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<h1 class="title is-1 publication-title" style="background: linear-gradient(to right, #6366f1, #ec4899); -webkit-background-clip: text; color: transparent; font-weight: 700;">
Reasoning Model Unlearning: Forgetting Traces, Not Just Answers, While Preserving Reasoning Skills
</h1>
<div class="is-size-5 publication-authors">
<span class="author-block">
<a href="https://changshengwang.me/">Changsheng Wang</a><sup>1,*</sup>,</span>
<span class="author-block">
<a href="https://chongyu-fan.netlify.app/">Chongyu Fan</a><sup>1,*</sup>,</span>
<span class="author-block">
<a href="https://www.yihua-zhang.com/">Yihua Zhang</a><sup>1</sup>,
</span>
<span class="author-block">
<a href="https://jinghanjia.netlify.app/">Jinghan Jia</a><sup>1</sup>,
</span>
<span class="author-block">
<a href="https://research.ibm.com/people/dennis-wei">Dennis Wei</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://rithram.github.io/">Parikshit Ram</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://research.ibm.com/people/nathalie-baracaldo-angel">Nathalie Baracaldo</a><sup>2</sup>,
</span>
<span class="author-block">
<a href="https://lsjxjtu.github.io/">Sijia Liu</a><sup>1,2</sup>,
</span>
</div>
<div class="is-size-5 publication-authors">
<span class="author-block"><sup>1</sup>Michigan State University,</span>
<span class="author-block"><sup>2</sup>IBM Research</span>
</div>
<div class="is-size-6 has-text-grey">
<span class="author-block"><sup>*</sup> Equal contribution</span>
</div>
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<span>Paper</span>
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<a href="https://arxiv.org/abs/2506.12963"
class="external-link button is-normal is-rounded is-dark">
<span class="icon">
<i class="ai ai-arxiv"></i>
</span>
<span>arXiv</span>
</a>
</span>
<!-- Video Link. -->
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<a href="https://github.com/OPTML-Group/Unlearn-R2MU"
class="external-link button is-normal is-rounded is-dark">
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</span>
<span>Code</span>
</a>
</span>
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<a href="https://huggingface.co/OPTML-Group/R2MU-DeepSeek-R1-Distill-Llama-8B"
class="external-link button is-normal is-rounded is-dark">
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<i class="far fa-flag"></i>
</span>
<span>Model</span>
</a>
</span>
</div>
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<section class="section">
<div class="container is-max-desktop">
<!-- Abstract -->
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<h2 class="title is-3 has-text-centered">Abstract</h2>
<hr>
<div class="content has-text-justified">
<p>
Recent advances in large reasoning models (LRMs) have enabled strong chain-of-thought (CoT) generation through test-time computation.
While these multi-step reasoning capabilities represent a major milestone in language model performance, they also introduce new safety risks.
In this work, we present the first systematic study to revisit the problem of machine unlearning in the context of LRMs.
Machine unlearning refers to the process of removing the influence of sensitive, harmful, or undesired data or knowledge from a trained model without full retraining.
We show that conventional unlearning algorithms, originally designed for non-reasoning models, are inadequate for LRMs.
In particular, even when final answers are successfully erased, sensitive information often persists within the intermediate reasoning steps, i.e., CoT trajectories.
To address this challenge, we extend conventional unlearning and propose
<strong>Reasoning-aware Representation Misdirection for Unlearning</strong> ($R^2MU$),
a novel method that effectively suppresses sensitive reasoning traces and prevents the generation of associated final answers,
while preserving the model's reasoning ability.
Our experiments demonstrate that $R^2MU$ significantly reduces sensitive information leakage within reasoning traces
and achieves strong performance across both safety and reasoning benchmarks,
evaluated on state-of-the-art models such as DeepSeek-R1-Distill-LLaMA-8B and DeepSeek-R1-Distill-Qwen-14B.
