# The Asymptotics of Language Model Alignment with Memory

arXiv: https://arxiv.org/abs/2610.01828 · HTML: https://mlsanity.com/paper/2610.01828/

## 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 15 of its 28 references that are in the map.
- First posted on arXiv 1 Oct 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, 15 of 15)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Neural Text Generation with Unlikelihood Training](https://mlsanity.com/paper/1908.04319/) (2019)
- [GeDi: Generative Discriminator Guided Sequence Generation](https://mlsanity.com/paper/2009.06367/) (2020)
- [Controlling Linguistic Style Aspects in Neural Language Generation](https://mlsanity.com/paper/1707.02633/) (2017)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Calibrating Sequence likelihood Improves Conditional Language Generation](https://mlsanity.com/paper/2210.00045/) (2022)
- [Variational Best-of-N Alignment](https://mlsanity.com/paper/2407.06057/) (2024)
- [Asymptotics of Language Model Alignment](https://mlsanity.com/paper/2404.01730/) (2024)
- [Large Language Models as Markov Chains](https://mlsanity.com/paper/2410.02724/) (2024)

## Abstract (arXiv)

Language model (LM) alignment broadly aims to perturb a given LM Q into an aligned LM q such that i) the outputs produced by q and Q are 'close' in probability, ii) q has a higher expected reward than Q. Two common techniques for LM alignment are: KL-constrained RL, which requires knowledge of the LM distribution and is computationally expensive, and the best-of-n algorithm, which requires only sampling from the LM. The work of Yang et al. established asymptotic closeness between the distributions produced by the two alignment methods for an m--length i.i.d. token sequence output by the LM, in the limit as m increases to infinity. However, the i.i.d. assumption is not representative of practical LMs, whose output sequences often have memory. In this paper, we extend the asymptotic closeness result to the case when the m--length token sequence outputted by the LM is Markovian. Further, for finite-length output sequences -- particularly, when m=1 -- we provide a complete characterization of LM distributions and reward functions for which the KL-divergence between the distributions produced by the two alignment methods is zero -- a question first posed in Yang et al.