://md.research.elamur.ai/free/en/authors/kai-yang/) · **Year:** 2026 · **Venue:** [Proceedings of the 13th Workshop on Argument Mining and Reasoning](https://md.research.elamur.ai/free/en/venues/argmining/) ([Workshop on Argument Mining 2026](https://md.research.elamur.ai/free/en/venues/argmining/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.argmining-1.1/) · [PDF](https://aclanthology.org/2026.argmining-1.1.pdf) · [DOI 10.18653/v1/2026.argmining-1.1](https://doi.org/10.18653/v1/2026.argmining-1.1) · [OpenAlex](https://openalex.org/W7166799084)

**Citations:** 0 citations (OpenAlex, 2026-10-14)

## Summary

The authors argue that chain-of-thought and code-generation methods often miss the hidden structure of reasoning problems. They also produce traces that are hard to audit. Their alternative follows how operations-research experts work: first build a model, then solve it. They define a problem class called Textual Constrained Optimization (TCO). In a TCO problem, a natural-language text implicitly encodes variables, constraints and an objective. They also release TCO-Bench, built by rewriting and extending GSM8K items into mixed logic-and-arithmetic puzzles.

Their framework, STCOR, maps reasoning onto a syllogism:
- **Major premise:** a prototype template is picked from a class-based library.
- **Minor premise:** the template is filled in from the query to form an explicit model.
- **Conclusion:** deterministic code is generated and run to get the answer.

A GRPO-based tri-level algorithm, TriRL, trains all three stages jointly. Across 9 math, causal, logical, commonsense and TCO datasets, STCOR beats the strongest baselines by more than 10% absolute accuracy on average. It also makes each step checkable, so faulty reasoning can be located and fixed.

## Key points

- **Formal model:** a TCO model is a five-tuple M = (p, t, V, C, O), standing for overview, model type, variables, constraints and objective. It is written in a flexible mix of text and symbols rather than a strict formal language.
- **Backbones and training:** experiments use Qwen2.5-7B-Instruct and Qwen2.5-1.5B-Instruct. GSM8K is the in-domain set, and all other datasets are out-of-domain.
- **Out-of-domain gains:** STCOR improves on the runner-up baseline (RL_code) by 17.6% with the 7B model and 18.1% with the 1.5B model.
- **Hard datasets:**
  - The 7B model gains up to 33% on K&K and 26.7% on the TCO-Bench Easy split.
  - The 1.5B model gains up to 60% on K&K and 16.7% on CB.
- **Ablations on CB, K&K and TCO-Bench:**
  - Every removed component lowers accuracy.
  - For the 7B model, swapping the solving layer for plain CoT hurts most, with a mean drop of 14.8 points.
  - For the 1.5B model, removing formalization hurts most, with a mean drop of 7.2 points.

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

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## Cite

Cite as: Keying Yang, Hao Wang, Chengtao Jian and Kai Yang. 2026. STCOR: A Trilevel Syllogism-Driven Reasoning Framework. Proceedings of the 13th Workshop on Argument Mining and Reasoning.

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

```bibtex
@inproceedings{yang2026stcor,
  title = {{STCOR: A Trilevel Syllogism-Driven Reasoning Framework}},
  author = {Keying Yang, Hao Wang, Chengtao Jian and Kai Yang},
  booktitle = {Proceedings of the 13th Workshop on Argument Mining and Reasoning},
  year = {2026},
  doi = {10.18653/v1/2026.argmining-1.1},
  url = {https://doi.org/10.18653/v1/2026.argmining-1.1}
}
```