</p>
</div>
</div>
</div>
</div>
</section>
<section class="section">
<div class="columns is-centered">
<div class="column is-four-fifths">
<h2 class="title is-3 has-text-centered">Can Existing Unlearning Adapt to LRMs?</h2>
<hr>
<div class="hero-body">
<center>
<img class="round" style="width:100%; border-radius:12px;" src="./static/images/intro_figure.png"/>
<br>
<p style="font-size:24px; color:#444; margin-top:4px;">
Figure: Demonstration of LRM unlearning challenges.
</p>
</center>
<br>
<ul style="margin:0; padding-left:1.2em;">
<li>
<p style="margin:0; font-size:20px;">
<span style="color:#c00; font-weight:700;">Challenge I:</span>
<span style="font-weight:700;"> Existing unlearning fails to “unthink.”</span>
<span style="font-weight:400;">
Current unlearning methods effectively sanitize final outputs but fail to eliminate
sensitive information embedded within the reasoning traces of LRM<span style="white-space:nowrap;">s.</span>
</span>
</p>
</li>
</ul>
<br>
<ul style="margin:0; padding-left:1.2em;">
<li>
<p style="margin:0; font-size:20px;">
<span style="color:#c00; font-weight:700;">Challenge II:</span>
<span style="font-weight:700;"> Degradation of reasoning ability.</span>
<span style="font-weight:400;">
Current unlearning methods substantially degrade the reasoning capability of LRMs.<span style="white-space:nowrap;"></span>
</span>
</p>
</li>
</ul>
<br>
</div>
</div>
</div>
</section>
<section class="section">
<div class="columns is-centered">
<div class="column is-four-fifths">
<h2 class="title is-3 has-text-centered">A New Evaluation Framework for Reasoning-based Unlearning</h2>
<hr>
<div class="columns is-vcentered">
<!-- Left: Pie chart -->
<div class="column is-one-third has-text-centered">
<img class="round" style="width:100%; max-width:350px; border-radius:12px;" src="./static/images/pie.png" alt="Unthinking categories pie chart">
<p style="font-size:14px; color:#555; margin-top:8px;">
<b>Figure:</b> Distribution of reasoning traces into unthinking categories (C1–C4) on the WMDP benchmark after applying RMU for LRM unlearning.
Categories C2–C4 indicate varying levels of sensitive information leakage, while only C1 is considered successful unthinking.
19.7% of evaluation samples fall into C2–C4, indicating unsafe forgetting.
</p>
</div>
<!-- Right: Text description -->
<div class="column is-two-thirds">
<p class="is-size-5 has-text-justified" style="line-height:1.6;">
Existing unlearning evaluation focuses primarily on final answers, which fails to capture the leakage of sensitive information embedded within <i>reasoning traces</i>.
To address this, we analyze the degree of sensitive information leakage in reasoning traces of unlearned LRMs, classifying each reasoning trace into one of four categories based on its unthinking behavior.
</p>
<br>
<p style="font-size:16px; line-height:1.6;">
<b>(C1)</b> contains <i>irrelevant content</i>, or <i>unrelated reasoning</i>;<br>
<b>(C2)</b> introduces <i>indirect factual or inferential knowledge</i> relevant to the sensitive question or answer;<br>
<b>(C3)</b> correctly <i>eliminates one or more incorrect options</i>;<br>
<b>(C4)</b> <i>indicates, supports, or analyzes</i> the correct answer.
</p>
<br>
<p class="is-italic" style="font-size:20px; color:#333;">
Categories C2–C4 reflect varying degrees of sensitive information leakage, indicating that <b>unthinking</b> remains an unsolved challenge for reasoning-based unlearning.
</p>
</div>
</div>
</div>
</div>
</section>
<section class="section" style="padding: 2rem 0 1.5rem 0;">
<div class="container" style="max-width: 1100px;">
<h2 class="title is-3 has-text-centered" style="margin-bottom: 0.3rem;">
Lessons Learned from Think Intervention:
</h2>
<h2 class="title is-3 has-text-centered" style="margin-top: 0;">
ZeroThink and the Reflection Token Penalty
</h2>
<hr style="margin: 1rem 0;">
<div class="columns is-vcentered" style="align-items: flex-start; margin-bottom: 0;">
<!-- Left column -->
<div class="column is-two-thirds" style="padding-right: 1.5rem;">
<p style="font-size: 20px; line-height: 1.6; margin-bottom: 0.8em;">
<b>(1) ZeroThink (ZT):</b> Enforces a response prefix consisting of an empty thought segment
<code><think></think></code>.
