%%% transportability

@inproceedings{pearl2011transportability,
  title={Transportability of causal and statistical relations: A formal approach},
  author={Pearl, Judea and Bareinboim, Elias},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={25},
  number={1},
  pages={247--254},
  year={2011}
}


@book{bookelias2025causalai,
  author    = {Elias Bareinboim},
  title     = {Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems},
  publisher = {Publisher Name},
  year      = {2025},
  url       = {https://causalai-book.net/},
}


@article{hu2022lora,
  title={Lora: Low-rank adaptation of large language models.},
  author={Hu, Edward J and Shen, Yelong and Wallis, Phillip and Allen-Zhu, Zeyuan and Li, Yuanzhi and Wang, Shean and Wang, Lu and Chen, Weizhu and others},
  journal={ICLR},
  volume={1},
  number={2},
  pages={3},
  year={2022}
}

@book{latour2007actortheory,
    author = {Latour, Bruno},
    title = {Reassembling the Social: An Introduction to Actor-Network-Theory},
    publisher = {Oxford University Press},
    year = {2005},
    month = {07},
    isbn = {9780199256044},
    doi = {10.1093/oso/9780199256044.001.0001},
    url = {https://doi.org/10.1093/oso/9780199256044.001.0001},
}


@incollection{psillos2010causalpluralism,
  title={Causal pluralism},
  author={Psillos, Stathis},
  booktitle={Worldviews, science and us: Studies of analytical metaphysics: A selection of topics from a methodological perspective},
  pages={131--151},
  year={2010},
  publisher={World Scientific}
}

@article{woodward2001manipulability,
  title={Causation and manipulability},
  author={Woodward, James},
  year={2001}
}

@article{ghrist2022cellular,
  title={Cellular sheaves of lattices and the Tarski Laplacian},
  author={Ghrist, Robert and Riess, Hans},
  journal={Homology, Homotopy and Applications},
  volume={24},
  number={1},
  year={2022}
}

@article{serre1955faisceaux,
  title={Faisceaux alg{\'e}briques coh{\'e}rents},
  author={Serre, Jean-Pierre},
  journal={Annals of Mathematics},
  pages={197--278},
  year={1955},
  publisher={JSTOR}
}

@article{bareinboim2016causal,
  title={Causal inference and the data-fusion problem},
  author={Bareinboim, Elias and Pearl, Judea},
  journal={Proceedings of the National Academy of Sciences},
  volume={113},
  number={27},
  pages={7345--7352},
  year={2016},
  publisher={National Academy of Sciences}
}

%%% transfer learning

@inproceedings{zhang2013domain,
  title={Domain adaptation under target and conditional shift},
  author={Zhang, Kun and Sch{\"o}lkopf, Bernhard and Muandet, Krikamol and Wang, Zhikun},
  booktitle={International Conference on Machine Learning},
  pages={819--827},
  year={2013},
  organization={PMLR}
}

@inproceedings{zhang2015multi,
  title={Multi-source domain adaptation: A causal view},
  author={Zhang, Kun and Gong, Mingming and Sch{\"o}lkopf, Bernhard},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={29},
  number={1},
  year={2015}
}

@inproceedings{gong2016domain,
  title={Domain adaptation with conditional transferable components},
  author={Gong, Mingming and Zhang, Kun and Liu, Tongliang and Tao, Dacheng and Glymour, Clark and Sch{\"o}lkopf, Bernhard},
  booktitle={International Conference on Machine Learning},
  pages={2839--2848},
  year={2016},
  organization={PMLR}
}

@article{rojas2018invariant,
  title={Invariant models for causal transfer learning},
  author={Rojas-Carulla, Mateo and Sch{\"o}lkopf, Bernhard and Turner, Richard and Peters, Jonas},
  journal={Journal of Machine Learning Research},
  volume={19},
  number={36},
  pages={1--34},
  year={2018}
}

@article{magliacane2018domain,
  title={Domain adaptation by using causal inference to predict invariant conditional distributions},
  author={Magliacane, Sara and Van Ommen, Thijs and Claassen, Tom and Bongers, Stephan and Versteeg, Philip and Mooij, Joris M},
  journal={Advances in Neural Information Processing Systems},
  volume={31},
  year={2018}
}

