# Learning Where It Matters: Geometric Anchoring for Robust Preference Alignment

arXiv: https://arxiv.org/abs/2602.04909 · HTML: https://mlsanity.com/paper/2602.04909/

## 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 26 of its 31 references that are in the map.
- First posted on arXiv 4 Feb 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, 26 of 26)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [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)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [Disentangling Length from Quality in Direct Preference Optimization](https://mlsanity.com/paper/2403.19159/) (2024)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Variance-based regularization with convex objectives](https://mlsanity.com/paper/1610.02581/) (2016)
- [Provably Robust DPO: Aligning Language Models with Noisy Feedback](https://mlsanity.com/paper/2403.00409/) (2024)
- [From CLIP to DINO: Visual Encoders Shout in Multi-modal Large Language Models](https://mlsanity.com/paper/2310.08825/) (2023)
- [Towards Robust Alignment of Language Models: Distributionally Robustifying Direct Preference Optimization](https://mlsanity.com/paper/2407.07880/) (2024)
- [Language Model Alignment with Elastic Reset](https://mlsanity.com/paper/2312.07551/) (2023)
- [AlphaDPO: Adaptive Reward Margin for Direct Preference Optimization](https://mlsanity.com/paper/2410.10148/) (2024)

## Abstract (arXiv)

Direct Preference Optimization (DPO) and related methods align large language models from pairwise preferences by regularizing updates against a fixed reference policy. As the policy drifts, a static reference, however, can become increasingly miscalibrated, leading to distributional mismatch and amplifying spurious preference signals under noisy supervision. Conversely, reference-free variants avoid mismatch but often suffer from unconstrained reward drift. We propose Geometric Anchor Preference Optimization (GAPO), which replaces the fixed reference with a dynamic, geometry-aware anchor: an adversarial local perturbation of the current policy within a small radius that serves as a pessimistic baseline. This anchor enables an adaptive reweighting mechanism, modulating the importance of each preference pair based on its local sensitivity. We further introduce the Anchor Gap, the reward discrepancy between the policy and its anchor, and show under smoothness conditions that it approximates worst-case local margin degradation. Optimizing a logistic objective weighted by this gap downweights geometrically brittle instances while emphasizing robust preference signals. Across diverse noise settings, GAPO consistently improves robustness while matching or improving performance on standard LLM alignment and reasoning benchmarks.