# Radioactive Feedback: Tracing Models Trained by Label-Only LLM Supervision

arXiv: https://arxiv.org/abs/2610.15685 · HTML: https://mlsanity.com/paper/2610.15685/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 39 of its 43 references that are in the map.
- First posted on arXiv 11 Oct 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 30 of 39)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Enhancing Chat Language Models by Scaling High-quality Instructional Conversations](https://mlsanity.com/paper/2305.14233/) (2023)
- [A Watermark for Large Language Models](https://mlsanity.com/paper/2301.10226/) (2023)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Turning Your Weakness Into a Strength: Watermarking Deep Neural Networks by Backdooring](https://mlsanity.com/paper/1802.04633/) (2018)
- [Robust Distortion-free Watermarks for Language Models](https://mlsanity.com/paper/2307.15593/) (2023)
- [Provable Robust Watermarking for AI-Generated Text](https://mlsanity.com/paper/2306.17439/) (2023)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [Embedding Watermarks into Deep Neural Networks](https://mlsanity.com/paper/1701.04082/) (2017)
- [Undetectable Watermarks for Language Models](https://mlsanity.com/paper/2306.09194/) (2023)
- [TACO: Topics in Algorithmic COde generation dataset](https://mlsanity.com/paper/2312.14852/) (2023)
- [CATER: Intellectual Property Protection on Text Generation APIs via Conditional Watermarks](https://mlsanity.com/paper/2209.08773/) (2022)
- [Instructional Fingerprinting of Large Language Models](https://mlsanity.com/paper/2401.12255/) (2024)

## Abstract (arXiv)

Conventional distillation transfers capability through teacher-generated demonstrations. LLM-as-a-Judge knowledge distillation offers a distinct and increasingly practical alternative. In the label-only variant studied here, the student generates every response and improves from scalar scores alone. Prior work shows that this non-demonstrative feedback can improve student capability, but it creates a fundamentally different provenance problem. No teacher-generated answer enters the student's training set, so any evaluator-specific trace must pass through a low-bandwidth reward signal rather than copied text. Existing watermarks and distillation detectors do not cover this score-only channel. We introduce Radioactive Feedback, which encodes a registered pattern of behavioral preferences in the rewards themselves. The evaluator applies bounded pointwise adjustments to quality-qualified responses, allowing repeated optimization to transfer the pattern to a student trained by another party. Experiments on code and mathematics show that the registered preferences transfer through scores alone and across datasets, enabling black-box detection against a fixed reference pool.