Nominal String Diagrams
Lead Research Organisation:
University College London
Department Name: Computer Science
Abstract
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Organisations
- University College London (Lead Research Organisation)
- UNIVERSITY OF OXFORD (Collaboration)
- University of Pisa (Collaboration)
- University of the Witwatersrand (Collaboration)
- UNIVERSITY OF BIRMINGHAM (Collaboration)
- Mount Allison University (Collaboration)
- UNIVERSITY OF JOHANNESBURG (Collaboration)
- Tallinn University (Collaboration)
- UNIVERSITY OF STRATHCLYDE (Collaboration)
Publications
Alvarez-Picallo M
(2022)
Rewriting for Monoidal Closed Categories
Alvarez-Picallo M
(2023)
Functorial String Diagrams for Reverse-Mode Automatic Differentiation
Boisseau, G.
(2022)
Graphical Piecewise-Linear Algebra
Bonchi F
(2022)
String diagram rewrite theory II: Rewriting with symmetric monoidal structure
in Mathematical Structures in Computer Science
Bonchi F
(2021)
Bialgebraic foundations for the operational semantics of string diagrams
in Information and Computation
Bonchi F
(2022)
String diagram rewrite theory III: Confluence with and without Frobenius
in Mathematical Structures in Computer Science
| Description | We developed new formalisms of string diagrams, new ways of formally reasoning about them, investigated their implementability, and applied them to relevant fields such as automatic differentiation. Our work also stimulated the development of new tools for reasoning about machine learning and AI, in particular about their safety and interpretability. |
| Exploitation Route | String diagrams are a great vehicle for dissemination of ideas, both between scientists and to the general public. These methodologies will also inspire the development of new software, based on principled methodologies that may ensure its modularity and trustworthiness. We are already witnessing this in the context of AI, compilation techniques, and quantum computation. |
| Sectors | Digital/Communication/Information Technologies (including Software) Education |
| Description | Companies have shown interest in applying our methodologies to the development of software for machine learning |
| First Year Of Impact | 2022 |
| Sector | Digital/Communication/Information Technologies (including Software) |
| Impact Types | Economic |
| Description | Structural approach to machine learning - towards trustworthy AI |
| Geographic Reach | Multiple continents/international |
| Policy Influence Type | Influenced training of practitioners or researchers |
| Impact | Our work provides the tools to reasoning about machine learning architectures structurally, thus giving methods to formally verify their behaviour, as well as building them in a way that is easier for the user to debug, understand, and interpret. Moreover, the abstraction provided by string diagrams allow to extend these methods to other classes of models, such as Boolean circuits and Arithmetic circuits. |
| Description | Categorical Deep Learning |
| Organisation | Mount Allison University |
| Country | Canada |
| Sector | Academic/University |
| PI Contribution | We developed compositional methods for gradient-based machine learning based on categorical structures such as lenses and differential categories. These methods include a diagrammatic calculus for neural networks architectures. |
| Collaborator Contribution | My partners brought expertise on some of the categorical structures involved as well as on machine learning techniques. |
| Impact | Publications at ESOP 2022 (shortlisted for best paper award), ICGT 2022, ACT 2021, Journal of Logical and Algebraic Methods in Programming. Several invited talks and tutorials. Our findings stimulated several initatives for creating research programmes in categorical deep learning both in the public and private sector. |
| Start Year | 2020 |
| Description | Categorical Deep Learning |
| Organisation | University of Strathclyde |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | We developed compositional methods for gradient-based machine learning based on categorical structures such as lenses and differential categories. These methods include a diagrammatic calculus for neural networks architectures. |
| Collaborator Contribution | My partners brought expertise on some of the categorical structures involved as well as on machine learning techniques. |
| Impact | Publications at ESOP 2022 (shortlisted for best paper award), ICGT 2022, ACT 2021, Journal of Logical and Algebraic Methods in Programming. Several invited talks and tutorials. Our findings stimulated several initatives for creating research programmes in categorical deep learning both in the public and private sector. |
| Start Year | 2020 |
| Description | Diagrammatic Algebra and Signal Flow Theory, with Filippo Bonchi and Pawel Sobocinski |
| Organisation | Tallinn University |
| Country | Estonia |
| Sector | Academic/University |
| PI Contribution | We wrote a survey on signal flow theory summarising years of contributions with the aim of disseminating to a wider audience. We also developed further specific topics of interest for the theory and applications of string diagrams, such as bialgebraic semantics and polyhedral algebra (for linear programming). |
| Collaborator Contribution | See above |
| Impact | - Publications with identifiers 10.1016/J.IC.2021.104767, 10.4230/LIPICS.CALCO.2021.9, and 10.1007/978-3-030-81701-5_2 - Talk at international conferences CALCO 2021 - Invited tutorial speakers at MFPS 2021 |
| Start Year | 2020 |
| Description | Diagrammatic Algebra and Signal Flow Theory, with Filippo Bonchi and Pawel Sobocinski |
| Organisation | University of Pisa |
| Country | Italy |
| Sector | Academic/University |
| PI Contribution | We wrote a survey on signal flow theory summarising years of contributions with the aim of disseminating to a wider audience. We also developed further specific topics of interest for the theory and applications of string diagrams, such as bialgebraic semantics and polyhedral algebra (for linear programming). |
