# OrthAlign: Orthogonal Subspace Decomposition for Non-Interfering Multi-Objective Alignment

arXiv: https://arxiv.org/abs/2509.24610 · HTML: https://mlsanity.com/paper/2509.24610/

## Key facts

- Cited by 7 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 52 of its 69 references that are in the map.
- First posted on arXiv 29 Sep 2025.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 30 of 52)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [A Survey on Evaluation of Large Language Models](https://mlsanity.com/paper/2307.03109/) (2023)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [Interpretable Preferences via Multi-Objective Reward Modeling and Mixture-of-Experts](https://mlsanity.com/paper/2406.12845/) (2024)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [Personalized Soups: Personalized Large Language Model Alignment via Post-hoc Parameter Merging](https://mlsanity.com/paper/2310.11564/) (2023)
- [RLHF Workflow: From Reward Modeling to Online RLHF](https://mlsanity.com/paper/2405.07863/) (2024)
- [Is DPO Superior to PPO for LLM Alignment? A Comprehensive Study](https://mlsanity.com/paper/2404.10719/) (2024)
- [PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preference](https://mlsanity.com/paper/2406.15513/) (2024)
- [Rewarded soups: towards Pareto-optimal alignment by interpolating weights fine-tuned on diverse rewards](https://mlsanity.com/paper/2306.04488/) (2023)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [Evolutionary Optimization of Model Merging Recipes](https://mlsanity.com/paper/2403.13187/) (2024)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Mitigating the Alignment Tax of RLHF](https://mlsanity.com/paper/2309.06256/) (2023)
- [Rewards-in-Context: Multi-objective Alignment of Foundation Models with Dynamic Preference Adjustment](https://mlsanity.com/paper/2402.10207/) (2024)
- [Arithmetic Control of LLMs for Diverse User Preferences: Directional Preference Alignment with Multi-Objective Rewards](https://mlsanity.com/paper/2402.18571/) (2024)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Beyond One-Preference-Fits-All Alignment: Multi-Objective Direct Preference Optimization](https://mlsanity.com/paper/2310.03708/) (2023)

## Built on by (most cited first, 7 of 7)

- [PointCoT: A Multi-modal Benchmark for Explicit 3D Geometric Reasoning](https://mlsanity.com/paper/2602.23945/) (2026)
- [Aetheria: A multimodal interpretable content safety framework based on multi-agent debate and collaboration](https://mlsanity.com/paper/2512.02530/) (2025)
- [Beyond Compromise: Pareto-Lenient Consensus for Efficient Multi-Preference LLM Alignment](https://mlsanity.com/paper/2604.05965/) (2026)
- [Rethinking RL Evaluation: Can Benchmarks Truly Reveal Failures of RL Methods?](https://mlsanity.com/paper/2510.10541/) (2025)
- [Explaining and Breaking the Safety-Helpfulness Ceiling via Preference Dimensional Expansion](https://mlsanity.com/paper/2605.11679/) (2026)
- [Spillover-Aware Multi-Value Steering for Pluralistic LLM Alignment](https://mlsanity.com/paper/2609.05800/) (2026)
- [Sparsity-Aware Voxel Attention and Foreground Modulation for 3D Semantic Scene Completion](https://mlsanity.com/paper/2604.05780/) (2026)

## Abstract (arXiv)

Large language model (LLM) alignment faces a critical dilemma when addressing multiple human preferences: improvements in one dimension frequently come at the expense of others, creating unavoidable trade-offs between competing objectives like helpfulness and harmlessness. While prior work mainly focuses on constraint-based optimization algorithms and data selection strategies to mitigate conflicts, these approaches overlook the fundamental issue of resolving conflicts directly at the parameter level. In this paper, we present OrthAlign, an innovative approach that pioneers a new paradigm by leveraging orthogonal subspace decomposition to fundamentally resolve gradient-level conflicts in multi-objective preference alignment. OrthAlign strategically decomposes parameter update spaces into orthogonal subspaces, ensuring that optimization toward different preferences occurs in mathematically non-interfering directions. Building upon this, we provide theoretical guarantees demonstrating that when parameter increments satisfy both orthogonal subspace constraints and spectral norm bounds, the resulting updates exhibit linear Lipschitz growth rather than exponential instability, ensuring stable convergence across all preference dimensions. Extensive experiments show that: I. OrthAlign achieves maximum single-preference improvements ranging from 34.61% to 50.89% after multiple-objective alignment across helpful, harmless, and truthful dimensions. II. With an average overall reward improvement of 13.96%.