@article{zhang2020domain,
  title={Domain adaptation as a problem of inference on graphical models},
  author={Zhang, Kun and Gong, Mingming and Stojanov, Petar and Huang, Biwei and Liu, Qingsong and Glymour, Clark},
  journal={Advances in Neural Information Processing Systems},
  volume={33},
  pages={4965--4976},
  year={2020}
}

%%% Abstraction

@inproceedings{rubenstein2017causal,
  title={Causal Consistency of Structural Equation Models},
  author={Rubenstein, P and Weichwald, S and Bongers, S and Mooij, J and Janzing, D and Grosse-Wentrup, M and Sch{\"o}lkopf, B},
  booktitle={33rd Conference on Uncertainty in Artificial Intelligence (UAI 2017)},
  pages={808--817},
  year={2017},
  organization={Curran Associates, Inc.}
}

@inproceedings{beckers2019abstracting,
  title={Abstracting causal models},
  author={Beckers, Sander and Halpern, Joseph Y},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={33},
  number={01},
  pages={2678--2685},
  year={2019}
}

@inproceedings{beckers2020approximate,
  title={Approximate causal abstractions},
  author={Beckers, Sander and Eberhardt, Frederick and Halpern, Joseph Y},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={606--615},
  year={2020},
  organization={PMLR}
}

@phdthesis{rischel2020category,
  title={The category theory of causal models},
  author={Rischel, Eigil Fjeldgren},
  year={2020},
  school={University of Copenhagen}
}

@inproceedings{
zennaro2022abstraction,
title={Abstraction between Structural Causal Models: {A} Review of Definitions and Properties},
author={Fabio Massimo Zennaro},
booktitle={UAI 2022 Workshop on Causal Representation Learning},
year={2022},
url={https://openreview.net/forum?id=GHZlIYDgZHE}
}

@inproceedings{rischel2021compositional,
  title={Compositional abstraction error and a category of causal models},
  author={Rischel, Eigil F and Weichwald, Sebastian},
  booktitle={Uncertainty in Artificial Intelligence},
  pages={1013--1023},
  year={2021},
  organization={PMLR}
}

@inproceedings{zennaro2023quantifying,
author = {Zennaro, Fabio Massimo and Turrini, Paolo and Damoulas, Theodoros},
title = {Quantifying consistency and information loss for causal abstraction learning},
year = {2023},
isbn = {978-1-956792-03-4},
url = {https://doi.org/10.24963/ijcai.2023/638},
doi = {10.24963/ijcai.2023/638},
booktitle = {Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence},
articleno = {638},
numpages = {8},
location = {Macao, P.R.China},
series = {IJCAI '23}
}

@inproceedings{massidda2023causal,
  title={Causal abstraction with soft interventions},
  author={Massidda, Riccardo and Geiger, Atticus and Icard, Thomas and Bacciu, Davide},
  booktitle={Conference on Causal Learning and Reasoning},
  pages={68--87},
  year={2023},
  organization={PMLR}
}

@inproceedings{zennaro2023jointly,
  title={Jointly learning consistent causal abstractions over multiple interventional distributions},
  author={Zennaro, Fabio Massimo and Dr{\'a}vucz, M{\'a}t{\'e} and Apachitei, Geanina and Widanage, W Dhammika and Damoulas, Theodoros},
  booktitle={Conference on Causal Learning and Reasoning},
  pages={88--121},
  year={2023},
  organization={PMLR}
}

@inproceedings{felekis2024causal,
  title={Causal Optimal Transport of Abstractions},
  author={Felekis, Yorgos and Zennaro, Fabio Massimo and Branchini, Nicola and Damoulas, Theodoros},
  booktitle={Causal Learning and Reasoning},
  pages={462--498},
  year={2024},
  organization={PMLR}
}

@inproceedings{xia2024neural,
  title={Neural causal abstractions},
  author={Xia, Kevin and Bareinboim, Elias},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={38},
  number={18},
  pages={20585--20595},
  year={2024}
}

@inproceedings{
massidda2024learning,
title={Learning Causal Abstractions of Linear Structural Causal Models},
author={Riccardo Massidda and Sara Magliacane and Davide Bacciu},
booktitle={The 40th Conference on Uncertainty in Artificial Intelligence},
year={2024},
url={https://openreview.net/forum?id=XlFqI9TMhf}
}

