Elamur Research⌕
☰
home / papers / 2025 / Interactive Evolution: A Neural-Symbolic Self-Training Framework For Large Language Models

Interactive Evolution: A Neural-Symbolic Self-Training Framework For Large Language Models

Paper · 2025 · Fangzhi Xu, Qiushi Sun, Kanzhi Cheng et al.

Summary

Large language models increasingly solve tasks by writing symbolic intermediate forms, such as programs, logic forms, or web actions, which an external environment then executes. Training data for this setting, with paired inputs, symbolic solutions, and outputs, is scarce and expensive to annotate. Existing workarounds either distill from a stronger teacher like GPT-4 or rely on reward models and reinforcement learning. The authors propose ENVISIONS, a self-training framework guided by the environment rather than by people or a teacher. The model samples several candidate solutions, executes them, and receives binary correctness feedback. It then revises its own attempts and scores them with a soft self-reward based on its average token log-probability. Good and bad trajectories are stored in a candidate pool. Training combines a standard objective with an RL-free loss that contrasts positive and negative pairs. Tests on LLaMA-2-Chat 7B and 13B cover web agents, math, and logical reasoning, and the paper reports gains over prior self-training methods. This suggests symbolic skills can improve without human labels or costly proprietary models.

Key points

  • Benchmarks: three domains, namely agent (MiniWob++), math reasoning (GSM8K, MATH, GSM-H, SVAMP, ASDiv), and logical reasoning (ProofWriter, RuleTaker).
  • Online exploration: a three-part loop of self-exploration, self-refinement, and self-rewarding, with execution feedback supplying the only supervision signal.
  • Average scores: in the ablation table, the full ENVISIONS averages 58.69 with LLaMA-2-Chat 7B and 63.56 with 13B. On MiniWob++ it reaches 85.38 (7B) and 87.12 (13B).
  • Ablation results: self-refinement and the contrastive L2 loss matter most. The L2 loss alone adds 3.10–4.57%, and 3.49–5.53% on agent tasks.
  • Why it works: the analysis credits balanced exploration and stability, a stable log-probability margin between positive and negative solutions, and more diverse correct trajectories. By contrast, one-round distillation from GPT-4 and Claude2 produced 10,831 and 8,561 trajectories, an approach the authors consider too costly to sustain.

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

 Fields, topics and concepts

Cite

Cite as Fangzhi Xu, Qiushi Sun, Kanzhi Cheng, Jun Liu, Yu Qiao and Zhiyong Wu. 2025. Interactive Evolution: A Neural-Symbolic Self-Training Framework For Large Language Models. Proceedings of the 63rd 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. DOI 10.18653/v1/2025.acl-long.635

@inproceedings{xu2025interactive,
  title = {{Interactive Evolution: A Neural-Symbolic Self-Training Framework For Large Language Models}},
  author = {Fangzhi Xu, Qiushi Sun, Kanzhi Cheng, Jun Liu, Yu Qiao and Zhiyong Wu},
  booktitle = {Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2025},
  doi = {10.18653/v1/2025.acl-long.635},
  url = {https://doi.org/10.18653/v1/2025.acl-long.635}
}

