Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs

Sagnik Mukherjee, Abhinav Chinta, Takyoung Kim, Tarun Anoop Sharma, Dilek Hakkani Tur
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:45109-45128, 2025.

Abstract

Chain-of-Thought (CoT) prompting enhances mathematical reasoning in large language models (LLMs) by enabling detailed step-by-step solutions. However, due to the verbosity of LLMs, the resulting reasoning chains can be long, making it harder to verify the reasoning steps and trace issues resulting from dependencies between the steps that may be farther away in the sequence of steps. Importantly, mathematical reasoning allows each step to be derived from a small set of premises, which are a subset of the preceding steps in the reasoning chain. In this paper, we present a framework that identifies the premises for each step, to improve the evaluation of reasoning. We restructure conventional linear reasoning chains into Premise Augmented Reasoning Chains (PARC) by introducing premise links, resulting in a directed acyclic graph where the nodes are the steps and the edges are the premise links. Through experiments with a PARC-based dataset that we built, namely (Premises and ERrors identification in LLMs), we demonstrate that LLMs can reliably identify premises within complex reasoning chains. In particular, even open-source LLMs achieve 90% recall in premise identification. We also show that PARC helps to identify errors in reasoning chains more reliably. The accuracy of error identification improves by 6% to 16% absolute when step-by-step verification is carried out in PARC under the premises. Our findings highlight the utility of premise-centric representations in addressing complex problem-solving tasks and open new avenues for improving the reliability of LLM-based reasoning evaluations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-mukherjee25a, title = {Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with {LLM}s}, author = {Mukherjee, Sagnik and Chinta, Abhinav and Kim, Takyoung and Sharma, Tarun Anoop and Tur, Dilek Hakkani}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {45109--45128}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/mukherjee25a/mukherjee25a.pdf}, url = {https://proceedings.mlr.press/v267/mukherjee25a.html}, abstract = {Chain-of-Thought (CoT) prompting enhances mathematical reasoning in large language models (LLMs) by enabling detailed step-by-step solutions. However, due to the verbosity of LLMs, the resulting reasoning chains can be long, making it harder to verify the reasoning steps and trace issues resulting from dependencies between the steps that may be farther away in the sequence of steps. Importantly, mathematical reasoning allows each step to be derived from a small set of premises, which are a subset of the preceding steps in the reasoning chain. In this paper, we present a framework that identifies the premises for each step, to improve the evaluation of reasoning. We restructure conventional linear reasoning chains into Premise Augmented Reasoning Chains (PARC) by introducing premise links, resulting in a directed acyclic graph where the nodes are the steps and the edges are the premise links. Through experiments with a PARC-based dataset that we built, namely (Premises and ERrors identification in LLMs), we demonstrate that LLMs can reliably identify premises within complex reasoning chains. In particular, even open-source LLMs achieve 90% recall in premise identification. We also show that PARC helps to identify errors in reasoning chains more reliably. The accuracy of error identification improves by 6% to 16% absolute when step-by-step verification is carried out in PARC under the premises. Our findings highlight the utility of premise-centric representations in addressing complex problem-solving tasks and open new avenues for improving the reliability of LLM-based reasoning evaluations.} }
Endnote
%0 Conference Paper %T Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs %A Sagnik Mukherjee %A Abhinav Chinta %A Takyoung Kim %A Tarun Anoop Sharma %A Dilek Hakkani Tur %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-mukherjee25a %I PMLR %P 45109--45128 %U https://proceedings.mlr.press/v267/mukherjee25a.html %V 267 %X Chain-of-Thought (CoT) prompting enhances mathematical reasoning in large language models (LLMs) by enabling detailed step-by-step solutions. However, due to the verbosity of LLMs, the resulting reasoning chains can be long, making it harder to verify the reasoning steps and trace issues resulting from dependencies between the steps that may be farther away in the sequence of steps. Importantly, mathematical reasoning allows each step to be derived from a small set of premises, which are a subset of the preceding steps in the reasoning chain. In this paper, we present a framework that identifies the premises for each step, to improve the evaluation of reasoning. We restructure conventional linear reasoning chains into Premise Augmented Reasoning Chains (PARC) by introducing premise links, resulting in a directed acyclic graph where the nodes are the steps and the edges are the premise links. Through experiments with a PARC-based dataset that we built, namely (Premises and ERrors identification in LLMs), we demonstrate that LLMs can reliably identify premises within complex reasoning chains. In particular, even open-source LLMs achieve 90% recall in premise identification. We also show that PARC helps to identify errors in reasoning chains more reliably. The accuracy of error identification improves by 6% to 16% absolute when step-by-step verification is carried out in PARC under the premises. Our findings highlight the utility of premise-centric representations in addressing complex problem-solving tasks and open new avenues for improving the reliability of LLM-based reasoning evaluations.
APA
Mukherjee, S., Chinta, A., Kim, T., Sharma, T.A. & Tur, D.H.. (2025). Premise-Augmented Reasoning Chains Improve Error Identification in Math reasoning with LLMs. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:45109-45128 Available from https://proceedings.mlr.press/v267/mukherjee25a.html.

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