@inproceedings{zhao-etal-2026-scope,
title = "{SCOPE}: Stepwise Calibration of Reasoning Confidence with Outcome-Grounded Prefix Evidence",
author = "Zhao, Huaqin and
Zhou, Yifan and
Sun, Bolun and
Cao, Chao and
Li, Yiwei and
Ding, Zhaojun and
Zhang, Lu and
Liu, Tianming and
Lu, Jin",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.2609/",
pages = "59284--59297",
ISBN = "979-8-89176-459-0",
abstract = "Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning using outcome-level supervision, but this supervision is temporally coarse: it indicates whether a trajectory ends with a correct answer, without revealing when the reasoning becomes reliable or silently fails. Existing verbalized-confidence methods typically calibrate a single confidence score after the final answer, leaving intermediate uncertainty unobserved. We propose SCOPE (Stepwise Calibration with Outcome-grounded Prefix Evidence), which trains reasoning models to emit confidence after each reasoning step. SCOPE interprets step confidence as the model{'}s prefix-conditioned belief in the gold answer: how likely the gold answer is under the reasoning prefix generated so far. During training, SCOPE constructs a soft target by scoring the gold answer conditioned on each reasoning prefix under the current policy. It then distills this signal with a two-stage masked RL objective: the first stage stabilizes the output format and final-answer accuracy, while the second stage performs calibration-only masked updates by applying stepwise and final-confidence rewards only to the numerical tokens inside the emitted confidence spans. Experiments on mathematical reasoning benchmarks show that SCOPE improves stepwise and final-confidence calibration while preserving final-answer reasoning performance. We further show that the resulting confidence signals support downstream inference-time control, enabling more reliable Learn-Then-Test risk control and stronger confidence-weighted aggregation."
}<?xml version="1.0" encoding="UTF-8"?>
<modsCollection xmlns="http://www.loc.gov/mods/v3">
<mods ID="zhao-etal-2026-scope">
<titleInfo>
<title>SCOPE: Stepwise Calibration of Reasoning Confidence with Outcome-Grounded Prefix Evidence</title>
</titleInfo>
<name type="personal">
<namePart type="given">Huaqin</namePart>
<namePart type="family">Zhao</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Yifan</namePart>
<namePart type="family">Zhou</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Bolun</namePart>
<namePart type="family">Sun</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Chao</namePart>
<namePart type="family">Cao</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Yiwei</namePart>
<namePart type="family">Li</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Zhaojun</namePart>
<namePart type="family">Ding</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Lu</namePart>
<namePart type="family">Zhang</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Tianming</namePart>
<namePart type="family">Liu</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Jin</namePart>
<namePart type="family">Lu</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<originInfo>
<dateIssued>2026-10</dateIssued>
</originInfo>
<typeOfResource>text</typeOfResource>
<relatedItem type="host">
<titleInfo>
<title>Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing</title>
</titleInfo>
<name type="personal">
<namePart type="given">Hung-Yi</namePart>
<namePart type="family">Lee</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Sunipa</namePart>
<namePart type="family">Dev</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Jessy</namePart>
<namePart type="family">Li</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Desmond</namePart>
<namePart type="family">Elliott</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<originInfo>
<publisher>Association for Computational Linguistics</publisher>
<place>
<placeTerm type="text">Budapest, Hungary</placeTerm>
</place>
</originInfo>
<genre authority="marcgt">conference publication</genre>
<identifier type="isbn">979-8-89176-459-0</identifier>
</relatedItem>
<abstract>Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning using outcome-level supervision, but this supervision is temporally coarse: it indicates whether a trajectory ends with a correct answer, without revealing when the reasoning becomes reliable or silently fails. Existing verbalized-confidence methods typically calibrate a single confidence score after the final answer, leaving intermediate uncertainty unobserved. We propose SCOPE (Stepwise Calibration with Outcome-grounded Prefix Evidence), which trains reasoning models to emit confidence after each reasoning step. SCOPE interprets step confidence as the model’s prefix-conditioned belief in the gold answer: how likely the gold answer is under the reasoning prefix generated so far. During training, SCOPE constructs a soft target by scoring the gold answer conditioned on each reasoning prefix under the current policy. It then distills this signal with a two-stage masked RL objective: the first stage stabilizes the output format and final-answer accuracy, while the second stage performs calibration-only masked updates by applying stepwise and final-confidence rewards only to the numerical tokens inside the emitted confidence spans. Experiments on mathematical reasoning benchmarks show that SCOPE improves stepwise and final-confidence calibration while preserving final-answer reasoning performance. We further show that the resulting confidence signals support downstream inference-time control, enabling more reliable Learn-Then-Test risk control and stronger confidence-weighted aggregation.</abstract>
<identifier type="citekey">zhao-etal-2026-scope</identifier>
<location>
<url>https://aclanthology.org/2026.emnlp-main.2609/</url>
</location>
<part>
<date>2026-10</date>
<extent unit="page">
<start>59284</start>
<end>59297</end>
</extent>
</part>
</mods>
</modsCollection>
%0 Conference Proceedings
%T SCOPE: Stepwise Calibration of Reasoning Confidence with Outcome-Grounded Prefix Evidence
%A Zhao, Huaqin
%A Zhou, Yifan
%A Sun, Bolun
%A Cao, Chao
%A Li, Yiwei
%A Ding, Zhaojun
%A Zhang, Lu
%A Liu, Tianming
%A Lu, Jin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F zhao-etal-2026-scope
%X Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning using outcome-level supervision, but this supervision is temporally coarse: it indicates whether a trajectory ends with a correct answer, without revealing when the reasoning becomes reliable or silently fails. Existing verbalized-confidence methods typically calibrate a single confidence score after the final answer, leaving intermediate uncertainty unobserved. We propose SCOPE (Stepwise Calibration with Outcome-grounded Prefix Evidence), which trains reasoning models to emit confidence after each reasoning step. SCOPE interprets step confidence as the model’s prefix-conditioned belief in the gold answer: how likely the gold answer is under the reasoning prefix generated so far. During training, SCOPE constructs a soft target by scoring the gold answer conditioned on each reasoning prefix under the current policy. It then distills this signal with a two-stage masked RL objective: the first stage stabilizes the output format and final-answer accuracy, while the second stage performs calibration-only masked updates by applying stepwise and final-confidence rewards only to the numerical tokens inside the emitted confidence spans. Experiments on mathematical reasoning benchmarks show that SCOPE improves stepwise and final-confidence calibration while preserving final-answer reasoning performance. We further show that the resulting confidence signals support downstream inference-time control, enabling more reliable Learn-Then-Test risk control and stronger confidence-weighted aggregation.
%U https://aclanthology.org/2026.emnlp-main.2609/
%P 59284-59297
Markdown (Informal)
[SCOPE: Stepwise Calibration of Reasoning Confidence with Outcome-Grounded Prefix Evidence](https://aclanthology.org/2026.emnlp-main.2609/) (Zhao et al., EMNLP 2026)
ACL
- Huaqin Zhao, Yifan Zhou, Bolun Sun, Chao Cao, Yiwei Li, Zhaojun Ding, Lu Zhang, Tianming Liu, and Jin Lu. 2026. SCOPE: Stepwise Calibration of Reasoning Confidence with Outcome-Grounded Prefix Evidence. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 59284–59297, Budapest, Hungary. Association for Computational Linguistics.