# Decomposing the Delta: What Do Models Actually Learn from Preference Pairs?

arXiv: https://arxiv.org/abs/2604.08723 · HTML: https://mlsanity.com/paper/2604.08723/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Process reward models for reasoning, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 37 of its 42 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/)

## Builds on (most cited first, 30 of 37)

- [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)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [SimPO: Simple Preference Optimization with a Reference-Free Reward](https://mlsanity.com/paper/2405.14734/) (2024)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Iterative Reasoning Preference Optimization](https://mlsanity.com/paper/2404.19733/) (2024)
- [HelpSteer2: Open-source dataset for training top-performing reward models](https://mlsanity.com/paper/2406.08673/) (2024)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [ROSCOE: A Suite of Metrics for Scoring Step-by-Step Reasoning](https://mlsanity.com/paper/2212.07919/) (2022)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [HelpSteer: Multi-attribute Helpfulness Dataset for SteerLM](https://mlsanity.com/paper/2311.09528/) (2023)
- [Aligning Diffusion Models by Optimizing Human Utility](https://mlsanity.com/paper/2404.04465/) (2024)
- [ReCEval: Evaluating Reasoning Chains via Correctness and Informativeness](https://mlsanity.com/paper/2304.10703/) (2023)
- [Evaluating Mathematical Reasoning Beyond Accuracy](https://mlsanity.com/paper/2404.05692/) (2024)
- [Unintentional Unalignment: Likelihood Displacement in Direct Preference Optimization](https://mlsanity.com/paper/2410.08847/) (2024)
- [Evaluating Step-by-step Reasoning Traces: A Survey](https://mlsanity.com/paper/2502.12289/) (2025)
- [MR-GSM8K: A Meta-Reasoning Benchmark for Large Language Model Evaluation](https://mlsanity.com/paper/2312.17080/) (2023)
- [Can Large Language Models Detect Errors in Long Chain-of-Thought Reasoning?](https://mlsanity.com/paper/2502.19361/) (2025)
- [MR-Ben: A Meta-Reasoning Benchmark for Evaluating System-2 Thinking in LLMs](https://mlsanity.com/paper/2406.13975/) (2024)

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

- [Smaller Models, Better Rejects: Preference Distillation Scaling](https://mlsanity.com/paper/2609.38987/) (2026)

## Abstract (arXiv)

Preference optimization methods such as DPO and KTO are widely used for aligning language models, yet little is understood about what properties of preference data drive downstream reasoning gains. We ask: what aspects of a preference pair improve a reasoning model's performance on general reasoning tasks? We investigate two distinct notions of quality delta in preference data: generator-level delta, arising from the differences in capability between models that generate chosen and rejected reasoning traces, and sample-level delta, arising from differences in judged quality differences within an individual preference pair. To study generator-level delta, we vary the generator's scale and model family, and to study sample-level delta, we employ an LLM-as-a-judge to rate the quality of generated traces along multiple reasoning-quality dimensions. We find that increasing generator-level delta steadily improves performance on out-of-domain reasoning tasks and filtering data by sample-level delta can enable more data-efficient training. Our results suggest a twofold recipe for improving reasoning performance through preference optimization: maximize generator-level delta when constructing preference pairs and exploit sample-level delta to select the most informative training examples.