# Answer-then-Edit: Reasoning Skeleton Editing for Anti-Distillation with Preserved Utility

arXiv: https://arxiv.org/abs/2607.20440 · HTML: https://mlsanity.com/paper/2607.20440/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 43 references that are in the map.
- First posted on arXiv 12 May 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Federated, robust and private distillation](https://mlsanity.com/distill/federated-robust-and-private-distillation/)

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [From Generation to Judgment: Opportunities and Challenges of LLM-as-a-judge](https://mlsanity.com/paper/2411.16594/) (2024)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Poisoning Language Models During Instruction Tuning](https://mlsanity.com/paper/2305.00944/) (2023)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Protecting Intellectual Property of Language Generation APIs with Lexical Watermark](https://mlsanity.com/paper/2112.02701/) (2021)
- [Instructional Fingerprinting of Large Language Models](https://mlsanity.com/paper/2401.12255/) (2024)
- [Do Large Language Model Benchmarks Test Reliability?](https://mlsanity.com/paper/2502.03461/) (2025)
- [Watermarking Pre-trained Language Models with Backdooring](https://mlsanity.com/paper/2210.07543/) (2022)
- [Improve LLM-as-a-Judge Ability as a General Ability](https://mlsanity.com/paper/2502.11689/) (2025)
- [Distillation-Resistant Watermarking for Model Protection in NLP](https://mlsanity.com/paper/2210.03312/) (2022)
- [Antidistillation Sampling](https://mlsanity.com/paper/2504.13146/) (2025)
- [ABKD: Pursuing a Proper Allocation of the Probability Mass in Knowledge Distillation via α-β-Divergence](https://mlsanity.com/paper/2505.04560/) (2025)
- [DOGe: Defensive Output Generation for LLM Protection Against Knowledge Distillation](https://mlsanity.com/paper/2505.19504/) (2025)

## Abstract (arXiv)

Proprietary large language models (LLMs) entail substantial intellectual and financial investment, making them valuable intellectual property (IP). However, even when deployed via black-box APIs, these models remain vulnerable to unauthorized knowledge distillation, which allows adversaries to cheaply extract and replicate model capabilities. To address this issue, anti-distillation (AD) has been proposed to generate defensive outputs that hinder distillation effectiveness, overcoming the limitation of watermarking-based approaches that rely on post-hoc verification. However, existing AD methods based on internal model perturbations struggle to balance anti-distillability and utility (e.g., answer accuracy and naturalness) of reasoning traces, with stronger defenses often causing significant utility loss. To fill this gap, we propose textbfunderlineSkeleton-textbfunderlineGuided textbfunderlineReasoning textbfunderlineEditing (SGRE), an textitAnswer-then-Edit framework that performs post-hoc trace modification for anti-distillation. In the answer stage, the teacher model first generates clean reasoning traces, preserving the original reasoning accuracy while enabling more flexible control over trace naturalness. In the editing stage, we draw inspiration from Cognitive Load Theory (CLT) and introduce a three-stage strategy consisting of reasoning skeleton extraction, skeleton graph coarsening, and skeleton verbalization. These operations jointly perturb reasoning structures and augment textual complexity to amplify extraneous load on student models, hindering their acquisition of underlying reasoning patterns. Extensive experiments across diverse LLMs demonstrate that SGRE achieves state-of-the-art performance in reducing distillation effectiveness, while maintaining lossless reasoning accuracy and superior trace naturalness.