@article{directdensityratiooptimizationa,
  title = {Direct Density Ratio Optimization: A Statistically Consistent Approach to Aligning Large Language Models},
  author = {Rei Higuchi and Taiji Suzuki},
  year = {2025},
  eprint = {2505.07558},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2505.07558v2},
}