# Tangent Space Fine-Tuning for Directional Preference Alignment in Large Language Models

arXiv: https://arxiv.org/abs/2602.01128 · HTML: https://mlsanity.com/paper/2602.01128/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 4 of its 8 references that are in the map.
- First posted on arXiv 1 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, 4 of 4)

- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
- [Task Arithmetic in the Tangent Space: Improved Editing of Pre-Trained Models](https://mlsanity.com/paper/2305.12827/) (2023)
- [Arithmetic Control of LLMs for Diverse User Preferences: Directional Preference Alignment with Multi-Objective Rewards](https://mlsanity.com/paper/2402.18571/) (2024)
- [SteerLM: Attribute Conditioned SFT as an (User-Steerable) Alternative to RLHF](https://mlsanity.com/paper/2310.05344/) (2023)

## Built on by (most cited first, 1 of 1)

- [Distilling Linearized Behavior into Non-Linear Fine-Tuning for Effective Task Arithmetic](https://mlsanity.com/paper/2605.18993/) (2026)

## Abstract (arXiv)

Our goal is to enable large language models (LLMs) to balance multiple human preference dimensions; such as helpfulness, safety, and verbosity, through principled and controllable alignment. Existing preference optimization methods, including Direct Preference Optimization (DPO), collapse feedback into a single scalar reward, fixing one balance among objectives and preventing traversal of the Pareto front. Recent work by Ortiz-Jimenez et al. (2023) showed that fine-tuning can be viewed in a model's tangent space, where linearized updates act as additive vectors that can be composed to jointly perform well on multiple tasks. Building on this formulation, we extend this idea to preference alignment and propose Tangent-Space Direct Preference Optimization (TS-DPO), which performs DPO within this locally linear regime to learn per-objective update directions. These directions can be linearly combined at inference to generate user-specified behaviors without additional optimization. Evaluated on the helpfulness-verbosity trade-off using the HelpSteer and UltraFeedback datasets, TS-DPO achieves broader Pareto-optimal coverage and smoother preference control than scalarized DPO. Canonical Correlation Analysis (CCA) further shows that tangent-space training amplifies canonical directions aligned with distinct preferences, improving disentanglement.