I believe a neuro-symbolic approach is the only way to realize truthworthy reasoning, thus achieving true intelligence. It is probably the only hope to bridge the seemingly insurmountable gap between “correlation” and “causality”.
Here are some useful cases of the neural symbolic approach. And by now neuro-symbolic reasoning has become mainstream. Here is a podcast where I talked about AI reasoning.
Synthesizing high-quality, verifiably correct reasoning steps on solving math problems. (Li et al., 2024).
Improving the autoformalization, a fundamental math capability of a neural model, through a hybrid neural-symbolic solution. (Li et al., 2024), (Tang et al., 2026).
@inproceedings{tang2026euclean,title={Euclean: Automated Geometry Problem Formalization with Unified Verification in Lean},author={Tang, Linbin and You, Jingyan and Kang, Zilin and Liu, Hanzhang and Zhang, Sophia and Li, Zenan and Cao, Chenrui and Song, Liangcheng and Wu, Jiaao and Zhang, Xian and Yang, Fan},booktitle={ICML 2026},year={2026},}
@article{starpolyamath26,title={{STAR-P\'{o}lyaMath}: Multi-Agent Reasoning under Persistent Meta-Strategic Supervision},author={Wu, Jiaao and Zhang, Xian and Liu, Hanzhang and Zhang, Sophia and Yang, Fan and Dong, Yinpeng},year={2026},journal={ArXiv},}
@inproceedings{loongRL26,title={LoongRL: Reinforcement Learning for Advanced Reasoning over Long Contexts},author={Wang, Siyuan and Zhang, Gaokai and Zhang, Li Lyna and Shang, Ning and Yang, Fan and Chen, Dongyao and Yang, Mao},year={2026},booktitle={International Conference on Learning Representations, {ICLR}},}
@inproceedings{inequalityiclr25,title={Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning},author={Li, Zenan and Li, Zhaoyu and Tang, Wen and Zhang, Xian and Yao, Yuan and Si, Xujie and Yang, Fan and Yang, Kaiyu and Ma, Xiaoxing},year={2025},booktitle={International Conference on Learning Representations, {ICLR}},}
@inproceedings{dspplus25,title={Reviving DSP for Advanced Theorem Proving in the Era of Reasoning Models},author={Cao, Chenrui and Song, Liangcheng and Li, Zenan and Le, Xinyi and Zhang, Xian and Xue, Hui and Yang, Fan},year={2025},booktitle={Advances in Neural Information Processing Systems, {NeurIPS}},}
@inproceedings{NEURIPS2024_NSMR,title={Neuro-Symbolic Data Generation for Math Reasoning},author={Li, Zenan and Zhou, Zhi and Yao, Yuan and Zhang, Xian and Li, Yu-Feng and Cao, Chun and Yang, Fan and Ma, Xiaoxing},year={2024},booktitle={Advances in Neural Information Processing Systems, {NeurIPS}},}
@inproceedings{NEURIPS2024_AutoFormalization,title={Autoformalize Mathematical Statements by Symbolic Equivalence and Semantic Consistency},author={Li, Zenan and Wu, Yifan and Li, Zhaoyu and Wei, Xinming and Zhang, Xian and Yang, Fan and Ma, Xiaoxing},year={2024},booktitle={Advances in Neural Information Processing Systems, {NeurIPS}},}