# Iterative Finetuning is Mostly Idempotent

arXiv: https://arxiv.org/abs/2605.01130 · HTML: https://mlsanity.com/paper/2605.01130/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 19 of its 23 references that are in the map.
- First posted on arXiv 1 May 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 19 of 19)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data](https://mlsanity.com/paper/2404.01413/) (2024)
- [A Tale of Tails: Model Collapse as a Change of Scaling Laws](https://mlsanity.com/paper/2402.07043/) (2024)
- [Pride and Prejudice: LLM Amplifies Self-Bias in Self-Refinement](https://mlsanity.com/paper/2402.11436/) (2024)
- [The Curious Decline of Linguistic Diversity: Training Language Models on Synthetic Text](https://mlsanity.com/paper/2311.09807/) (2023)
- [Subliminal Learning: Language models transmit behavioral traits via hidden signals in data](https://mlsanity.com/paper/2507.14805/) (2025)
- [Model Organisms for Emergent Misalignment](https://mlsanity.com/paper/2506.11613/) (2025)
- [How Bad is Training on Synthetic Data? A Statistical Analysis of Language Model Collapse](https://mlsanity.com/paper/2404.05090/) (2024)
- [Systematic Evaluation of LLM-as-a-Judge in LLM Alignment Tasks: Explainable Metrics and Diverse Prompt Templates](https://mlsanity.com/paper/2408.13006/) (2024)
- [Persistent Pre-Training Poisoning of LLMs](https://mlsanity.com/paper/2410.13722/) (2024)
- [Embarrassingly Simple Self-Distillation Improves Code Generation](https://mlsanity.com/paper/2604.01193/) (2026)
- [LLM Probability Concentration: How Alignment Shrinks the Generative Horizon](https://mlsanity.com/paper/2506.17871/) (2025)
- [Bias Amplification in Language Model Evolution: An Iterated Learning Perspective](https://mlsanity.com/paper/2404.04286/) (2024)
- [Bias Amplification: Large Language Models as Increasingly Biased Media](https://mlsanity.com/paper/2410.15234/) (2024)
- [The Lock-in Hypothesis: Stagnation by Algorithm](https://mlsanity.com/paper/2506.06166/) (2025)
- [The Impact of AI-Generated Text on the Internet](https://mlsanity.com/paper/2604.26965/) (2026)

## Abstract (arXiv)

If a model has some behavioral tendency, such as sycophancy or misalignment, and it is trained on its own outputs, will the tendency be amplified in the next generation of models? We study this question by training a series of models where each model is finetuned on data generated by its predecessor, and the initial model is seeded with some persona or belief. We test three settings: supervised finetuning (SFT) on instruct models, synthetic document finetuning (SDF) on base models, and direct preference optimization (DPO). In the SFT and SDF settings, traits mostly decay or remain constant so that further finetuning cycles do nothing. In rare cases when amplification occurs, it generally comes at the cost of coherence. In the DPO setting, trait amplification can reliably occur when a model is continually trained with a preference for its own outputs, but vanishes when models are reinitialized at each cycle. Overall, our results suggest that amplification most likely comes from continual post-training, and limiting this stage may be an effective defense. For non-RL finetuning, trait amplification is rare and very sensitive to data quantity, making it significantly less likely to occur accidentally. Finally, the amplification-coherence tradeoff serves as a natural deterrent against trait amplification.