%%% Equivalence

@incollection{verma2022equivalence,
  title={Equivalence and synthesis of causal models},
  author={Verma, Thomas S and Pearl, Judea},
  booktitle={Probabilistic and causal inference: {T}he works of Judea Pearl},
  pages={221--236},
  year={2022}
}

@inproceedings{beckers2021equivalent,
  title={Equivalent causal models},
  author={Beckers, Sander},
  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},
  volume={35},
  number={7},
  pages={6202--6209},
  year={2021}
}

@inproceedings{otsuka2022equivalence,
  title={On the equivalence of causal models: {A} category-theoretic approach},
  author={Otsuka, Jun and Saigo, Hayato},
  booktitle={Conference on Causal Learning and Reasoning},
  pages={634--646},
  year={2022},
  organization={PMLR}
}

@inproceedings{dacunto2024extracting,
  title={Extracting the Multiscale Causal Backbone of Brain Dynamics},
  author={D'Acunto, Gabriele and Bonchi, Francesco and De Francisci Morales, Gianmarco and Petri, Giovanni},
  booktitle={Causal Learning and Reasoning},
  pages={265--295},
  year={2024},
  organization={PMLR}
}

@book{absil2008optimization,
  title={Optimization algorithms on matrix manifolds},
  author={Absil, P-A and Mahony, Robert and Sepulchre, Rodolphe},
  year={2008},
  publisher={Princeton University Press}
}

@book{boumal2023introduction,
  title={An introduction to optimization on smooth manifolds},
  author={Boumal, Nicolas},
  year={2023},
  publisher={Cambridge University Press}
}

@book{mac2013categories,
  title={Categories for the working mathematician},
  author={Mac Lane, Saunders},
  volume={5},
  year={2013},
  publisher={Springer Science \& Business Media}
}

@book{perrone2024starting,
  title={Starting category theory},
  author={Perrone, Paolo},
  year={2024},
  publisher={World Scientific}
}

@book{curry2014sheaves,
  title={Sheaves, cosheaves and applications},
  author={Curry, Justin Michael},
  year={2014},
  publisher={University of Pennsylvania}
}

@phdthesis{hansen2020laplacians,
  title={Laplacians of Cellular Sheaves: Theory and Applications},
  author={Hansen, Jakob},
  year={2020},
  school={University of Pennsylvania}
}

@article{d'acunto2023learning,
title={Learning Multiscale Non-stationary Causal Structures},
author={Gabriele D'Acunto and Gianmarco De Francisci Morales and Paolo Bajardi and Francesco Bonchi},
journal={Transactions on Machine Learning Research},
issn={2835-8856},
year={2023},
url={https://openreview.net/forum?id=SQnPE63jtA},
note={}
}

@book{pearl2009causality,
  title={Causality},
  author={Pearl, Judea},
  year={2009},
  publisher={Cambridge University Press}
}

@article{hansen2019toward,
  title={Toward a spectral theory of cellular sheaves},
  author={Hansen, Jakob and Ghrist, Robert},
  journal={Journal of Applied and Computational Topology},
  volume={3},
  number={4},
  pages={315--358},
  year={2019},
  publisher={Springer}
}

@article{eberhardt2007interventions,
  title={Interventions and causal inference},
  author={Eberhardt, Frederick and Scheines, Richard},
  journal={Philosophy of science},
  volume={74},
  number={5},
  pages={981--995},
  year={2007},
  publisher={Cambridge University Press}
}

@article{fritz2009convex,
  title={Convex spaces {I}: Definition and examples},
  author={Fritz, Tobias},
  journal={arXiv preprint arXiv:0903.5522},
  year={2009}
}

@inproceedings{jacobs2019causal,
  title={Causal inference by string diagram surgery},
  author={Jacobs, Bart and Kissinger, Aleks and Zanasi, Fabio},
  booktitle={Foundations of Software Science and Computation Structures: 22nd International Conference, FOSSACS 2019, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2019, Prague, Czech Republic, April 6--11, 2019, Proceedings 22},
  pages={313--329},
  year={2019},
  organization={Springer}
}

@book{peters2017elements,
  title={Elements of causal inference: {F}oundations and learning algorithms},
  author={Peters, Jonas and Janzing, Dominik and Sch{\"o}lkopf, Bernhard},
  year={2017},
  publisher={The MIT Press}
}