</p>
<p style="font-size: 20px; line-height: 1.6; margin-bottom: 0.6em;">
<b>(2) Reflection Token Penalty (RTP):</b> Suppresses reflection token generation
(e.g., <code><wait></code>, <code><but></code>, <code><Hmm></code>)
to promote <i>unthinking</i>.
</p>
<!-- Takeaways directly below -->
<div style="margin-top: 0.5rem;">
<p style="font-size: 21px; font-weight: 700; color: #006400; margin-bottom: 0.3em;">Takeaways:</p>
<p style="font-size: 20px; line-height: 1.6; margin: 0;">
(1) Token-level interventions (e.g., forcing <code><think></think></code> or penalizing reflection words)
do not solve unthinking.<br>
(2) While suppressing surface-level tokens, reasoning traces still leak sensitive information.
</p>
</div>
</div>
<!-- Right column: Fixed-size figure -->
<div class="column is-one-third has-text-centered" style="padding-left: 1.5rem;">
<div style="width:100%; max-width:360px; height:260px; display:flex; align-items:center; justify-content:center; margin:0 auto;">
<img
src="./static/images/category_distribution_safe_unsafe.png"
alt="ZeroThink and Reflection Token Penalty results"
style="width:100%; height:auto; max-height:250px; border-radius:10px; object-fit:contain; display:block;"
/>
</div>
<p style="font-size: 14px; color: #555; line-height: 1.4; margin-top: 6px;">
<b>Figure 2.</b> Reasoning trace safety category-wise distribution of RMU, RMU w/ ZT, and RMU w/ RTP
using LRM, evaluated by GPT-o3-mini.
Cases are grouped by sensitivity leakage, where <b>safe</b> indicates successful unthinking and
<b>unsafe</b> reflects harmful information leakage in reasoning trace.
</p>
</div>
</div>
</div>
</section>
<section class="section" style="padding: 2rem 0 1.5rem 0;">
<div class="container" style="max-width: 1100px;">
<!-- Title -->
<h2 class="title is-3 has-text-centered" style="margin-bottom: 0.3rem;">
<span style="font-variant: small-caps;">R<sup>2</sup>MU</span>: Toward Effective Unthinking with Reasoning Preservation
</h2>
<hr style="margin: 1rem 0;">
<!-- Component 1 -->
<p style="font-size: 18px; line-height: 1.6; margin-bottom: 1em;">
<b style="font-size:20px;">Component 1: Unthinking via reasoning trace representation misdirection.</b>
Given a forget sample <i>x</i>, we split it into <i>N</i> token-level segments and prepend each with a reasoning trigger
to generate CoT traces <i>r<sub>1</sub>, … , r<sub>N</sub></i>.
