About

I am a senior research scientist in the Compositional Intelligence team at Quantinuum. In my work I apply category theory and string diagrams to formalise various topics across science, including:

  • Quantum foundations
  • Interpretability of artificial intelligence
  • Causal reasoning
  • Models of cognition, including conceptual spaces and active inference
  • Theories of consciousness such as Integrated Information Theory

I am also a founding member of the Association for Mathematical Consciousness Science.

Bio

I took the MMath in Mathematics at the University of Cambridge before completing a DPhil in the Quantum Group of the Computer Science Department at the University of Oxford, supervised by Bob Coecke and Chris Heunen. My thesis was titled Categorical Operational Physics.

From 2018 to 2019 I held postdoctoral positions in the Oxford Quantum group and the School of Informatics at the University of Edinburgh.

Since December 2019 I have been a researcher in the Oxford branch of Quantinuum (formerly Cambridge Quantum Computing).

News

  • 11 Jan 2024: Co-organised the Causal Cognition in Humans and Machines conference in the Department of Computer Science at the University of Oxford! For more details see the conference webpage and booklet.
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  • Apr 2023: Co-organised the Categories for Consciousness Science (Cats4Consc) workshop in the Mathematical Institute at the University of Oxford; see the conference webpage.

Papers


Sean Tull, Razin A Shaikh, Sara Sabrina Zemljic, Stephen Clark (2024). From conceptual spaces to quantum concepts: formalising and learning structured conceptual models. Quantum Machine Intelligence.

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Sean Tull, Robin Lorenz, Stephen Clark, Ilyas Khan, Bob Coecke (2024). Towards Compositional Interpretability for XAI.

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Sean Tull, Johannes Kleiner, Toby St Clere Smithe (2023). Active Inference in String Diagrams: A Categorical Account of Predictive Processing and Free Energy.

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Robin Lorenz, Sean Tull (2023). Causal models in string diagrams.

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Razin A Shaikh, Sara Sabrina Zemljic, Sean Tull, Stephen Clark (2022). The Conceptual VAE.

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Sean Tull (2021). A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces. Proceedings of ACT 2021.

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Sean Tull, Johannes Kleiner (2020). Integrated Information in Process Theories. Proceedings of SEMSPACE 2020 (To appear).

Sean Tull (2020). Monoidal Categories for Formal Concept Analysis. Proceedings of SEMSPACE 2020 (To appear).

Marino Gran, Chris Heunen, Sean Tull (2020). Monoidal characterisation of groupoids and connectors. Topology and its Applications.

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Pau Enrique Moliner, Chris Heunen, Sean Tull (2020). Tensor topology. Journal of Pure and Applied Algebra.

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Johannes Kleiner, Sean Tull (2020). The mathematical structure of integrated information theory. arXiv preprint arXiv:2002.07655.

Sean Tull (2019). Deriving Dagger Compactness. Proceedings of QPL 2019..

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Sean Tull (2019). Quotient Categories and Phases. Theory and Applications of Categories, Vol. 34.

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Sean Tull (2018). Categorical Operational Physics (DPhil Thesis).

Pau Enrique Moliner, Chris Heunen, Sean Tull (2018). Space in Monoidal Categories. m̊ Proceedings 14th International Conference on Quantum Physics and Logic, ̊Nijmegen, The Netherlands, 3-7 July 2017.

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Bob Coecke, John Selby, Sean Tull (2018). Two Roads to Classicality. m̊ Proceedings 14th International Conference on Quantum Physics and Logic, ̊Nijmegen, The Netherlands, 3-7 July 2017.

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Sean Tull (2017). Condition for an n-permutable category to be Mal’tsev. Cahiers de Topologie et Géométrie Différentielle Catégoriques.

Aleks Kissinger, Sean Tull, Bas Westerbaan (2017). Picture-perfect Quantum Key Distribution.

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S. Tull (2016). Operational Theories of Physics as Categories.

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Chris Heunen, Sean Tull (2015). Categories of relations as models of quantum theory. Proceedings of the 12th International Workshop on Quantum Physics and Logic, Oxford, U.K., July 15-17, 2015.

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Talks

  • Towards Compositional Interpretability for XAI. Applied Category Theory 2024, Unversity of Oxford. 21/06/24.

  • Active Inference in String Diagrams. Paris Mathematical Models of Cognition and Consciousness Seminar, Sorbonne Université, Paris. 29/05/24.

  • Causal Cognition via String Diagrams. Causal Cognition in Humans Machines, University of Oxford. 12/01/24.

  • Active Inference in String Diagrams. Active Inference Livestream. 01/09/2023. Video.

  • Active Inference in String Diagrams: A Categorical Account of Predictive Processing and the Free Energy Principle. Applied Category Theory 2023, University of Maryland. 04/08/23.

  • Causal Models in String Diagrams. Applied Category Theory 2023, University of Maryland. 02/08/23.

  • Causal Models in Compositional Intelligence. Quantum Natural Langauge Processing 2023. Chalmers University of Technology, Gothenburg, Sweden. 17/05/23.

  • A Categorical Formulation of Predictive Processing. Category Theory for Consciousness Science workshop, University of Oxford. 15/04/23.

  • Compositional Approaches in Cognition. Learning and Reasoning Seminar (online). 15/03/23.

  • A categorical formulation of Predictive Processing and Active Inference. Models of Consciousness 2022, Stanford University. 06/09/22.

  • Category Theory for Consciousness Science (Tutorial). Models of Consciousness 2022, Pre-Conference Virtual Bootcamp. 30/08/22.

  • A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces. Applied Category Theory 2021. 12/07/21. Video.

  • Monoidal Categories for Formal Concept Analysis. SEMSPACE 2020. 07/08/20. Video.

  • Integrated Information in Process Theories. SEMSPACE 2020. 07/08/20. Video.

  • Generalised Integrated Information Theories. Models of Consciousness Conference, Mathematical Institute, University of Oxford. 09/09/19. Video.

  • Deriving Dagger Compactness. Quantum Physics and Logic Conference, Chapman University California, 14/06/19.

  • Superpositions and Categorical Quantum Reconstructions. Symposium on Compositional Structures, University of Strathclyde, Glasgow, 17/12/18.

  • A Categorical Reconstruction of Quantum Theory. Quantum Physics and Logic XV Conference, Dalhousie University, 07/06/18. 6th World Congress of Universal Logic, Vichy, 23/06/18.

  • Two Roads to Classicality. Quantum Physics and Logic XIV Conference, Radboud University Nijmegen, 05/07/17. Video.

  • Operational Theories of Physics as Categories. Foundations of Physics 2016 Conference, London School of Economics, 18/07/16.

  • Operational physics, logic and categories. Categories, Logic and Physics Workshop, University of Edinburgh, 14/04/16. Video.

  • A new perspective on internal groupoids and crossed modules. UCL-ULB-VUB Category Theory Seminar, Free University Brussels, 25/01/16.

  • Categories of relations as models of quantum theory. Quantum Physics and Logic XII Conference, University of Oxford, 17/07/15. Video.