@article{bodnar2022neural,
  title={Neural sheaf diffusion: A topological perspective on heterophily and oversmoothing in gnns},
  author={Bodnar, Cristian and Di Giovanni, Francesco and Chamberlain, Benjamin and Lio, Pietro and Bronstein, Michael},
  journal={Advances in Neural Information Processing Systems},
  volume={35},
  pages={18527--18541},
  year={2022}
}

@book{bollen1989structural,
  title={Structural equations with latent variables},
  author={Bollen, Kenneth A},
  volume={210},
  year={1989},
  publisher={John Wiley \& Sons}
}

@article{d2023learning,
  title={Learning multiscale non-stationary causal structures},
  author={D'Acunto, Gabriele and Morales, Gianmarco De Francisci and Bajardi, Paolo and Bonchi, Francesco},
  journal={Transactions on Machine Learning Research},
  year={2023}
}

@article{hansen2021opinion,
  title={Opinion dynamics on discourse sheaves},
  author={Hansen, Jakob and Ghrist, Robert},
  journal={SIAM Journal on Applied Mathematics},
  volume={81},
  number={5},
  pages={2033--2060},
  year={2021},
  publisher={SIAM}
}

@book{pearl2018book,
  title={The book of why: {T}he new science of cause and effect},
  author={Pearl, Judea and Mackenzie, Dana},
  year={2018},
  publisher={Basic books}
}

@inproceedings{
richens2024robust,
title={Robust agents learn causal world models},
author={Jonathan Richens and Tom Everitt},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=pOoKI3ouv1}
}

@book{bredon2012sheaf,
  title={Sheaf theory},
  author={Bredon, Glen E},
  volume={170},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@book{griffiths2014principles,
  title={Principles of algebraic geometry},
  author={Griffiths, Phillip and Harris, Joseph},
  year={2014},
  publisher={John Wiley \& Sons}
}

@article{mclarty2003rising,
  title={The Rising Sea: Grothendieck on simplicity and generality {I}},
  author={McLarty, Colin},
  year={2003}
}

@inproceedings{strinati2024goal,
  title={Goal-oriented and semantic communication in {6G} {AI}-native networks: {T}he {6G}-{GOALS} approach},
  author={Strinati, Emilio Calvanese and Di Lorenzo, Paolo and Sciancalepore, Vincenzo and Aijaz, Adnan and Kountouris, Marios and G{\"u}nd{\"u}z, Deniz and Popovski, Petar and Sana, Mohamed and Stavrou, Photios A and Soret, Beatriz and others},
  booktitle={2024 Joint European Conference on Networks and Communications \& 6G Summit (EuCNC/6G Summit)},
  pages={1--6},
  year={2024},
  organization={IEEE}
}

@book{villani2021topics,
  title={Topics in optimal transportation},
  author={Villani, C{\'e}dric},
  volume={58},
  year={2021},
  publisher={American Mathematical Society}
}

@inproceedings{
d2025causal,
title={Causal Abstraction Learning based on the Semantic Embedding Principle},
author={D'Acunto, Gabriele and Zennaro, Fabio Massimo and Felekis, Yorgos and Di Lorenzo, Paolo},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=J16AIOkjjY}
}

@inproceedings{zhang2009identifiability,
  title={On the identifiability of the post-nonlinear causal model},
  author={Zhang, Kun and Hyv{\"a}rinen, Aapo},
  booktitle={Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence},
  pages={647--655},
  year={2009}
}

@inproceedings{kaltenpoth2023nonlinear,
  title={Nonlinear causal discovery with latent confounders},
  author={Kaltenpoth, David and Vreeken, Jilles},
  booktitle={International Conference on Machine Learning},
  pages={15639--15654},
  year={2023},
  organization={PMLR}
}

@inproceedings{immer2023identifiability,
  title={On the identifiability and estimation of causal location-scale noise models},
  author={Immer, Alexander and Schultheiss, Christoph and Vogt, Julia E and Sch{\"o}lkopf, Bernhard and B{\"u}hlmann, Peter and Marx, Alexander},
  booktitle={International Conference on Machine Learning},
  pages={14316--14332},
  year={2023},
  organization={PMLR}
}