# Test-time reward-guided alignment of language models by importance sampling on pre-logit space

arXiv: https://arxiv.org/abs/2510.26219 · HTML: https://mlsanity.com/paper/2510.26219/

## 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 39 of its 53 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Placed in

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

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

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- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [A Contrastive Framework for Neural Text Generation](https://mlsanity.com/paper/2202.06417/) (2022)
- [Advancing LLM Reasoning Generalists with Preference Trees](https://mlsanity.com/paper/2404.02078/) (2024)
- [RAIN: Your Language Models Can Align Themselves without Finetuning](https://mlsanity.com/paper/2309.07124/) (2023)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)
- [Controlled Decoding from Language Models](https://mlsanity.com/paper/2310.17022/) (2023)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [Aligning Language Models with Preferences through f-divergence Minimization](https://mlsanity.com/paper/2302.08215/) (2023)
- [Is Best-of-N the Best of Them? Coverage, Scaling, and Optimality in Inference-Time Alignment](https://mlsanity.com/paper/2503.21878/) (2025)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [BOND: Aligning LLMs with Best-of-N Distillation](https://mlsanity.com/paper/2407.14622/) (2024)
- [Revisiting Mahalanobis Distance for Transformer-Based Out-of-Domain Detection](https://mlsanity.com/paper/2101.03778/) (2021)
- [Aligning Large Language Models with Representation Editing: A Control Perspective](https://mlsanity.com/paper/2406.05954/) (2024)
- [GenARM: Reward Guided Generation with Autoregressive Reward Model for Test-time Alignment](https://mlsanity.com/paper/2410.08193/) (2024)
- [Value Augmented Sampling for Language Model Alignment and Personalization](https://mlsanity.com/paper/2405.06639/) (2024)
- [Transfer Q Star: Principled Decoding for LLM Alignment](https://mlsanity.com/paper/2405.20495/) (2024)
- [Asymptotics of Language Model Alignment](https://mlsanity.com/paper/2404.01730/) (2024)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)

## Abstract (arXiv)

Test-time alignment of large language models (LLMs) attracts attention because fine-tuning of LLMs requires high computational costs. In this paper, we propose a new test-time reward-guided alignment method called adaptive importance sampling on pre-logits (AISP) on the basis of the sampling-based model predictive control with the stochastic control input. AISP applies the Gaussian perturbation into pre-logits, which are outputs of the penultimate layer, so as to maximize expected rewards with respect to the mean of the perturbation. We demonstrate that the optimal mean is obtained by importance sampling with sampled rewards. AISP outperforms best-of-n sampling in terms of rewards over the number of used samples and achieves higher rewards than other reward-based test-time alignment methods.