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 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.
Iterative alignment methods based on purely greedy updates are remarkably effective in practice, yet existing theoretical guarantees of O(logT) KL-regularized regret can seem pessimistic relative to their empirical performance. In this paper, we argue that this mismatch arises from the regret criterion itself: KL-regularized regret conflates the statistical cost of learning with the exploratory randomization induced by the softened training policy. To separate these effects, we study the traditional temperature-zero regret criterion, which evaluates only the top-ranked response at inference time. Under this decision-centric notion of performance, we prove that standard greedy online alignment methods, including online RLHF and online DPO, achieve constant (O(1)) cumulative regret. By isolating the cost of identifying the best response from the stochasticity induced by regularization, our results provide a sharper theoretical explanation for the practical superb efficiency of greedy alignment.
Post-training alignment algorithms are predominantly evaluated as black boxes, obscuring how they reshape language models' internal computations. We present a systematic mechanistic analysis of six preference-optimization methods: PPO, DPO, SimPO, ORPO, GRPO, and KTO across three open-weight model families. By integrating layer-wise linear probing, Sparse Autoencoders, and crosscoders, we localize preference representations and quantify alignment-induced geometric transformations in latent space. We find that preference signals consistently concentrate in early--mid or mid--late layers, but different objectives induce qualitatively distinct representational shifts. KTO and GRPO enhance linear separability through constructive feature sharing and sparse, high-salience recruitment. In contrast, DPO and ORPO degrade separability via non-constructive geometric rotation and feature attenuation, while PPO and SimPO largely preserve baseline geometry. These transformations exhibit architecture-dependent variability, demonstrating that behavioral alignment does not imply uniform internal restructuring. Our findings establish alignment as a heterogeneous intervention, motivate standardized feature-level auditing for safety and interpretability, and highlight the need for mechanism-aware optimization objectives.
The alignment of large language models with human preferences is commonly achieved through Reinforcement Learning from Human Feedback or Direct Preference Optimization. However, these methods are vulnerable to the significant noise prevalent in real-world preference datasets. To address this critical issue, we present a theoretical framework for unbiased alignment, introducing the Unbiased Reward Model (URM) loss and the Unbiased Direct Preference Optimization (UDPO) loss. By mathematically correcting the distortion induced by preference noise, our novel objectives enable unbiased model training directly from noisy datasets, without requiring clean ground-truth supervision. We provide rigorous theoretical analyses demonstrating that our methods are noise-tolerant, parameter downward compatible, and classification-calibrated. Comprehensive experiments across diverse datasets demonstrate that our approaches outperform state-of-the-art baselines. Code available at: https://github.com/cswjl/unbiased-alignment.