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 **C**ritical **R**epresentation **F**ine-**T**uning (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. Notably, our method improves the accuracy of LLaMA-2-7B and ReFT by 18.2 and 3.8, respectively, on GSM8K, while using only 0.016 of the model parameters, significantly less than other PEFT methods. 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.

Exploiting large language models (LLMs) to tackle reasoning has garnered growing attention. It still remains highly challenging to achieve satisfactory results in complex logical problems, characterized by plenty of premises within the context and requiring multi-hop reasoning. In particular, the reasoning capabilities of LLMs are brittle to disorder and distractibility. In this work, we first examine the mechanism from the perspective of information flow and reveal that LLMs confront difficulties akin to human-like cognitive biases when dealing with disordered and irrelevant content in reasoning tasks. However, in contrast to LLMs, disordered and irrelevant content does not significantly decrease human performance, as humans have a propensity to distill the most relevant information and systematically organize their thoughts, aiding them in responding to questions.Stem from that, we further propose a novel reasoning approach named Concise and Organized Perception (COP). COP carefully analyzes the given statements to identify the most pertinent information while eliminating redundancy efficiently. It then prompts the LLMs in a more organized form that adapts to the model’s inference process. By perceiving concise and organized context, the reasoning abilities of LLMs can be better elicited. Extensive experimental results on several popular logical benchmarks (ProofWriter, PrOntoQA, PrOntoQA-OOD, and FOLIO) and mathematical benchmark (DI-GSM) show that COP significantly outperforms previous state-of-the-art methods.

Large Vision Language Models (LVLMs) achieve great performance on visual-language reasoning tasks, however, the black-box nature of LVLMs hinders in-depth research on the reasoning mechanism. As all images need to be converted into image tokens to fit the input format of large language models (LLMs) along with natural language prompts, sequential visual representation is essential to the performance of LVLMs, and the information flow analysis approach can be an effective tool for determining interactions between these representations. In this paper, we propose integrating attention analysis with LLaVA-CAM, concretely, attention scores highlight relevant regions during forward propagation, while LLaVA-CAM captures gradient changes through backward propagation, revealing key image features. By exploring the information flow from the perspective of visual representation contribution, we observe that it tends to converge in shallow layers but diversify in deeper layers. To validate our analysis, we conduct comprehensive experiments with truncation strategies across various LVLMs for visual question answering and image captioning tasks, and experimental results not only verify our hypothesis but also reveal a consistent pattern of information flow convergence in the corresponding layers, and the information flow cliff layer will be different due to different contexts.