We then apply RMU-style loss<sup>[2]</sup> to align each <i>r<sub>i</sub></i>’s representation with random features:
</p>
<div style="text-align:center; margin: 1.2rem 0;">
<img src="./static/images/loss_unthink.png" alt="unthink loss" style="width:55%; max-width:800px;">
</div>
<!-- Component 2 -->
<p style="font-size: 18px; line-height: 1.6; margin-bottom: 1em;">
<b style="font-size:20px;">Component 2: Reasoning ability preservation via CoT supervision.</b>
We introduce an auxiliary dataset <i>D<sub>CoT</sub></i>
(e.g., a math reasoning dataset such as LIMO<sup>[3]</sup>)
where <i>r ∈ D<sub>CoT</sub></i> denotes the CoT explanation paired with each question,
to preserve reasoning ability in line with RMU’s utility preservation strategy:
</p>
<div style="text-align:center; margin: 1.2rem 0;">
<img src="./static/images/loss_cot.png" alt="cot loss" style="width:53%; max-width:800px;">
</div>
<!-- Joint objective -->
<p style="font-size: 18px; line-height: 1.6; margin-bottom: 1em;">
<b style="font-size:20px;">Full Objective:</b>
The final <span style="font-variant: small-caps;">R<sup>2</sup>MU</span> objective combines both unthinking and CoT supervision losses:
</p>
<div style="text-align:center; margin: 1.2rem 0;">
<img src="./static/images/loss_total.png" alt="r2mu total loss" style="width:80%; max-width:800px;">
</div>
</div>
</section>
<section class="section" style="padding: 2rem 0 1.5rem 0;">
<div class="container" style="max-width: 1100px;">
<!-- Title -->
<h2 class="title is-3 has-text-centered" style="margin-bottom: 0.3rem;">
Effectiveness of <span style="font-variant: small-caps;">R<sup>2</sup>MU</span> on WMDP Dataset
</h2>
<hr style="margin: 1rem 0;">
<!-- Figure centered -->
<div style="text-align:center; margin: 1.2rem 0;">
<img
src="./static/images/exp.png"
alt="Effectiveness of R2MU on WMDP"
style="width:85%; max-width:850px; border-radius:10px; display:inline-block;"
/>
<p style="font-size: 14px; color: #555; line-height: 1.4; margin-top: 6px;">
<b>Table.</b> Performance overview of <span style="font-variant: small-caps;">R<sup>2</sup>MU</span>
on WMDP across two reasoning LLMs (DeepSeek-R1-Distill-LLaMA-8B and Qwen-14B).
</p>
</div>
<!-- Experiment Settings -->
<p style="font-size: 18px; line-height: 1.6; margin-top: 1.2rem;">
<b style="font-size: 20px;">Experiment Settings.</b>
We evaluate <span style="font-variant: small-caps;">R<sup>2</sup>MU</span> on WMDP across
DeepSeek-R1-Distill-LLaMA-8B and Qwen-14B, comparing unlearning effectiveness (FA-UA, RT-UA),
reasoning ability (AIME-2024, MATH-500, GPQA-Diamond), and general utility (MMLU)
against RMU, RMU w/ ZT, RMU w/ RTP, and R²MU-v0.
</p>
<!-- Conclusion -->
<div style="margin-top: 1.5rem;">
<p style="font-size: 18px; font-weight: 700; margin-bottom: 0.6rem;">
Conclusion: <span style="font-weight: 400;">Our findings reveal significant insights.</span>
</p>
<ul style="list-style: none; padding-left: 0; font-size: 17px; line-height: 1.6; margin-top: 0.5rem;">
<li style="margin-bottom: 0.4rem;">
⚡ <b>Selective reasoning-trace forgetting:</b>
<span style="font-weight: 400;">
<span style="font-variant: small-caps;">R<sup>2</sup>MU</span> achieves the lowest RT-UA without
compromising FA-UA, outperforming all baselines.
</span>
</li>
<li style="margin-bottom: 0.4rem;">
⚡ <b>Preserved reasoning ability:</b>
<span style="font-weight: 400;">
Unlike R²MU-v0, which collapses on reasoning benchmarks,
<span style="font-variant: small-caps;">R<sup>2</sup>MU</span> maintains strong reasoning performance.
</span>
</li>
<li>
⚡ <b>Balanced performance–utility trade-off:</b>
<span style="font-weight: 400;">
While slightly increasing training cost,
<span style="font-variant: small-caps;">R<sup>2</sup>MU</span> achieves a superior balance between
unlearning precision, reasoning competence, and model utility.
</span>
</li>
</ul>
</div>
</div>
</section>
<section class="section" style="padding: 2rem 0 1.5rem 0;">
<div class="container" style="max-width: 1100px;">
<!-- Title -->
<h2 class="title is-3 has-text-centered" style="margin-bottom: 0.3rem;">
Effectiveness of <span style="font-variant: small-caps;">R<sup>2</sup>MU</span> in LRM Safety Enhancement
</h2>
<hr style="margin: 1rem 0;">
<!-- Figure/Table centered -->
<div style="text-align:center; margin: 1.2rem 0;">
<img
src="./static/images/safety.png"
alt="R2MU LRM safety enhancement"
style="width:85%; max-width:850px; border-radius:10px; display:inline-block;"
/>
<p style="font-size: 14px; color: #555; line-height: 1.4; margin-top: 6px;">
<b>Table.</b> Comparison of unlearning methods across two models with respect to unlearning efficacy
,
reasoning ability, and general utility.