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## References

44 references, 18 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Maciej Besta, Nils Blach, Ales Kubicek, Robert Gerstenberger, Michal Podstawski, Lukas Gianinazzi, Joanna Gajda, Tomasz Lehmann, Hubert Niewiadomski, and Piotr Nyczyk. 2024. Graph of thoughts: Solving elaborate problems with large language models. In Proceedings of the AAAI Conference on Artificial… [find](https://scholar.google.com/scholar?q=Maciej+Besta%2C+Nils+Blach%2C+Ales+Kubicek%2C+Robert+Gerstenberger%2C+Michal+Podstawski%2C+Lukas+Gianinazzi%2C+Joanna+Gajda%2C+Tomasz+Lehmann%2C+Hubert+Niewiadomski%2C+and+Piotr+Nyczyk%2E+2024%2E+Graph+of+thoughts%3A+Solving)
2. While STCOR provides a principled reasoning framework, it currently relies on manually curated templates, which requires significant expert effort and limits scalability to new domains. Future work will explore dynamic template generation through self-iterative learning and few-shot template adaptat… [find](https://scholar.google.com/scholar?q=While+STCOR+provides+a+principled+reasoning+framework%2C+it+currently+relies+on+manually+curated+templates%2C+which+requires+significant+expert+effort+and+limits+scalability+to+new+domains%2E+Future+work+wi)
3. Wenhu Chen, Xueguang Ma, Xinyi Wang, and William W Cohen. 2022. Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks. arXiv preprint arXiv:2211.12588. [find](https://scholar.google.com/scholar?q=Wenhu+Chen%2C+Xueguang+Ma%2C+Xinyi+Wang%2C+and+William+W+Cohen%2E+2022%2E+Program+of+thoughts+prompting%3A+Disentangling+computation+from+reasoning+for+numerical+reasoning+tasks%2E+arXiv+preprint+arXiv%3A2211%2E12588%2E)
4. Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Helyar, Aleksander Madry, Alex Beutel, and Alex Carney. 2024. [Openai o1 system card](https://md.research.elamur.ai/free/en/papers/openai-2024-openai-o1-system-card/). arXiv preprint arXiv:2412.16720.
5. Xiaoxia Cheng, Zeqi Tan, Wei Xue, and Weiming Lu. 2024. Information re-organization improves reasoning in large language models. Advances in Neural Information Processing Systems, 37:130214–130236. [find](https://scholar.google.com/scholar?q=Xiaoxia+Cheng%2C+Zeqi+Tan%2C+Wei+Xue%2C+and+Weiming+Lu%2E+2024%2E+Information+re%2Dorganization+improves+reasoning+in+large+language+models%2E+Advances+in+Neural+Information+Processing+Systems%2C+37%3A130214%E2%80%93130236%2E)
6. Chengtao Jian, Kai Yang, and Yang Jiao. 2024. Tri-level navigator: LLM-empowered tri-level learning for time series ood generalization. Advances in Neural Information Processing Systems, 37:110613–110642. [find](https://scholar.google.com/scholar?q=Chengtao+Jian%2C+Kai+Yang%2C+and+Yang+Jiao%2E+2024%2E+Tri%2Dlevel+navigator%3A+LLM%2Dempowered+tri%2Dlevel+learning+for+time+series+ood+generalization%2E+Advances+in+Neural+Information+Processing+Systems%2C+37%3A110613%E2%80%93110)
7. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, and Reiichiro Nakano. 2021. [Training verifiers to solve math word problems](https://md.research.elamur.ai/free/en/papers/cobbe-2021-training-verifiers-solve-math-word/). arXiv preprint arXiv:2110.14168.
8. Chengtao Jian, Kai Yang, Ye Ouyang, and Xiaozhou Ye. 2025. Stable preference optimization for LLMs: A bilevel approach beyond direct preference optimization. arXiv e-prints, pages arXiv–2507. [find](https://scholar.google.com/scholar?q=Chengtao+Jian%2C+Kai+Yang%2C+Ye+Ouyang%2C+and+Xiaozhou+Ye%2E+2025%2E+Stable+preference+optimization+for+LLMs%3A+A+bilevel+approach+beyond+direct+preference+optimization%2E+arXiv+e%2Dprints%2C+pages+arXiv%E2%80%932507%2E)
9. Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. 2019. [Bert: Pre-training of deep bidirectional transformers for language understanding](https://md.research.elamur.ai/free/en/papers/devlin-2019-bert-pre-training-deep-bidirectional/). In Proceedings of the 2019 conference of the North American chapter of the association for computational linguistics: human language technologies,…
10. Yang Jiao, Kai Yang, and Chengtao Jian. 2025. Dtzo: Distributed trilevel zeroth order learning with provable non-asymptotic convergence. In Forty-second International Conference on Machine Learning. [find](https://scholar.google.com/scholar?q=Yang+Jiao%2C+Kai+Yang%2C+and+Chengtao+Jian%2E+2025%2E+Dtzo%3A+Distributed+trilevel+zeroth+order+learning+with+provable+non%2Dasymptotic+convergence%2E+In+Forty%2Dsecond+International+Conference+on+Machine+Learning%2E)
11. Yang Jiao, Kai Yang, Tiancheng Wu, Chengtao Jian, and Jianwei Huang. 2024. Provably convergent federated trilevel learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 12928–12937. [find](https://scholar.google.com/scholar?q=Yang+Jiao%2C+Kai+Yang%2C+Tiancheng+Wu%2C+Chengtao+Jian%2C+and+Jianwei+Huang%2E+2024%2E+Provably+convergent+federated+trilevel+learning%2E+In+Proceedings+of+the+AAAI+Conference+on+Artificial+Intelligence%2C+volume+38%2C)
12. Luyu Gao, Aman Madaan, Shuyan Zhou, Uri Alon, Pengfei Liu, Yiming Yang, Jamie Callan, and Graham Neubig. 2023. Pal: Program-aided language models. In International Conference on Machine Learning, pages 10764–10799. PMLR. [find](https://scholar.google.com/scholar?q=Luyu+Gao%2C+Aman+Madaan%2C+Shuyan+Zhou%2C+Uri+Alon%2C+Pengfei+Liu%2C+Yiming+Yang%2C+Jamie+Callan%2C+and+Graham+Neubig%2E+2023%2E+Pal%3A+Program%2Daided+language+models%2E+In+International+Conference+on+Machine+Learning%2C+page)
13. Junlong Li, Daya Guo, Dejian Yang, Runxin Xu, Yu Wu, and Junxian He. 2025. [Codei/o: Condensing reasoning patterns via code input-output prediction](https://md.research.elamur.ai/free/en/papers/li-2025-codei-o-condensing-reasoning/). arXiv preprint arXiv:2502.07316.
14. Zhibin Gou, Zhihong Shao, Yeyun Gong, Yelong Shen, Yujiu Yang, Minlie Huang, Nan Duan, and Weizhu Chen. 2024. [Tora: A tool-integrated reasoning agent for mathematical problem solving](https://md.research.elamur.ai/free/en/papers/gou-2023-tora-tool-integrated-reasoning-agent/). In The Eleventh International Conference on Learning Representations.
15. Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, and Alex Ray. 2022. [Training language models to follow instructions with human feedback](https://md.research.elamur.ai/free/en/papers/ouyang-2022-training-language-models-follow-instructions/). Advances in neural information processing systems, 35:27730–27744.
16. Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, and Xiao Bi. 2025. [Deepseek-r1: Incentivizing reasoning capability in LLMs via reinforcement learning](https://md.research.elamur.ai/free/en/papers/deepseek-ai-2025-deepseek-r1-incentivizing-reasoning-capability/). arXiv preprint arXiv:2501.12948.
17. Liangming Pan, Alon Albalak, Xinyi Wang, and William Yang Wang. 2023. [Logic-lm: Empowering large language models with symbolic solvers for faithful logical reasoning](https://md.research.elamur.ai/free/en/papers/pan-2023-logic-lm-empowering-large-language/). arXiv preprint arXiv:2305.12295.
18. Shibo Hao, Yi Gu, Haodi Ma, Joshua Hong, Zhen Wang, Daisy Wang, and Zhiting Hu. 2023. Reasoning with language model is planning with world model. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 8154–8173, Singapore. Association for Computational Lingu… [find](https://scholar.google.com/scholar?q=Shibo+Hao%2C+Yi+Gu%2C+Haodi+Ma%2C+Joshua+Hong%2C+Zhen+Wang%2C+Daisy+Wang%2C+and+Zhiting+Hu%2E+2023%2E+Reasoning+with+language+model+is+planning+with+world+model%2E+In+Proceedings+of+the+2023+Conference+on+Empirical+Met)
19. Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. 2023. [Direct preference optimization: Your language model is secretly a reward model](https://md.research.elamur.ai/free/en/papers/rafailov-2023-direct-preference-optimization-language-model/). Advances in Neural Information Processing Systems, 36:53728– 53741.
20. Ruixin Hong, Hongming Zhang, Xiaoman Pan, Dong Yu, and Changshui Zhang. 2024. Abstraction-of-thought makes language models better reasoners. arXiv preprint arXiv:2406.12442. [find](https://scholar.google.com/scholar?q=Ruixin+Hong%2C+Hongming+Zhang%2C+Xiaoman+Pan%2C+Dong+Yu%2C+and+Changshui+Zhang%2E+2024%2E+Abstraction%2Dof%2Dthought+makes+language+models+better+reasoners%2E+arXiv+preprint+arXiv%3A2406%2E12442%2E)
21. Sohini Roychowdhury. 2024. Journey of hallucination-minimized generative ai solutions for financial decision makers. In Proceedings of the 17th ACM International Conference on Web Search and Data Mining, pages 1180–1181. [find](https://scholar.google.com/scholar?q=Sohini+Roychowdhury%2E+2024%2E+Journey+of+hallucination%2Dminimized+generative+ai+solutions+for+financial+decision+makers%2E+In+Proceedings+of+the+17th+ACM+International+Conference+on+Web+Search+and+Data+Mini)
22. Jian Hu. 2025. [Reinforce++: A simple and efficient approach for aligning large language models](https://md.research.elamur.ai/free/en/papers/hu-2025-reinforce-stabilizing-critic-free-policy/). arXiv preprint arXiv:2501.03262.
23. John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347. [find](https://scholar.google.com/scholar?q=John+Schulman%2C+Filip+Wolski%2C+Prafulla+Dhariwal%2C+Alec+Radford%2C+and+Oleg+Klimov%2E+2017%2E+Proximal+policy+optimization+algorithms%2E+arXiv+preprint+arXiv%3A1707%2E06347%2E)
24. Yancheng Huang, Kai Yang, Zelin Zhu, and Leian Chen. 2024. Triadic-OCD: Asynchronous Online Change Detection with Provable Robustness, Optimality, and Convergence. In Proceedings of the 41st International Conference on Machine Learning (ICML), volume 238 of Proceedings of Machine Learning Research,… [find](https://scholar.google.com/scholar?q=Yancheng+Huang%2C+Kai+Yang%2C+Zelin+Zhu%2C+and+Leian+Chen%2E+2024%2E+Triadic%2DOCD%3A+Asynchronous+Online+Change+Detection+with+Provable+Robustness%2C+Optimality%2C+and+Convergence%2E+In+Proceedings+of+the+41st+Internati)
25. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, and Y Wu. 2024. [Deepseekmath: Pushing the limits of mathematical reasoning in open language models](https://md.research.elamur.ai/free/en/papers/shao-2024-deepseekmath-pushing-limits-mathematical-reasoning/). arXiv preprint arXiv:2402.03300. the 6th ACM SIGPLAN international symposium on machine pro…
26. Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. 2024. [Scaling LLM test-time compute optimally can be more effective than scaling model parameters](https://md.research.elamur.ai/free/en/papers/snell-2024-scaling-llm-test-time-compute/). arXiv preprint arXiv:2408.03314.
27. An Yang, Baosong Yang, Beichen Zhang, Binyuan Hui, Bo Zheng, Bowen Yu, Chengyuan Li, Dayiheng Liu, Fei Huang, and Haoran Wei. 2024a. Qwen2. 5 technical report. arXiv preprint arXiv:2412.15115. [find](https://scholar.google.com/scholar?q=An+Yang%2C+Baosong+Yang%2C+Beichen+Zhang%2C+Binyuan+Hui%2C+Bo+Zheng%2C+Bowen+Yu%2C+Chengyuan+Li%2C+Dayiheng+Liu%2C+Fei+Huang%2C+and+Haoran+Wei%2E+2024a%2E+Qwen2%2E+5+technical+report%2E+arXiv+preprint+arXiv%3A2412%2E15115%2E)
