# A Common Pitfall of Margin-based Language Model Alignment: Gradient Entanglement

arXiv: https://arxiv.org/abs/2410.13828 · HTML: https://mlsanity.com/paper/2410.13828/

## Key facts

- Cited by 10 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 19 of its 27 references that are in the map.
- First posted on arXiv 17 Oct 2024.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [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)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Contrastive Preference Optimization: Pushing the Boundaries of LLM Performance in Machine Translation](https://mlsanity.com/paper/2401.08417/) (2024)
- [Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive](https://mlsanity.com/paper/2402.13228/) (2024)
- [Self-Play Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2405.00675/) (2024)
- [Disentangling Length from Quality in Direct Preference Optimization](https://mlsanity.com/paper/2403.19159/) (2024)
- [Controlled Decoding from Language Models](https://mlsanity.com/paper/2310.17022/) (2023)
- [RL on Incorrect Synthetic Data Scales the Efficiency of LLM Math Reasoning by Eight-Fold](https://mlsanity.com/paper/2406.14532/) (2024)
- [TLCR: Token-Level Continuous Reward for Fine-grained Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2407.16574/) (2024)

## Built on by (most cited first, 10 of 10)

- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [AMaPO: Adaptive Margin-attached Preference Optimization for Language Model Alignment](https://mlsanity.com/paper/2511.09385/) (2025)
- [Towards Disentangled Preference Optimization Dynamics: Suppress the Loser, Preserve the Winner](https://mlsanity.com/paper/2604.18239/) (2026)
- [Future Policy Approximation for Offline Reinforcement Learning in LLM Reasoning](https://mlsanity.com/paper/2509.19893/) (2025)
- [Beyond Binary Preference: Aligning Diffusion Models to Fine-grained Criteria by Decoupling Attributes](https://mlsanity.com/paper/2601.04300/) (2026)
- [Gradient-Gated DPO: Stabilizing Preference Optimization in Language Models](https://mlsanity.com/paper/2605.02626/) (2026)
- [ChainPrune: Evaluating and Reducing Redundancy in Long Chain-of-Thought Reasoning](https://mlsanity.com/paper/2608.21860/) (2026)
- [Smaller Models, Better Rejects: Preference Distillation Scaling](https://mlsanity.com/paper/2609.38987/) (2026)
- [Masking Frequent Tokens Sharpens Direct Preference Optimization](https://mlsanity.com/paper/2609.32445/) (2026)
- [Gradient-Aligned Pair Selection for Personalized Preference Optimization](https://mlsanity.com/paper/2610.00061/) (2026)

## Abstract (arXiv)

Reinforcement Learning from Human Feedback (RLHF) has become the predominant approach for language model (LM) alignment. At its core, RLHF uses a margin-based loss for preference optimization, specifying ideal LM behavior only by the difference between preferred and dispreferred responses. In this paper, we identify a common pitfall of margin-based methods -- the under-specification of ideal LM behavior on preferred and dispreferred responses individually, which leads to two unintended consequences as the margin increases: (1) The probability of dispreferred (e.g., unsafe) responses may increase, resulting in potential safety alignment failures. (2) The probability of preferred responses may decrease, even when those responses are ideal. We demystify the reasons behind these problematic behaviors: margin-based losses couple the change in the preferred probability to the gradient of the dispreferred one, and vice versa, often preventing the preferred probability from increasing while the dispreferred one decreases, and thus causing a synchronized increase or decrease in both probabilities. We term this effect, inherent in margin-based objectives, gradient entanglement. Formally, we derive conditions for general margin-based alignment objectives under which gradient entanglement becomes concerning: the inner product of the gradients of preferred and dispreferred log-probabilities is large relative to the individual gradient norms. We theoretically investigate why such inner products can be large when aligning language models and empirically validate our findings. Empirical implications of our framework extend to explaining important differences in the training dynamics of various preference optimization algorithms, and suggesting potential algorithm designs to mitigate the under-specification issue of margin-based methods and thereby improving language model alignment.