How to cite?

If you are using the pyhgf package for your research, we ask you to cite the following paper in the final publication:

Legrand, N., Weber, L., Waade, P. T., Møller Daugaard, A. H., Khodadadi, M., Mikuš, N., & Mathys, C. (2026). pyhgf: A neural network library for predictive coding. PLOS Computational Biology, 22(6), Article e1014340. https://doi.org/10.1371/journal.pcbi.1014340

@article{Legrand2026,
  author = {Legrand, Nicolas and Weber, Lilian and Waade, Peter Thestrup and Møller Daugaard, Anna Hedvig and Khodadadi, Mojtaba and Mikuš, Nace and Mathys, Christoph},
  title = {pyhgf: A neural network library for predictive coding},
  journal = {PLOS Computational Biology},
  volume = {22},
  number = {6},
  pages = {e1014340},
  year = {2026},
  doi = {10.1371/journal.pcbi.1014340},
  url = {https://doi.org/10.1371/journal.pcbi.1014340}
}

If your application is using the generalised Hierarchical Gaussian Filter, we also ask you to cite the following publication:

Weber, L. A., Waade, P. T., Legrand, N., Møller, A. H., Stephan, K. E., & Mathys, C. (2026). The generalized Hierarchical Gaussian Filter. eLife, 15, Article RP110174. https://doi.org/10.7554/eLife.110174.1

@article{Weber2026,
  author = {Weber, Lilian Aline and Waade, Peter Thestrup and Legrand, Nicolas and Møller, Anna Hedvig and Stephan, Klaas Enno and Mathys, Christoph},
  title = {The generalized Hierarchical Gaussian Filter},
  journal = {eLife},
  volume = {15},
  pages = {RP110174},
  year = {2026},
  doi = {10.7554/eLife.110174.1},
  url = {https://doi.org/10.7554/eLife.110174.1}
}

If you used the unbounded updates for volatility parents, you should reference it using:

Mathys, C., Legrand, N., Waade, P. T., Mikuš, N., & Weber, L. A. (2026). Robust volatility updates for Hierarchical Gaussian Filtering (arXiv:2605.00966). arXiv. https://doi.org/10.48550/arXiv.2605.00966

@misc{Mathys2026,
  author = {Mathys, Christoph and Legrand, Nicolas and Waade, Peter Thestrup and Mikuš, Nace and Weber, Lilian Aline},
  title = {Robust volatility updates for Hierarchical Gaussian Filtering},
  year = {2026},
  eprint = {2605.00966},
  archivePrefix = {arXiv},
  primaryClass = {cs.LG},
  doi = {10.48550/arXiv.2605.00966},
  url = {https://arxiv.org/abs/2605.00966}
}

If you want to refer to the foundational description of the Hierarchical Gaussian Filter, or other important mathematical derivations, please refer to the following publications:

Mathys, C., Daunizeau, J., Friston, K. J., & Stephan, K. E. (2011). A Bayesian foundation for individual learning under uncertainty. Frontiers in Human Neuroscience, 5, Article 39. https://doi.org/10.3389/fnhum.2011.00039

@article{2011:mathys,
  author = {Mathys, Christoph and Daunizeau, Jean and Friston, Karl J. and Stephan, Klaas E.},
  title = {A Bayesian foundation for individual learning under uncertainty},
  journal = {Frontiers in Human Neuroscience},
  volume = {5},
  pages = {39},
  year = {2011},
  doi = {10.3389/fnhum.2011.00039},
  url = {https://doi.org/10.3389/fnhum.2011.00039}
}

Mathys, C. D., Lomakina, E. I., Daunizeau, J., Iglesias, S., Brodersen, K. H., Friston, K. J., & Stephan, K. E. (2014). Uncertainty in perception and the Hierarchical Gaussian Filter. Frontiers in Human Neuroscience, 8, Article 825. https://doi.org/10.3389/fnhum.2014.00825

@article{2014:mathys,
  author = {Mathys, Christoph D. and Lomakina, Ekaterina I. and Daunizeau, Jean and Iglesias, Sandra and Brodersen, Kay H. and Friston, Karl J. and Stephan, Klaas E.},
  title = {Uncertainty in perception and the Hierarchical Gaussian Filter},
  journal = {Frontiers in Human Neuroscience},
  volume = {8},
  pages = {825},
  year = {2014},
  doi = {10.3389/fnhum.2014.00825},
  url = {https://doi.org/10.3389/fnhum.2014.00825}
}