Meta-Reasoning Agents: Adaptive Error Analysis and Self-Repair for Mathematical Object Derivation

TL;DR: Imagine a model that not only solves math problems but, when it gets stuck or makes an error, can explain why and try a different approach. The experiment would train LLMs to reflect on their own failed reasoning chains, identify likely sources of error, and iteratively repair their solutions—much like a student learning from mistakes.

Research Question: Can an LLM equipped with a meta-reasoning module that performs explicit error analysis and self-repair outperform standard aggregation and on-policy approaches, especially on the Principia suite and similar benchmarks?

Hypothesis: Models that are trained to analyze and repair their own intermediate errors will not only improve final answer accuracy on structured mathematical object derivation, but also generate more interpretable, robust solution paths than models using only test-time aggregation.

Experiment Plan: - Extend the Principia benchmark with annotated error types for failed solutions.

• Develop a meta-reasoning module that, after each failed attempt, prompts the LLM to hypothesize error sources (e.g., misapplied formula, algebraic slip) and propose corrections.
• Compare performance, error rates, and interpretability to models using standard test-time aggregation and on-policy judge training.
• Assess gains in both accuracy and error localization, as well as user trust in the reasoning process.

References:

• Aggarwal, P., Ghazvininejad, M., Kim, S., Kulikov, I., Lanchantin, J., Li, X., Li, T., Liu, B., Neubig, G., Ovalle, A., Saha, S., Sukhbaatar, S., Welleck, S., Weston, J., Whitehouse, C., Williams, A., Xu, J., Yu, P., Yuan, W., Zhang, J., & Zhao, W. (2026). Reasoning over mathematical objects: on-policy reward modeling and test time aggregation.
• Oh, S., Park, J., & Baek, H. (2026). Performance Evaluation of OpenAI’s o4-mini on CSAT Mathematics: Multimodal Reasoning and the Reasoning–Verification–Reanalysis Loop. IEEE Access.