<span style="font-variant: small-caps;">R<sup>2</sup>MU</span> (Ours) significantly improves safety while maintaining
competitive reasoning and utility performance.
</p>
</div>
<!-- Experiment Description -->
<p style="font-size: 18px; line-height: 1.6; margin-top: 1.2rem;">
<b style="font-size: 20px;">Performance of R<sup>2</sup>MU in LRM Safety Enhancement.</b>
We perform LRM unlearning using the STAR-1 dataset to assess its potential for enhancing LRM safety.
<span style="font-variant: small-caps;">R<sup>2</sup>MU</span> is compared with other unlearning baselines across three dimensions:
unlearning efficacy (measured by safety rate on <i>StrongReject</i>, <i>JBB</i>, and <i>WildJailbreak</i>),
general utility (<i>MMLU</i>), and reasoning ability (<i>AIME 2024</i>, <i>MATH-500</i>, <i>GPQA Diamond</i>).
</p>
<!-- Summary/Conclusion -->
<div style="margin-top: 1.5rem;">
<p style="font-size: 18px; font-weight: 700; margin-bottom: 0.6rem;">
Conclusion: <span style="font-weight: 400;">R<sup>2</sup>MU enhances safety without trade-offs.</span>
</p>
<ul style="list-style: none; padding-left: 0; font-size: 17px; line-height: 1.6; margin-top: 0.5rem;">
<li style="margin-bottom: 0.4rem;">
🧠 <b>Stronger safety robustness:</b>
<span style="font-weight: 400;">
15–25% safety gain across major jailbreak benchmarks.
</span>
</li>
<li style="margin-bottom: 0.4rem;">
💡 <b>Preserved reasoning and utility:</b>
<span style="font-weight: 400;">
No significant loss in MMLU, AIME-2024, or GPQA performance.
</span>
</li>
<li>
🔒 <b>Effective reasoning-trace unlearning:</b>
<span style="font-weight: 400;">
Demonstrates broad applicability of reasoning-aware forgetting for safer LRMs.
</span>
</li>
</ul>
</div>
</div>
</section>
<section class="section" id="Paper">
<div class="container is-max-desktop content">
<table align="center" width="600px">
<h2 class="is-centered has-text-centered">Paper</h2>
<hr>
<tr>
<td style="width: 200px; text-align: center;">
<a href="https://arxiv.org/pdf/2506.12963">
<img class="layered-paper-big" style="height:175px; border-radius: 10px;" src="./static/images/cover.png" alt="Paper cover"/>
</a>
</td>
<td style="padding-left: 20px;">
<span style="font-size:18px; line-height:1.6;">
<b>Changsheng Wang</b>, Chongyu Fan, Yihua Zhang, Jinghan Jia, Dennis Wei, Parikshit Ram, Nathalie Baracaldo, Sijia Liu.<br>
<b>Reasoning Model Unlearning: Forgetting Traces, Not Just Answers, While Preserving Reasoning Skills.</b><br>
(<a href="https://arxiv.org/abs/2506.12963" target="_blank">EMNLP Main Paper</a>, 2025)<br>
</span>
</td>
</tr>
</table>
</div>
</section>
<section class="section" id="BibTeX">
<div class="container is-max-desktop content">
<h2 class="title">BibTeX</h2>
<pre><code>@inproceedings{wang-etal-2025-reasoning,
title = "Reasoning Model Unlearning: Forgetting Traces, Not Just Answers, While Preserving Reasoning Skills",
author = "Wang, Changsheng and Fan, Chongyu and Zhang, Yihua and Jia, Jinghan and Wei, Dennis and Ram, Parikshit and Baracaldo, Nathalie and Liu, Sijia",
booktitle = "Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing",
month = nov,
year = "2025",
publisher = "Association for Computational Linguistics",
pages = "4427--4443",
ISBN = "979-8-89176-332-6",
}</code></pre>
</div>
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