The provided paper introduces Unsupervised Prefix Fine-Tuning (UPFT), a novel method to improve the reasoning abilities of large language models. This technique leverages the observation that initial reasoning steps are often consistent across different solution attempts, a phenomenon the authors term "Prefix Self-Consistency." Instead of requiring labeled data or computationally intensive sampling of full solutions, UPFT fine-tunes models using only the first few tokens of generated reasoning paths. Experiments demonstrate that UPFT matches or surpasses the performance of supervised fine-tuning methods while significantly reducing training time and computational cost. This approach offers an efficient and scalable way to enhance reasoning in LLMs by focusing on the crucial initial stages of problem-solving.