References

58 references, 31 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

  1. Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 2023. Gpt-4 technical report. arXiv preprint arXiv:2303.08774.
  2. Rohan Anil, Andrew M Dai, Orhan Firat, Melvin Johnson, Dmitry Lepikhin, Alexandre Passos, Siamak Shakeri, Emanuel Taropa, Paige Bailey, Zhifeng Chen, et al. 2023. Palm 2 technical report. arXiv preprint arXiv:2305.10403.
  3. Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster, Marco Dos Santos, Stephen Marcus McAleer, Albert Q Jiang, Jia Deng, Stella Biderman, and Sean Welleck. 2023. Llemma: An open language model for mathematics. In The Twelfth International Conference on Learning Representations.
  4. Boxi Cao, Keming Lu, Xinyu Lu, Jiawei Chen, Mengjie Ren, Hao Xiang, Peilin Liu, Yaojie Lu, Ben He, Xianpei Han, et al. 2024. Towards scalable automated alignment of llms: A survey. arXiv preprint arXiv:2406.01252. — [arXiv:2406.01252](https://arxiv.org/abs/2406.01252) find
  5. Wenhu Chen, Xueguang Ma, Xinyi Wang, and William W. Cohen. 2023. Program of thoughts prompting: Disentangling computation from reasoning for numerical reasoning tasks. Transactions on Machine Learning Research. find
  6. Zixiang Chen, Yihe Deng, Huizhuo Yuan, Kaixuan Ji, and Quanquan Gu. 2024. Self-play fine-tuning converts weak language models to strong language models. arXiv preprint arXiv:2401.01335. find
  7. Kanzhi Cheng, Qiushi Sun, Yougang Chu, Fangzhi Xu, Yantao Li, Jianbing Zhang, and Zhiyong Wu. 2024. Seeclick: Harnessing gui grounding for advanced visual gui agents. arXiv preprint arXiv:2401.10935.
  8. Peter Clark, Oyvind Tafjord, and Kyle Richardson. 2021. Transformers as soft reasoners over language. In Proceedings of the Twenty-Ninth International Conference on International Joint Conferences on Artificial Intelligence, pages 3882–3890.
  9. Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. 2021. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168.
  10. DeepSeek-AI. 2024. Deepseek llm: Scaling open-source language models with longtermism. arXiv preprint arXiv:2401.02954. find
  11. Yihe Deng, Weitong Zhang, Zixiang Chen, and Quanquan Gu. 2023. Rephrase and respond: Let large language models ask better questions for themselves. arXiv preprint arXiv:2311.04205.
  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 Proceedings of the 40th International Conference on Machine Learning, volume 202 of Proceedings of Machine Learning Research, pages 10764–10799. PMLR. find
  13. Zhibin Gou, Zhihong Shao, Yeyun Gong, Yujiu Yang, Minlie Huang, Nan Duan, Weizhu Chen, et al. 2023. Tora: A tool-integrated reasoning agent for mathematical problem solving. arXiv preprint arXiv:2309.17452.
  14. Caglar Gulcehre, Tom Le Paine, Srivatsan Srinivasan, Ksenia Konyushkova, Lotte Weerts, Abhishek Sharma, Aditya Siddhant, Alex Ahern, Miaosen Wang, Chenjie Gu, et al. 2023. Reinforced self-training (rest) for language modeling. arXiv preprint arXiv:2308.08998.
  15. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. 2021. Measuring mathematical problem solving with the math dataset. In Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2).
  16. Ilya Loshchilov and Frank Hutter. 2017. Decoupled weight decay regularization. arXiv preprint arXiv:1711.05101. find
  17. Jiwoo Hong, Noah Lee, and James Thorne. 2024. Reference-free monolithic preference optimization with odds ratio. arXiv preprint arXiv:2403.07691. find
  18. Shen-Yun Miao, Chao-Chun Liang, and Keh-Yih Su. 2020. A diverse corpus for evaluating and developing english math word problem solvers. In Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, pages 975–984. find
  19. Hanxu Hu, Hongyuan Lu, Huajian Zhang, Yun-Ze Song, Wai Lam, and Yue Zhang. 2023. Chain-of-symbol prompting elicits planning in large langauge models. arXiv preprint arXiv:2305.10276. — [arXiv:2305.10276](https://arxiv.org/abs/2305.10276) find
  20. Muye Huang, Han Lai, Xinyu Zhang, Wenjun Wu, Jie Ma, Lingling Zhang, and Jun Liu. 2025a. Evochart: A benchmark and a self-training approach towards real-world chart understanding. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 3680–3688. find
  21. Muye Huang, Lingling Zhang, Han Lai, Wenjun Wu, Xinyu Zhang, and Jun Liu. 2025b. Vprochart: Answering chart question through visual perception alignment agent and programmatic solution reasoning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 3689–3696. find
