# Answer-Conditioned Chains of Thought Degrade Verifiable-Reasoning Distillation in Large Language Models

arXiv: https://arxiv.org/abs/2607.14552 · HTML: https://mlsanity.com/paper/2607.14552/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)
- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 23 of 23)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [V-STaR: Training Verifiers for Self-Taught Reasoners](https://mlsanity.com/paper/2402.06457/) (2024)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [CRISP: Compressed Reasoning via Iterative Self-Policy Distillation](https://mlsanity.com/paper/2603.05433/) (2026)
- [Nemotron-Cascade: Scaling Cascaded Reinforcement Learning for General-Purpose Reasoning Models](https://mlsanity.com/paper/2512.13607/) (2025)
- [Reverse Thinking Makes LLMs Stronger Reasoners](https://mlsanity.com/paper/2411.19865/) (2024)
- [Mitigating Spurious Correlations Between Question and Answer via Chain-of-Thought Correctness Perception Distillation](https://mlsanity.com/paper/2509.05602/) (2025)
- [HEAL: Hindsight Entropy-Assisted Learning for Reasoning Distillation](https://mlsanity.com/paper/2603.10359/) (2026)
- [RAFT: Data Refinement and Adaptive Distillation for Domain Fine-Tuning with Alleviated Forgetting](https://mlsanity.com/paper/2606.00147/) (2026)
- [Robust Reasoning via Dynamic Token Selection for Distribution-Aligned Self-Distillation](https://mlsanity.com/paper/2606.00628/) (2026)

## Built on by (most cited first, 7 of 7)

- [Faster Block-Diffusion Serving with Distribution-Free Risk Guarantees](https://mlsanity.com/paper/2609.33887/) (2026)
- [Risk-Controlled Selective LLM Answering by Pricing Label-Free Checks](https://mlsanity.com/paper/2609.37493/) (2026)
- [Recovering Off-Policy Supervision for Speculative Decoding](https://mlsanity.com/paper/2609.38795/) (2026)
- [Refusal Localizes, the Damage Relocates: Safety Layers Under Few-Sample Fine-Tuning](https://mlsanity.com/paper/2610.00320/) (2026)
- [Distilling Directional Verification](https://mlsanity.com/paper/2610.00997/) (2026)
- [ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models](https://mlsanity.com/paper/2610.07803/) (2026)
- [CV-OPD: Contrastive Vision On-policy Distillation](https://mlsanity.com/paper/2610.13264/) (2026)

## Abstract (arXiv)

A standard recipe for distilling the reasoning ability of large language models (LLMs) is to sample chains of thought from the model, keep those that reach the correct final answer, and fine-tune on the survivors. When sampling fails, a common fix shows the generator the gold answer and asks it to write a chain that reaches that answer. We show that this second step degrades the training data in a way that correctness filtering cannot catch. We run a controlled experiment that fixes the generator, the problem set, and the correctness filter, and varies only whether the chain is generated under answer-conditioning, the gold answer shown with a request to reach it. Training a strong instruction-tuned reasoning model on its own answer-conditioned chains sharply lowers its verifiable-reasoning accuracy. The loss grows with difficulty, reaching as much as about 27 points on the hardest competition problems. The mechanism is legible in the chains themselves, which rationalize backward from the shown answer instead of deriving it, with the early final-answer statement as the measurable symptom. The harm is a property of the data rather than the generator, read off unlabeled generations before any fine-tuning, ordering the penalty across eight thinking models from four families, and transferring across teacher families. A prompt ablation localizes it to the rationalize-toward instruction rather than the answer's bare visibility. The practical takeaway is to generate answer-blind, because no correctness filter can see this damage in the data.