---
title: "Explain in Your Own Words — paper by Kim and Baek (2026)"
description: "The authors propose TSD-KD, an on-policy, student-centric scheme with three token-selective parts… 41 references, cited by 6 papers here."
authors: ["Minsang Kim", "Seung Jun Baek"]
year: 2026
venue: "arXiv:2603.13260"
source: "https://arxiv.org/abs/2603.13260"
doi: "10.48550/arxiv.2603.13260"
arxiv: "2603.13260"
licence: "CC BY 4.0 (arXiv)"
licence_url: "http://creativecommons.org/licenses/by/4.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/kim-2026-explain-own-words-improving-reasoning/"
---
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# Explain in Your Own Words: Improving Reasoning via Token-Selective Dual Knowledge Distillation

**Authors:** Minsang Kim and Seung Jun Baek · **Year:** 2026 · **Venue:** arXiv:2603.13260 · **Licence:** [CC BY 4.0 (arXiv)](http://creativecommons.org/licenses/by/4.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/2603.13260) · [PDF](https://arxiv.org/pdf/2603.13260) · [DOI 10.48550/arxiv.2603.13260](https://doi.org/10.48550/arxiv.2603.13260) · [arXiv 2603.13260](https://arxiv.org/abs/2603.13260) · [OpenAlex](https://openalex.org/W7138152349)

**Citations:** 0 citations (OpenAlex, 2026-10-14) · 6 in our library, of the 149,439 papers whose bibliographies we read

## Summary
Small language models that learn reasoning from larger ones through knowledge distillation (KD) often struggle when made to copy the teacher's full token distribution at every step. A low-capacity student can be overloaded by this, and the gap between teacher and student reasoning styles causes distribution mismatch. The authors propose TSD-KD, an on-policy, student-centric scheme with three token-selective parts:
- **Indirect distillation.** The student proposes its own top-k next-token candidates in the early "opener" segment, where high-entropy branching tokens cluster. The teacher only re-ranks these candidates, and the student learns from that ranking through a Plackett-Luce preference objective.
- **Direct distillation.** A divergence-based loss is restricted to tokens on which the teacher shows high confidence while the student lacks it.
- **Entropy regularization.** Selective entropy minimization keeps the student confident during training.

Across 10 reasoning benchmarks, TSD-KD reports state-of-the-art accuracy and sometimes surpasses the teacher. This suggests that light, targeted guidance can beat full imitation for compressing chain-of-thought reasoning.

## Key points
- Evaluation covers 10 challenging reasoning benchmarks, including math (MATH) and code (MBPP) tasks. The gains reach 54.4% over the baseline student and 40.3% over the second-best method.
- In four cases the distilled student outperformed its own teacher, by as much as 20.3%.
- The preference-based indirect step uses the Plackett-Luce model. The direct step builds on GKD-style generalized JSD, which interpolates between forward and reverse KL.
- In qualitative comparisons against Qwen2.5-1.5B and GKD:
  - TSD-KD correctly converted a string to lower case where both alternatives produced a check function.
  - On a MATH problem, TSD-KD respected a "cents" unit constraint, while GKD collapsed mid-reasoning.
- Code is released at github.com/kmswin1/TSD-KD.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Korea University](https://md.research.elamur.ai/free/en/universities/korea-university/) — University, Seoul, South Korea · 26 works · 9,490 citations

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🧭 Topics (1): [🧮 Reasoning](https://md.research.elamur.ai/free/en/topics/reasoning/) · 1,426 works

## Cite

Cite as: Minsang Kim and Seung Jun Baek. 2026. Explain in Your Own Words: Improving Reasoning via Token-Selective Dual Knowledge Distillation. arXiv:2603.13260.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{kim2026explain,
  title = {{Explain in Your Own Words: Improving Reasoning via Token-Selective Dual Knowledge Distillation}},
  author = {Minsang Kim and Seung Jun Baek},
  year = {2026},
  doi = {10.48550/arxiv.2603.13260},
  eprint = {2603.13260},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.2603.13260}
}
```

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*Updated 30 October 2026*