28. Kaya Stechly, Matthew Marquez, and Subbarao Kambhampati. 2023. Gpt-4 doesn’t know it’s wrong: An analysis of iterative prompting for reasoning problems. arXiv preprint arXiv:2310.12397. — [arXiv:2310.12397](https://arxiv.org/abs/2310.12397) [find](https://scholar.google.com/scholar?q=Kaya+Stechly%2C+Matthew+Marquez%2C+and+Subbarao+Kambhampati%2E+2023%2E+Gpt%2D4+doesn%E2%80%99t+know+it%E2%80%99s+wrong%3A+An+analysis+of+iterative+prompting+for+reasoning+problems%2E+arXiv+preprint+arXiv%3A2310%2E12397%2E+%E2%80%94+%5BarXiv%3A2310%2E)
29. Ling Yang, Zhaochen Yu, Tianjun Zhang, Shiyi Cao, Minkai Xu, Wentao Zhang, Joseph E Gonzalez, and Bin Cui. 2024b. [Buffer of thoughts: Thought-augmented reasoning with large language models](https://md.research.elamur.ai/free/en/papers/yang-2024-buffer-thoughts-thought-augmented-reasoning/). Advances in Neural Information Processing Systems, 37:113519–113544.
30. Ye Tian, Baolin Peng, Linfeng Song, Lifeng Jin, Dian Yu, Lei Han, Haitao Mi, and Dong Yu. 2024. [Toward self-improvement of LLMs via imagination, searching, and criticizing](https://md.research.elamur.ai/free/en/papers/tian-2024-toward-self-improvement-llms-imagination/). Advances in Neural Information Processing Systems, 37:52723–52748.
31. Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. 2023. Tree of thoughts: Deliberate problem solving with large language models. Advances in neural information processing systems, 36:11809–11822. [find](https://scholar.google.com/scholar?q=Shunyu+Yao%2C+Dian+Yu%2C+Jeffrey+Zhao%2C+Izhak+Shafran%2C+Tom+Griffiths%2C+Yuan+Cao%2C+and+Karthik+Narasimhan%2E+2023%2E+Tree+of+thoughts%3A+Deliberate+problem+solving+with+large+language+models%2E+Advances+in+neural+inf)
32. Ziyu Wan, Yunxiang Li, Yan Song, Hanjing Wang, Linyi Yang, Mark Schmidt, Jun Wang, Weinan Zhang, Shuyue Hu, and Ying Wen. 2025. Rema: Learning to meta-think for LLMs with multi-agent reinforcement learning. arXiv preprint arXiv:2503.09501. — [arXiv:2503.09501](https://arxiv.org/abs/2503.09501) [find](https://scholar.google.com/scholar?q=Ziyu+Wan%2C+Yunxiang+Li%2C+Yan+Song%2C+Hanjing+Wang%2C+Linyi+Yang%2C+Mark+Schmidt%2C+Jun+Wang%2C+Weinan+Zhang%2C+Shuyue+Hu%2C+and+Ying+Wen%2E+2025%2E+Rema%3A+Learning+to+meta%2Dthink+for+LLMs+with+multi%2Dagent+reinforcement+lea)
33. Xi Ye, Qiaochu Chen, Isil Dillig, and Greg Durrett. 2023. [Satlm: Satisfiability-aided language models using declarative prompting](https://md.research.elamur.ai/free/en/papers/ye-2023-satlm-satisfiability-aided-language-models/). Advances in Neural Information Processing Systems, 36:45548–45580.
34. Lei Wang, Wanyu Xu, Yihuai Lan, Zhiqiang Hu, Yunshi Lan, Roy Ka-Wei Lee, and Ee-Peng Lim. 2023. Plan-and-solve prompting: Improving zero-shot chain-of-thought reasoning by large language models. arXiv preprint arXiv:2305.04091. [find](https://scholar.google.com/scholar?q=Lei+Wang%2C+Wanyu+Xu%2C+Yihuai+Lan%2C+Zhiqiang+Hu%2C+Yunshi+Lan%2C+Roy+Ka%2DWei+Lee%2C+and+Ee%2DPeng+Lim%2E+2023%2E+Plan%2Dand%2Dsolve+prompting%3A+Improving+zero%2Dshot+chain%2Dof%2Dthought+reasoning+by+large+language+models%2E+arXiv)
35. Junchi Yu, Ran He, and Rex Ying. 2024. Thought propagation: An analogical approach to complex reasoning with large language models. In The Eleventh International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Junchi+Yu%2C+Ran+He%2C+and+Rex+Ying%2E+2024%2E+Thought+propagation%3A+An+analogical+approach+to+complex+reasoning+with+large+language+models%2E+In+The+Eleventh+International+Conference+on+Learning+Representations)
36. Denny Zhou, Nathanael Schärli, Le Hou, Jason Wei, Nathan Scales, Xuezhi Wang, Dale Schuurmans, Claire Cui, Olivier Bousquet, and Quoc Le. 2024a. [Least-to-most prompting enables complex reasoning in large language models](https://md.research.elamur.ai/free/en/papers/al-2022-least-most-prompting-enables-complex/). In The Eleventh International Conference on Learning Representations.
