@inproceedings{wu-etal-2026-reasonmap,
title = "{R}eason{M}ap: Making Implicit Mathematical Knowledge Explicit in Long Chain-of-Thought Traces",
author = "Wu, Haodong and
He, Yuhang and
Zhang, Yongqi",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.1517/",
pages = "32308--32326",
ISBN = "979-8-89176-462-0",
abstract = "Long chain-of-thought (CoT) traces provide observable natural-language rationales for mathematical problem solving, but they rarely expose the named definitions and theorems that justify the written solution. We treat each problem{--}trace pair as carrying a recoverable knowledge footprint: a trace-grounded support set of named definitions and theorems. Inspired by formal proofs, where supporting premises are recorded more explicitly than in free-form CoT, we formulate Mathematical Support Set Extraction (MSSE): given a problem and a completed long CoT trace, recover the canonical support set that supports the written solution. We propose ReasonMap, which attributes this support set to make solutions auditable, reusable, and easier to repair. ReasonMap follows a two-stage pipeline: proof-to-CoT support transfer adapts premise-explicit proof supervision to premise-implicit long CoT traces, and hard-negative support calibration applies preference optimization against plausible-but-wrong support sets. Experiments show that ReasonMap improves support-set extraction over strong baselines and that ReasonMap-generated support hints aid downstream reasoning in both frontier-model and self-generated settings. The GitHub repository is available at \url{https://github.com/kui253/ReasonMap}."
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<abstract>Long chain-of-thought (CoT) traces provide observable natural-language rationales for mathematical problem solving, but they rarely expose the named definitions and theorems that justify the written solution. We treat each problem–trace pair as carrying a recoverable knowledge footprint: a trace-grounded support set of named definitions and theorems. Inspired by formal proofs, where supporting premises are recorded more explicitly than in free-form CoT, we formulate Mathematical Support Set Extraction (MSSE): given a problem and a completed long CoT trace, recover the canonical support set that supports the written solution. We propose ReasonMap, which attributes this support set to make solutions auditable, reusable, and easier to repair. ReasonMap follows a two-stage pipeline: proof-to-CoT support transfer adapts premise-explicit proof supervision to premise-implicit long CoT traces, and hard-negative support calibration applies preference optimization against plausible-but-wrong support sets. Experiments show that ReasonMap improves support-set extraction over strong baselines and that ReasonMap-generated support hints aid downstream reasoning in both frontier-model and self-generated settings. The GitHub repository is available at https://github.com/kui253/ReasonMap.</abstract>
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%0 Conference Proceedings
%T ReasonMap: Making Implicit Mathematical Knowledge Explicit in Long Chain-of-Thought Traces
%A Wu, Haodong
%A He, Yuhang
%A Zhang, Yongqi
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F wu-etal-2026-reasonmap
%X Long chain-of-thought (CoT) traces provide observable natural-language rationales for mathematical problem solving, but they rarely expose the named definitions and theorems that justify the written solution. We treat each problem–trace pair as carrying a recoverable knowledge footprint: a trace-grounded support set of named definitions and theorems. Inspired by formal proofs, where supporting premises are recorded more explicitly than in free-form CoT, we formulate Mathematical Support Set Extraction (MSSE): given a problem and a completed long CoT trace, recover the canonical support set that supports the written solution. We propose ReasonMap, which attributes this support set to make solutions auditable, reusable, and easier to repair. ReasonMap follows a two-stage pipeline: proof-to-CoT support transfer adapts premise-explicit proof supervision to premise-implicit long CoT traces, and hard-negative support calibration applies preference optimization against plausible-but-wrong support sets. Experiments show that ReasonMap improves support-set extraction over strong baselines and that ReasonMap-generated support hints aid downstream reasoning in both frontier-model and self-generated settings. The GitHub repository is available at https://github.com/kui253/ReasonMap.
%U https://aclanthology.org/2026.findings-emnlp.1517/
%P 32308-32326
Markdown (Informal)
[ReasonMap: Making Implicit Mathematical Knowledge Explicit in Long Chain-of-Thought Traces](https://aclanthology.org/2026.findings-emnlp.1517/) (Wu et al., Findings 2026)
ACL