Large reasoning models have recently demonstrated strong performance on complex tasks that require long chain-of-thought reasoning, through supervised fine-tuning on large-scale and high-quality datasets. To construct such datasets, existing pipelines generate long reasoning data from more capable Large Language Models (LLMs) and apply manually heuristic or naturalness-based selection methods to filter high-quality samples. Despite the proven effectiveness of naturalness-based data selection, which ranks data by the average log probability assigned by LLMs, our analysis shows that, when applied to LLM reasoning datasets, it systematically prefers samples with longer reasoning steps (i.e., more tokens per step) rather than higher-quality ones, a phenomenon we term step length confounding. Through quantitative analysis, we attribute this phenomenon to low-probability first tokens in reasoning steps; longer steps dilute their influence, thereby inflating the average log probabilities. To address this issue, we propose two variant methods: ASLEC-DROP, which drops first-token probabilities when computing average log probability, and ASLEC-CASL, which applies a causal debiasing regression to remove the first tokens’ confounding effect. Experiments across four LLMs and five evaluation benchmarks demonstrate the effectiveness of our approach in mitigating the step length confounding problem.

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.