From Solver Trajectories to Teaching Trajectories: Cognition-Aligned Reasoning Distillation

Authors: Yashuo Luo , Qianren Mao , Ziqi Qin , Junnan Liu , Haitao Li , Qili Zhang , Yuan Gao , Zhijun Chen , Xu Wang

View a PDF of the paper titled From Solver Trajectories to Teaching Trajectories: Cognition-Aligned Reasoning Distillation, by Yashuo Luo and 8 other authors

View PDF

HTML (experimental)

Abstract: Knowledge distillation from large reasoning models (LRMs) often uses raw teacher trajectories as supervision. However, this practice creates a mismatch between the goal of distillation and the nature of teacher trajectories. Advanced LRMs typically improve their reasoning capabilities through reward-driven post-training, such as RLHF. This training optimizes them as strong solvers, rather than as teachers that produce reasoning processes smaller models can easily learn. Since smaller models have different "cognitive capacities" compared to their larger teachers, directly imitating raw teacher trajectories can sometimes be ineffective and often requires a substantial number of high-quality samples. To bridge this mismatch, we propose Cognition-Aligned Reasoning Distillation (CARD), an RL-based framework that transforms solver trajectories into teaching trajectories aligned with the student's cognition. Avoiding expensive resampling, our framework directly transforms existing trajectories. We optimize CARD with two reward signals: (1) a Distribution Alignment Reward that matches the student's predictive distribution, and (2) a Logical Coherence Reward that reduces misleading failed reasoning steps. Comprehensive evaluations across multiple student models and settings demonstrate that CARD outperforms distillation from raw teacher trajectories in in-domain settings while achieving substantial gains in out-of-distribution performance. Code is available at this https URL .

Subjects:

Artificial Intelligence (cs.AI)

Cite as:

arXiv:2610.36445 [cs.AI]

(or

arXiv:2610.36445v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.36445

Focus to learn more

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Yashuo Luo [ view email ]

[v1]

Tue, 27 Oct 2026 00:46:23 UTC (1,613 KB)

Full-text links:

Access Paper:

View a PDF of the paper titled From Solver Trajectories to Teaching Trajectories: Cognition-Aligned Reasoning Distillation, by Yashuo Luo and 8 other authors

View PDF

HTML (experimental)

TeX Source

view license

Additional Features

Audio Summary

Current browse context:

cs.AI

< prev

next >

new

recent

| 2026-10

Change to browse by:

cs

References & Citations

SciX

Google Scholar

Semantic Scholar

export BibTeX citation

Loading...

BibTeX formatted citation

loading...

Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Bibliographic Explorer ( What is the Explorer? )

Connected Papers Toggle

Connected Papers ( What is Connected Papers? )

Litmaps Toggle

Litmaps ( What is Litmaps? )

scite.ai Toggle

scite Smart Citations ( What are Smart Citations? )

Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle

alphaXiv ( What is alphaXiv? )

Links to Code Toggle

CatalyzeX Code Finder for Papers ( What is CatalyzeX? )

DagsHub Toggle

DagsHub ( What is DagsHub? )

GotitPub Toggle

Gotit.pub ( What is GotitPub? )

Huggingface Toggle

Hugging Face ( What is Huggingface? )

ScienceCast Toggle

ScienceCast ( What is ScienceCast? )

Demos

Demos

Replicate Toggle

Replicate ( What is Replicate? )

Spaces Toggle

Hugging Face Spaces ( What is Spaces? )

Spaces Toggle

TXYZ.AI ( What is TXYZ.AI? )

Related Papers

Recommenders and Search Tools

Link to Influence Flower

Influence Flower ( What are Influence Flowers? )

Core recommender toggle

CORE Recommender ( What is CORE? )

Author

Venue

Institution

Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Which authors of this paper are endorsers? |

Disable MathJax ( What is MathJax? )