# PORT: Preference Optimization on Reasoning Traces

arXiv: https://arxiv.org/abs/2406.16061 · HTML: https://mlsanity.com/paper/2406.16061/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 37 of its 73 references that are in the map.
- First posted on arXiv 23 Jun 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)
- 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)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [A General Theoretical Paradigm to Understand Learning from Human Preferences](https://mlsanity.com/paper/2310.12036/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Galactica: A Large Language Model for Science](https://mlsanity.com/paper/2211.09085/) (2022)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [Zephyr: Direct Distillation of LM Alignment](https://mlsanity.com/paper/2310.16944/) (2023)
- [Reinforced Self-Training (ReST) for Language Modeling](https://mlsanity.com/paper/2308.08998/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [SLiC-HF: Sequence Likelihood Calibration with Human Feedback](https://mlsanity.com/paper/2305.10425/) (2023)
- [Beyond Human Data: Scaling Self-Training for Problem-Solving with Language Models](https://mlsanity.com/paper/2312.06585/) (2023)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [KTO: Model Alignment as Prospect Theoretic Optimization](https://mlsanity.com/paper/2402.01306/) (2024)
- [AI Alignment: A Comprehensive Survey](https://mlsanity.com/paper/2310.19852/) (2023)

## Built on by (most cited first, 6 of 6)

- [Accurate and Diverse LLM Mathematical Reasoning via Automated PRM-Guided GFlowNets](https://mlsanity.com/paper/2504.19981/) (2025)
- [Communication Enables Cooperation in LLM Agents: A Comparison with Curriculum-Based Approaches](https://mlsanity.com/paper/2510.05748/) (2025)
- [Semantic Communication meets System 2 ML: How Abstraction, Compositionality and Emergent Languages Shape Intelligence](https://mlsanity.com/paper/2505.20964/) (2025)
- [Control-R: Towards controllable test-time scaling](https://mlsanity.com/paper/2506.00189/) (2025)
- [RACE-Align: Retrieval-Augmented and Chain-of-Thought Enhanced Preference Alignment for Large Language Models](https://mlsanity.com/paper/2506.02726/) (2025)
- [Visual Compliance via Executable Safety Rule Entailment](https://mlsanity.com/paper/2609.18328/) (2026)

## Abstract (arXiv)

Preference optimization methods have been successfully applied to improve not only the alignment of large language models (LLMs) with human values, but also specific natural language tasks such as summarization and stylistic continuations. This paper proposes using preference optimization methods on Chain-of-Thought steps in order to improve the mathematical reasoning performances of language models. While the chosen answers are obtained from datasets that include reasoning traces, we propose two complementary schemes for generating rejected answers: weak LLM prompting, and digit corruption. Our approach leads to increased accuracy on the GSM8K and AQuA-RAT mathematical reasoning benchmarks for Falcon2-11B and Mistral-7B. Additionally, the improved abilities transfer to non-mathematical tasks, including the ARC benchmark and symbolic reasoning challenges. For example, our method can lead to up to relative 8.47% and 18.73% increases in accuracy on the GSM8K and AQuA benchmarks respectively, without any extra annotations. This work suggests that the path towards better language reasoning abilities goes through spending resources on creating high-quality datasets of reasoning traces.