@article{howarelinearrepresentationslearnedexacts,
  title = {How are linear representations learned? Exact solutions to the dynamics of abstraction},
  author = {William W. Yang and Andrew M. Saxe and Peter E. Latham},
  year = {2026},
  eprint = {2607.08843},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.08843},
}