  22. Hamish Ivison, Yizhong Wang, Valentina Pyatkin, Nathan Lambert, Matthew Peters, Pradeep Dasigi, Joel Jang, David Wadden, Noah A. Smith, Iz Beltagy, and Hannaneh Hajishirzi. 2023. Camels in a changing climate: Enhancing lm adaptation with tulu 2.
  23. Andreas Köpf, Yannic Kilcher, Dimitri von Rütte, Sotiris Anagnostidis, Zhi Rui Tam, Keith Stevens, Abdullah Barhoum, Duc Nguyen, Oliver Stanley, Richárd Nagyfi, et al. 2024. Openassistant conversations-democratizing large language model alignment. Advances in Neural Information Processing Systems, 3…
  24. Nicholas Lee, Thanakul Wattanawong, Sehoon Kim, Karttikeya Mangalam, Sheng Shen, Gopala Anu-manchipali, Michael W Mahoney, Kurt Keutzer, and Amir Gholami. 2024. Llm2llm: Boosting llms with novel iterative data enhancement. arXiv preprint arXiv:2403.15042. find
  25. Bo Liu, Yuqian Jiang, Xiaohan Zhang, Qiang Liu, Shiqi Zhang, Joydeep Biswas, and Peter Stone. 2023a. Llm+ p: Empowering large language models with optimal planning proficiency. arXiv preprint arXiv:2304.11477.
  26. Evan Zheran Liu, Kelvin Guu, Panupong Pasupat, Tianlin Shi, and Percy Liang. 2018. Reinforcement learning on web interfaces using workflow-guided exploration. In International Conference on Learning Representations (ICLR).
  27. Tianqi Liu, Yao Zhao, Rishabh Joshi, Misha Khalman, Mohammad Saleh, Peter J Liu, and Jialu Liu. 2023b. Statistical rejection sampling improves preference optimization. In The Twelfth International Conference on Learning Representations.
  28. Subhabrata (Subho) Mukherjee, Arindam Mitra, Ganesh Jawahar, Sahaj Agarwal, Hamid Palangi, and Ahmed Awadallah. 2023. Orca: Progressive learning from complex explanation traces of gpt-4. arXiv: Computation and Language.
  29. Ansong Ni, Jeevana Priya Inala, Chenglong Wang, Alex Polozov, Christopher Meek, Dragomir Radev, and Jianfeng Gao. 2022. Learning math reasoning from self-sampled correct and partially-correct solutions. In The Eleventh International Conference on Learning Representations. find
  30. Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al. 2022. Training language models to follow instructions with human feedback. Advances in neural information processing systems, 35:27730–27744.
  31. Liangming Pan, Alon Albalak, Xinyi Wang, and William Wang. 2023. Logic-lm: Empowering large language models with symbolic solvers for faithful logical reasoning. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 3806–3824.
  32. Arkil Patel, Satwik Bhattamishra, and Navin Goyal. 2021. Are nlp models really able to solve simple math word problems? In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. Association for Computational Lin…
  33. Yujia Qin, Shihao Liang, Yining Ye, Kunlun Zhu, Lan Yan, Yaxi Lu, Yankai Lin, Xin Cong, Xiangru Tang, Bill Qian, et al. 2023. Toolllm: Facilitating large language models to master 16000+ real-world apis. arXiv preprint arXiv:2307.16789.
  34. Rafael Rafailov, Archit Sharma, Eric Mitchell, Christopher D Manning, Stefano Ermon, and Chelsea Finn. 2024. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems, 36.
  35. Corby Rosset, Ching-An Cheng, Arindam Mitra, Michael Santacroce, Ahmed Awadallah, and Tengyang Xie. 2024. Direct nash optimization: Teaching language models to self-improve with general preferences. arXiv preprint arXiv:2404.03715. find
  36. Avi Singh, John D Co-Reyes, Rishabh Agarwal, Ankesh Anand, Piyush Patil, Peter J Liu, James Harrison, Jaehoon Lee, Kelvin Xu, Aaron Parisi, et al. 2023. Beyond human data: Scaling self-training for problem-solving with language models. arXiv preprint arXiv:2312.06585.
  37. Yifan Song, Da Yin, Xiang Yue, Jie Huang, Sujian Li, and Bill Yuchen Lin. 2024. Trial and error: Exploration-based trajectory optimization of LLM agents. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 7584–7600, Bangkok, Thai…
  38. Qiushi Sun, Zhirui Chen, Fangzhi Xu, Kanzhi Cheng, Chang Ma, Zhangyue Yin, Jianing Wang, Chengcheng Han, Renyu Zhu, Shuai Yuan, et al. 2024. A survey of neural code intelligence: Paradigms, advances and beyond. arXiv preprint arXiv:2403.14734. — [arXiv:2403.14734](https://arxiv.org/abs/2403.14734) find
  39. Oyvind Tafjord, Bhavana Dalvi, and Peter Clark. 2021. Proofwriter: Generating implications, proofs, and abductive statements over natural language. In Findings of the Association for Computational Linguistics: ACL-IJCNLP 2021, pages 3621–3634.
