# Enhancing Chain-of-Thought Reasoning with Critical Representation Fine-tuning

arXiv: https://arxiv.org/abs/2507.10085 · HTML: https://mlsanity.com/paper/2507.10085/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 29 of its 41 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [DoLa: Decoding by Contrasting Layers Improves Factuality in Large Language Models](https://mlsanity.com/paper/2309.03883/) (2023)
- [Explain Yourself! Leveraging Language Models for Commonsense Reasoning](https://mlsanity.com/paper/1906.02361/) (2019)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [LLM-Adapters: An Adapter Family for Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2304.01933/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Label Words are Anchors: An Information Flow Perspective for Understanding In-Context Learning](https://mlsanity.com/paper/2305.14160/) (2023)
- [A Simple Method for Commonsense Reasoning](https://mlsanity.com/paper/1806.02847/) (2018)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [ReFT: Representation Finetuning for Language Models](https://mlsanity.com/paper/2404.03592/) (2024)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Tell Your Model Where to Attend: Post-hoc Attention Steering for LLMs](https://mlsanity.com/paper/2311.02262/) (2023)
- [RAVEL: Evaluating Interpretability Methods on Disentangling Language Model Representations](https://mlsanity.com/paper/2402.17700/) (2024)
- [Unveiling and Harnessing Hidden Attention Sinks: Enhancing Large Language Models without Training through Attention Calibration](https://mlsanity.com/paper/2406.15765/) (2024)
- [WorldTree: A Corpus of Explanation Graphs for Elementary Science Questions supporting Multi-Hop Inference](https://mlsanity.com/paper/1802.03052/) (2018)
- [SocialIQA: Commonsense Reasoning about Social Interactions](https://mlsanity.com/paper/1904.09728/) (2019)
- [Advancing Parameter Efficiency in Fine-tuning via Representation Editing](https://mlsanity.com/paper/2402.15179/) (2024)
- [The LLM Language Network: A Neuroscientific Approach for Identifying Causally Task-Relevant Units](https://mlsanity.com/paper/2411.02280/) (2024)
- [Focus on Your Question! Interpreting and Mitigating Toxic CoT Problems in Commonsense Reasoning](https://mlsanity.com/paper/2402.18344/) (2024)

## Built on by (most cited first, 3 of 3)

- [How Far Ahead Do LLMs Plan? Uncovering the Latent Horizon in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2602.02103/) (2026)
- [Bias-Restrained Prefix Representation Finetuning for Mathematical Reasoning](https://mlsanity.com/paper/2511.10707/) (2025)
- [Representation Finetuning for Continual Learning](https://mlsanity.com/paper/2603.11201/) (2026)

## Abstract (arXiv)

Representation Fine-tuning (ReFT), a recently proposed Parameter-Efficient Fine-Tuning (PEFT) method, has attracted widespread attention for significantly improving parameter efficiency by editing representation space alone. In this work, we investigate applying ReFT to complex reasoning tasks. However, directly using the native ReFT method, which modifies fixed representations at the beginning and end of each layer, yields suboptimal performance, as these fixed-position representations have uncertain impact on the outputs. We observe that, in complex reasoning tasks, there often exist certain critical representations. These representations either integrate significant information from preceding layers or regulate subsequent layer representations. Through layer-by-layer propagation, they exert a substantial influence on the final output. Naturally, fine-tuning these critical representations has the potential to greatly enhance reasoning performance. Building upon these insights, we propose Critical Representation Fine-Tuning (CRFT), a novel method that identifies and optimizes these critical representations through information flow analysis. CRFT operates within a supervised learning framework, dynamically optimizing critical representations in a low-rank linear subspace while freezing the base model. The effectiveness and efficiency of our method are validated across eight benchmarks for arithmetic and commonsense reasoning, using LLaMA and Mistral model families. Furthermore, our method also adapts effectively to few-shot settings, boosting one-shot accuracy by 16.4%. Our work highlights the untapped potential of representation-level optimization for CoT reasoning, offering a lightweight yet powerful alternative to traditional PEFT methods.