On the Rejection Criterion for Proxy-based Test-time Alignment

Aligning large language models (LLMs) with diverse user preferences is a critical yet challenging task. While post-training methods can adapt models to specific needs, they often require costly data curation and additional training. Test-time scaling (TTS) presents an efficient, training-free alternative, but its application has been largely limited to verifiable domains like mathematics and coding, where response correctness is easily judged. To extend TTS to preference alignment, we introduce a novel framework that models the task as a realignment problem, since the base model often fails to sufficiently align with the stated preference. Our key insight is to decompose the underlying reward function into two components: one related to the question and the other to preference information. This allows us to derive a REAlignment Reward (REAR) that selectively rescales the proportions of these two reward terms. We then show that REAR can be formulated as a linear combination of token-level policy log-probabilities, making it computationally efficient and easy to integrate with various TTS algorithms such as best-of-$N$ sampling and tree search. Experiments show that compared to other test-time baselines, REAR not only enables scalable test-time realignment for preference alignment tasks under diverse user requirements, but also generalizes to mathematical and visual tasks under appropriate preference settings.

When aligning frontier models through post-training techniques, it is not possible to directly demonstrate all of the behaviours we want a model to exhibit in all possible deployment environments; our model must generalise outside of the post-training distribution. One proposed solution is alignment midtraining (AMT), which continues pretraining on large volumes of alignment-relevant documents to encourage generalisation in later stages of training. Despite the prominence of AMT as an alignment approach, there is limited public evidence for its effectiveness. To resolve this, we identify several assumptions around midtraining and evaluate them across scale: up to 110 billion-parameter models and 1 billion midtraining tokens. For instance, we study a scenario where post-training data is ambiguous between two possible motivations. We find that midtraining can steer the model's motivation in simple versions of this setting. However, the presence of a tiny fraction of finetuning data which suggests a competing motivation erases the effects of AMT. We also study scenarios in which we want an AI to follow a number of rules, but only demonstrate a subset of them. We find that demonstrations must be present either in midtraining or post-training datasets for these rules to be robustly learned. Based on these and other findings, we do not believe that there is sufficient public evidence for us to confidently state that midtraining can address the core difficulties inherent in aligning powerful AI systems.

Language model (LM) alignment improves model outputs to reflect human preferences while preserving the capabilities of the base model. The most common alignment approaches are (i) reinforcement learning, which maximizes the expected reward under a KL-divergence constraint, and (ii) best-of-$N$ alignment, which selects the highest-reward output among $N$ independent samples. Despite their widespread use, the fundamental limits of reward improvement under a KL budget remain poorly understood. We characterize the information-theoretic limits of KL-regularized alignment by deriving the maximum achievable expected reward gain for a fixed KL-divergence budget. Our first result provides a closed-form expression for the optimal reward improvement, governed by a Jeffreys divergence term rather than the $\sqrt{\texttt{KL}}$ used in prior analyses. We further reformulate this expression as a covariance under the base model, yielding a practical estimator that predicts achievable alignment gains from base model samples alone. We extend our analysis to the proxy reward setting, showing that the gap between ideal and proxy alignment (reward hacking) grows with the magnitude of reward error and when the KL penalty factor decreases. We then prove that reward ensembling mitigates reward hacking, providing a theoretical justification for this technique used in practice. Empirically, we compute the KL-reward Pareto frontier for two tasks for LMs, safety and summarization, and show that best-of-$N$ closely approaches the theoretical limit, while PPO and GRPO remain substantially suboptimal. Our theoretical results shed light on several empirically observed phenomena in the alignment literature and suggest that algorithmic improvements are needed to achieve optimal alignment without high inference costs.