  40. Zhengwei Tao, Ting-En Lin, Xiancai Chen, Hangyu Li, Yuchuan Wu, Yongbin Li, Zhi Jin, Fei Huang, Dacheng Tao, and Jingren Zhou. 2024. A survey on self-evolution of large language models. arXiv preprint arXiv:2404.14387. — [arXiv:2404.14387](https://arxiv.org/abs/2404.14387) find
  41. Rohan Taori, Ishaan Gulrajani, Tianyi Zhang, Yann Dubois, Xuechen Li, Carlos Guestrin, Percy Liang, and Tatsunori B. Hashimoto. 2023. Stanford alpaca: An instruction-following llama model. https://github.com/tatsu-lab/stanford_alpaca. ↗
  42. Gemini Team, Rohan Anil, Sebastian Borgeaud, Yonghui Wu, Jean-Baptiste Alayrac, Jiahui Yu, Radu Soricut, Johan Schalkwyk, Andrew M Dai, Anja Hauth, et al. 2023. Gemini: a family of highly capable multimodal models. arXiv preprint arXiv:2312.11805.
  43. Jianing Wang, Qiushi Sun, Nuo Chen, Chengyu Wang, Jun Huang, Ming Gao, and Xiang Li. 2023a. Uncertainty-aware parameter-efficient self-training for semi-supervised language understanding. In Findings of the Association for Computational Linguistics: EMNLP 2023, pages 7873–7884, Singapore. Associatio… find
  44. Yizhong Wang, Yeganeh Kordi, Swaroop Mishra, Alisa Liu, Noah A. Smith, Daniel Khashabi, and Hannaneh Hajishirzi. 2023b. Self-instruct: Aligning language models with self-generated instructions. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long… find
  45. Jerry Wei, Le Hou, Andrew Lampinen, Xiangning Chen, Da Huang, Yi Tay, Xinyun Chen, Yifeng Lu, Denny Zhou, Tengyu Ma, and Quoc Le. 2023. Symbol tuning improves in-context learning in language models. find
  46. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pages 968–979, Singapore. Association for Computational Linguistics. find
  47. Zhiyong Wu, Chengcheng Han, Zichen Ding, Zhenmin Weng, Zhoumianze Liu, Shunyu Yao, Tao Yu, and Lingpeng Kong. 2024. Os-copilot: Towards generalist computer agents with self-improvement. arXiv preprint arXiv:2402.07456.
  48. Can Xu, Qingfeng Sun, Kai Zheng, Xiubo Geng, Pu Zhao, Jiazhan Feng, Chongyang Tao, and Daxin Jiang. 2023a. Wizardlm: Empowering large language models to follow complex instructions. arXiv preprint arXiv:2304.12244.
  49. Fangzhi Xu, Qika Lin, Jiawei Han, Tianzhe Zhao, Jun Liu, and Erik Cambria. 2025. Are large language models really good logical reasoners? a comprehensive evaluation and beyond. IEEE Transactions on Knowledge and Data Engineering.
  50. Fangzhi Xu, Zhiyong Wu, Qiushi Sun, Siyu Ren, Fei Yuan, Shuai Yuan, Qika Lin, Yu Qiao, and Jun Liu. 2024. Symbol-llm: Towards foundational symbol-centric interface for large language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Pa… find
  51. Qiantong Xu, Fenglu Hong, Bo Li, Changran Hu, Zhengyu Chen, and Jian Zhang. 2023b. On the tool manipulation capability of open-sourced large language models. In NeurIPS 2023 Foundation Models for Decision Making Workshop. find
  52. Zonghan Yang, Peng Li, Ming Yan, Ji Zhang, Fei Huang, and Yang Liu. 2024. React meets actre: Autonomous annotations of agent trajectories for contrastive self-training. arXiv preprint arXiv:2403.14589. — [arXiv:2403.14589](https://arxiv.org/abs/2403.14589) find
  53. Zhangyue Yin, Qiushi Sun, Qipeng Guo, Jiawen Wu, Xipeng Qiu, and Xuanjing Huang. 2023. Do large language models know what they don’t know? In Findings of the Association for Computational Linguistics: ACL 2023, pages 8653–8665, Toronto, Canada. Association for Computational Linguistics. find
  54. Weizhe Yuan, Richard Yuanzhe Pang, Kyunghyun Cho, Sainbayar Sukhbaatar, Jing Xu, and Jason Weston. 2024. Self-rewarding language models. arXiv preprint arXiv:2401.10020. find
  55. Xiang Yue, Xingwei Qu, Ge Zhang, Yao Fu, Wenhao Huang, Huan Sun, Yu Su, and Wenhu Chen. 2023. Mammoth: Building math generalist models through hybrid instruction tuning. arXiv preprint arXiv:2309.05653.
  56. Eric Zelikman, Yuhuai Wu, Jesse Mu, and Noah Goodman. 2022. Star: Bootstrapping reasoning with reasoning. Advances in Neural Information Processing Systems, 35:15476–15488.
  57. Aohan Zeng, Mingdao Liu, Rui Lu, Bowen Wang, Xiao Liu, Yuxiao Dong, and Jie Tang. 2023. Agenttuning: Enabling generalized agent abilities for llms.
  58. Longtao Zheng, Rundong Wang, and Bo An. 2023. Synapse: Leveraging few-shot exemplars for human-level computer control. arXiv preprint arXiv:2306.07863. — [arXiv:2306.07863](https://arxiv.org/abs/2306.07863) find

Updated

↑ back to top

This page in Markdown → https://md.research.elamur.ai/free/en/papers/xu-2025-interactive-evolution-neural-symbolic-self/