# Bias-Restrained Prefix Representation Finetuning for Mathematical Reasoning

arXiv: https://arxiv.org/abs/2511.10707 · HTML: https://mlsanity.com/paper/2511.10707/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 13 Nov 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [Emergent Linear Representations in World Models of Self-Supervised Sequence Models](https://mlsanity.com/paper/2309.00941/) (2023)
- [The Unlocking Spell on Base LLMs: Rethinking Alignment via In-Context Learning](https://mlsanity.com/paper/2312.01552/) (2023)
- [Delta Tuning: A Comprehensive Study of Parameter Efficient Methods for Pre-trained Language Models](https://mlsanity.com/paper/2203.06904/) (2022)
- [Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization](https://mlsanity.com/paper/2311.06243/) (2023)
- [Sparse Low-rank Adaptation of Pre-trained Language Models](https://mlsanity.com/paper/2311.11696/) (2023)
- [ATTEMPT: Parameter-Efficient Multi-task Tuning via Attentional Mixtures of Soft Prompts](https://mlsanity.com/paper/2205.11961/) (2022)
- [Aligning Large Language Models with Human Preferences through Representation Engineering](https://mlsanity.com/paper/2312.15997/) (2023)
- [IncreLoRA: Incremental Parameter Allocation Method for Parameter-Efficient Fine-tuning](https://mlsanity.com/paper/2308.12043/) (2023)
- [Advancing Parameter Efficiency in Fine-tuning via Representation Editing](https://mlsanity.com/paper/2402.15179/) (2024)
- [Unlocking General Long Chain-of-Thought Reasoning Capabilities of Large Language Models via Representation Engineering](https://mlsanity.com/paper/2503.11314/) (2025)
- [The First Few Tokens Are All You Need: An Efficient and Effective Unsupervised Prefix Fine-Tuning Method for Reasoning Models](https://mlsanity.com/paper/2503.02875/) (2025)
- [Improving Reasoning Performance in Large Language Models via Representation Engineering](https://mlsanity.com/paper/2504.19483/) (2025)
- [Shallow Preference Signals: Large Language Model Aligns Even Better with Truncated Data?](https://mlsanity.com/paper/2505.17122/) (2025)
- [Enhancing Chain-of-Thought Reasoning with Critical Representation Fine-tuning](https://mlsanity.com/paper/2507.10085/) (2025)

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

- [RuleWeaver: Benchmarking Rule-Centered Scenario Reasoning for Large Language Models](https://mlsanity.com/paper/2608.26832/) (2026)

## Abstract (arXiv)

Parameter-Efficient finetuning (PEFT) enhances model performance on downstream tasks by updating a minimal subset of parameters. Representation finetuning (ReFT) methods further improve efficiency by freezing model weights and optimizing internal representations with fewer parameters than PEFT, outperforming PEFT on several tasks. However, ReFT exhibits a significant performance decline on mathematical reasoning tasks. To address this problem, the paper demonstrates that ReFT's poor performance on mathematical tasks primarily stems from its struggle to generate effective reasoning prefixes during the early inference phase. Moreover, ReFT disturbs the numerical encoding and the error accumulats during the CoT stage. Based on these observations, this paper proposes Bias-REstrained Prefix Representation FineTuning (BREP ReFT), which enhances ReFT's mathematical reasoning capability by truncating training data to optimize the generation of initial reasoning prefixes, intervening on the early inference stage to prevent error accumulation, and constraining the intervention vectors' magnitude to avoid disturbing numerical encoding. Extensive experiments across diverse model architectures demonstrate BREP's superior effectiveness, efficiency, and robust generalization capability, outperforming both standard ReFT and weight-based PEFT methods on the task of mathematical reasoning. The source code is available at https://github.com/LiangThree/BREP.