Mind the Gap: Structure-Aware Consistency in Preference Learning

Aligning Large Language Models (LLMs) with human intent, whether through explicit reward modeling or direct methods such as DPO, fundamentally relies on minimizing a surrogate loss as a proxy for the true pairwise ranking objective. We prove that this reliance is flawed for the standard surrogate losses used: for the equicontinuous hypothesis sets characteristic of neural networks, no standard surrogate provides a meaningful consistency guarantee. Minimizing the surrogate loss to zero can leave the true ranking error arbitrarily high. To resolve this, we formulate LLM alignment within a margin-shifted ranking framework and derive $H$-consistency bounds showing that enforcing a confidence margin $\gamma$ is not merely beneficial but necessary for consistency. We further introduce Structure-Aware $H$-consistency and a corresponding objective (SA-DPO) that adapts the margin to the semantic distance between responses, preventing instability on near-synonymous pairs. Finally, we analyze the trade-off between the margin required for consistency and the model's finite capacity to satisfy it, revealing a strict hierarchy of surrogate losses: heavy-tailed surrogates (e.g., the Polynomial Hinge family) offer strictly superior consistency guarantees for capacity-bounded models compared to the logistic loss used in DPO. Experiments on UltraFeedback and Argilla DPO-Mix-7k confirm that SA-DPO consistently outperforms DPO and SimPO, with a 58.5% head-to-head win-rate in downstream generation quality.