# TPO: Aligning Large Language Models with Multi-branch & Multi-step Preference Trees

arXiv: https://arxiv.org/abs/2410.12854 · HTML: https://mlsanity.com/paper/2410.12854/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 43 of its 59 references that are in the map.
- First posted on arXiv 10 Oct 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 43)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [MetaMath: Bootstrap Your Own Mathematical Questions for Large Language Models](https://mlsanity.com/paper/2309.12284/) (2023)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [ORPO: Monolithic Preference Optimization without Reference Model](https://mlsanity.com/paper/2403.07691/) (2024)
- [Multi-Agent Collaboration: Harnessing the Power of Intelligent LLM Agents](https://mlsanity.com/paper/2306.03314/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs](https://mlsanity.com/paper/2406.18629/) (2024)
- [Smaug: Fixing Failure Modes of Preference Optimisation with DPO-Positive](https://mlsanity.com/paper/2402.13228/) (2024)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Explicit Inductive Bias for Transfer Learning with Convolutional Networks](https://mlsanity.com/paper/1802.01483/) (2018)

## Built on by (most cited first, 19 of 19)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [A Survey of Direct Preference Optimization](https://mlsanity.com/paper/2503.11701/) (2025)
- [Ontology-Guided Reverse Thinking Makes Large Language Models Stronger on Knowledge Graph Question Answering](https://mlsanity.com/paper/2502.11491/) (2025)
- [ProMed: Shapley Information Gain Guided Reinforcement Learning for Proactive Medical LLMs](https://mlsanity.com/paper/2508.13514/) (2025)
- [LearNAT: Learning NL2SQL with AST-guided Task Decomposition for Large Language Models](https://mlsanity.com/paper/2504.02327/) (2025)
- [Anchoring Values in Temporal and Group Dimensions for Flow Matching Model Alignment](https://mlsanity.com/paper/2512.12387/) (2025)
- [SuperWriter: Reflection-Driven Long-Form Generation with Large Language Models](https://mlsanity.com/paper/2506.04180/) (2025)
- [Magical: Medical Lay Language Generation via Semantic Invariance and Layperson-tailored Adaptation](https://mlsanity.com/paper/2508.08730/) (2025)
- [InterMT: Multi-Turn Interleaved Preference Alignment with Human Feedback](https://mlsanity.com/paper/2505.23950/) (2025)
- [3DS: Medical Domain Adaptation of LLMs via Decomposed Difficulty-based Data Selection](https://mlsanity.com/paper/2410.10901/) (2024)
- [The Differences Between Direct Alignment Algorithms are a Blur](https://mlsanity.com/paper/2502.01237/) (2025)
- [SPPD: Self-training with Process Preference Learning Using Dynamic Value Margin](https://mlsanity.com/paper/2502.13516/) (2025)
- [ASPO: Adaptive Sentence-Level Preference Optimization for Fine-Grained Multimodal Reasoning](https://mlsanity.com/paper/2505.19100/) (2025)
- [DFAMS: Dynamic-flow guided Federated Alignment based Multi-prototype Search](https://mlsanity.com/paper/2508.20353/) (2025)
- [Aligning Deep Implicit Preferences by Learning to Reason Defensively](https://mlsanity.com/paper/2510.11194/) (2025)
- [Ambiguity Awareness Optimization: Towards Semantic Disambiguation for Direct Preference Optimization](https://mlsanity.com/paper/2511.23391/) (2025)
- [AdaFuse: Accelerating Dynamic Adapter Inference via Token-Level Pre-Gating and Fused Kernel Optimization](https://mlsanity.com/paper/2603.11873/) (2026)
- [MASS-DPO: Multi-negative Active Sample Selection for Direct Policy Optimization](https://mlsanity.com/paper/2605.10784/) (2026)
- [ATLAS: A Multi-LLM Training Framework for EvoDPO with Adaptive Reference Evolution](https://mlsanity.com/paper/2602.02709/) (2026)

## Abstract (arXiv)

In the domain of complex reasoning tasks, such as mathematical reasoning, recent advancements have proposed the use of Direct Preference Optimization (DPO) to suppress output of dispreferred responses, thereby enhancing the long-chain reasoning capabilities of large language models (LLMs). To this end, these studies employed LLMs to generate preference trees via Tree-of-thoughts (ToT) and sample the paired preference responses required by the DPO algorithm. However, the DPO algorithm based on binary preference optimization is unable to learn multiple responses with varying degrees of preference/dispreference that provided by the preference trees, resulting in incomplete preference learning. In this work, we introduce Tree Preference Optimization (TPO), that does not sample paired preference responses from the preference tree; instead, it directly learns from the entire preference tree during the fine-tuning. Specifically, TPO formulates the language model alignment as a Preference List Ranking problem, where the policy can potentially learn more effectively from a ranked preference list of responses given the prompt. In addition, to further assist LLMs in identifying discriminative steps within long-chain reasoning and increase the relative reward margin in the preference list, TPO utilizes Adaptive Step Reward to adjust the reward values of each step in trajectory for performing fine-grained preference optimization. We carry out extensive experiments on mathematical reasoning tasks to evaluate TPO. The experimental results indicate that TPO consistently outperforms DPO across five public large language models on four datasets. Our code is publicly available at https://github.com/MrBlankness/TPO.git.