37. Zhiyuan Wang, Bokui Chen, Yinya Huang, Qingxing Cao, Ming He, Jianping Fan, and Xiaodan Liang. 2025. Ormind: A cognitive-inspired end-to-end reasoning framework for operations research. arXiv preprint arXiv:2506.01326. [find](https://scholar.google.com/scholar?q=Zhiyuan+Wang%2C+Bokui+Chen%2C+Yinya+Huang%2C+Qingxing+Cao%2C+Ming+He%2C+Jianping+Fan%2C+and+Xiaodan+Liang%2E+2025%2E+Ormind%3A+A+cognitive%2Dinspired+end%2Dto%2Dend+reasoning+framework+for+operations+research%2E+arXiv+preprint)
38. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, and Denny Zhou. 2022. [Chain-of-thought prompting elicits reasoning in large language models](https://md.research.elamur.ai/free/en/papers/wei-2022-chain-thought-prompting-elicits-reasoning/). Advances in neural information processing systems, 35:24824–24837.
39. Jin Peng Zhou, Charles Staats, Wenda Li, Christian Szegedy, Kilian Q Weinberger, and Yuhuai Wu. 2024b. Don’t trust: Verify–grounding LLM quantitative reasoning with autoformalization. In The Eleventh International Conference on Learning Representations. [find](https://scholar.google.com/scholar?q=Jin+Peng+Zhou%2C+Charles+Staats%2C+Wenda+Li%2C+Christian+Szegedy%2C+Kilian+Q+Weinberger%2C+and+Yuhuai+Wu%2E+2024b%2E+Don%E2%80%99t+trust%3A+Verify%E2%80%93grounding+LLM+quantitative+reasoning+with+autoformalization%2E+In+The+Eleventh+)
40. Violet Xiang, Charlie Snell, Kanishk Gandhi, Alon Albalak, Anikait Singh, Chase Blagden, Duy Phung, Rafael Rafailov, Nathan Lile, and Dakota Mahan. 2025. Towards system 2 reasoning in LLMs: Learning how to think with meta chain-of-though. arXiv preprint arXiv:2501.04682. [find](https://scholar.google.com/scholar?q=Violet+Xiang%2C+Charlie+Snell%2C+Kanishk+Gandhi%2C+Alon+Albalak%2C+Anikait+Singh%2C+Chase+Blagden%2C+Duy+Phung%2C+Rafael+Rafailov%2C+Nathan+Lile%2C+and+Dakota+Mahan%2E+2025%2E+Towards+system+2+reasoning+in+LLMs%3A+Learning+h)
41. Yu Zhu and Kai Yang. 2026. Llm-driven multi-turn task-oriented dialogue synthesis for realistic reasoning. arXiv preprint arXiv:2602.23610. — [arXiv:2602.23610](https://arxiv.org/abs/2602.23610) [find](https://scholar.google.com/scholar?q=Yu+Zhu+and+Kai+Yang%2E+2026%2E+Llm%2Ddriven+multi%2Dturn+task%2Doriented+dialogue+synthesis+for+realistic+reasoning%2E+arXiv+preprint+arXiv%3A2602%2E23610%2E+%E2%80%94+%5BarXiv%3A2602%2E23610%5D%28https%3A%2F%2Farxiv%2Eorg%2Fabs%2F2602%2E23610%29)
42. Ziyang Xiao, Dongxiang Zhang, Yangjun Wu, Lilin Xu, Yuan Jessica Wang, Xiongwei Han, Xiaojin Fu, Tao Zhong, Jia Zeng, and Mingli Song. 2023. Chain-of-experts: When LLMs meet complex operations research problems. In The twelfth international conference on learning representations. [find](https://scholar.google.com/scholar?q=Ziyang+Xiao%2C+Dongxiang+Zhang%2C+Yangjun+Wu%2C+Lilin+Xu%2C+Yuan+Jessica+Wang%2C+Xiongwei+Han%2C+Xiaojin+Fu%2C+Tao+Zhong%2C+Jia+Zeng%2C+and+Mingli+Song%2E+2023%2E+Chain%2Dof%2Dexperts%3A+When+LLMs+meet+complex+operations+researc)
43. Wantong Xie, Yi-Xiang Hu, Jieyang Xu, Feng Wu, and Xiangyang Li. Murka: Multi-reward reinforcement learning with knowledge alignment for optimization tasks. In The Thirty-ninth Annual Conference on Neural Information Processing Systems. [find](https://scholar.google.com/scholar?q=Wantong+Xie%2C+Yi%2DXiang+Hu%2C+Jieyang+Xu%2C+Feng+Wu%2C+and+Xiangyang+Li%2E+Murka%3A+Multi%2Dreward+reinforcement+learning+with+knowledge+alignment+for+optimization+tasks%2E+In+The+Thirty%2Dninth+Annual+Conference+on+Ne)
44. Frank F Xu, Uri Alon, Graham Neubig, and Vincent Josua Hellendoorn. 2022. [A systematic evaluation of large language models of code](https://md.research.elamur.ai/free/en/papers/xu-2022-systematic-evaluation-large-language-models/). In Proceedings of

*Updated 2 November 2026*