@article{forwardversusbackwardcomparingreasoningo,
  title = {Forward versus Backward: Comparing Reasoning Objectives in Direct Preference Optimization},
  author = {Murtaza Nikzad and Raghuram Ramanujan},
  year = {2026},
  eprint = {2601.07199},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2601.07199},
}