| Collaborator Contribution | See above |
| Impact | - Publications with identifiers 10.1016/J.IC.2021.104767, 10.4230/LIPICS.CALCO.2021.9, and 10.1007/978-3-030-81701-5_2 - Talk at international conferences CALCO 2021 - Invited tutorial speakers at MFPS 2021 |
| Start Year | 2020 |
| Description | Graphical Piecewise-Linear Algebra, with Guillaume Boisseau, University of Oxford |
| Organisation | University of Oxford |
| Department | Department of Computer Science |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | Research expertise, writing a scientific article. |
| Collaborator Contribution | Research expertise, writing scientific articles, dissemination in seminars, conferences and workshops. |
| Impact | A scientific article accepted for publication in an international conference. |
| Start Year | 2021 |
| Description | Modal string diagrams |
| Organisation | University of Johannesburg |
| Country | South Africa |
| Sector | Academic/University |
| PI Contribution | Both modal logic and string diagrams are widespread formalisms in the theory of computation, particularly in the compositional specification of system properties. We are exploring the possibility of bridging the two formalisms using recent findings on the string diagrammatic theory of Pierce's existential graphs. |
| Collaborator Contribution | My collaborators are experts in modal logic and algebraic semantics. |
| Impact | For now this collaboration has produced an exchange of methodologies and insights between two research areas that were not previously communicating. We are just at the beginning and more outcomes are to be expected. |
| Start Year | 2023 |
| Description | Modal string diagrams |
| Organisation | University of the Witwatersrand |
| Country | South Africa |
| Sector | Academic/University |
| PI Contribution | Both modal logic and string diagrams are widespread formalisms in the theory of computation, particularly in the compositional specification of system properties. We are exploring the possibility of bridging the two formalisms using recent findings on the string diagrammatic theory of Pierce's existential graphs. |
| Collaborator Contribution | My collaborators are experts in modal logic and algebraic semantics. |
| Impact | For now this collaboration has produced an exchange of methodologies and insights between two research areas that were not previously communicating. We are just at the beginning and more outcomes are to be expected. |
| Start Year | 2023 |
| Description | String Diagram Rewrite Theory |
| Organisation | Tallinn University |
| Country | Estonia |
| Sector | Academic/University |
| PI Contribution | We systematised the corpus of results on string diagram rewriting and published them in a series of three journal articles, to serve as a reference on the subject. |
| Collaborator Contribution | See above |
| Impact | A series of three articles published by the Journal of the ACM and Mathematical Structures in Computer Science. These results nowadays are at the basis of several implementations of string diagrammatic reasoning. These tools are being used in quantum computation, compilation, and automatic differentiation. |
| Start Year | 2020 |
| Description | String Diagram Rewrite Theory |
| Organisation | University of Oxford |
| Department | Oxford Hub |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | We systematised the corpus of results on string diagram rewriting and published them in a series of three journal articles, to serve as a reference on the subject. |
| Collaborator Contribution | See above |
| Impact | A series of three articles published by the Journal of the ACM and Mathematical Structures in Computer Science. These results nowadays are at the basis of several implementations of string diagrammatic reasoning. These tools are being used in quantum computation, compilation, and automatic differentiation. |
| Start Year | 2020 |
| Description | String Diagram Rewrite Theory |
| Organisation | University of Pisa |
| Country | Italy |
| Sector | Academic/University |
| PI Contribution | We systematised the corpus of results on string diagram rewriting and published them in a series of three journal articles, to serve as a reference on the subject. |
| Collaborator Contribution | See above |
| Impact | A series of three articles published by the Journal of the ACM and Mathematical Structures in Computer Science. These results nowadays are at the basis of several implementations of string diagrammatic reasoning. These tools are being used in quantum computation, compilation, and automatic differentiation. |
| Start Year | 2020 |
| Description | String Diagram Rewriting for Automatic Differentiation |
| Organisation | University of Birmingham |
| Department | University of Birmingham, Liver Tissue bank |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | We developed string diagrammatic methods for proving formal properties and giving semantics to higher order computation, specifically in the area of automatic differentiation. |
| Collaborator Contribution | Collaborators from University of Birmingham provided expertise on authomatic differentiation and semantics of higher order computation. |
| Impact | - Talks at international conferences FSCD 2022 and CSL 2023. - Invited talk at the Workshop on Differentiable Programming (Paris, 2022). - Papers accepted for publications at international conferences FSCD and CSL. - Book in preparation on the subject of diagrammatic methods for higher order programming, published by Cambridge University Press |
| Start Year | 2020 |
| Description | String Diagram Rewriting for Automatic Differentiation |
| Organisation | University of Birmingham |
| Country | United Kingdom |
| Sector | Academic/University |
| PI Contribution | We developed string diagrammatic methods for proving formal properties and giving semantics to higher order computation, specifically in the area of automatic differentiation. |
| Collaborator Contribution | Collaborators from University of Birmingham provided expertise on authomatic differentiation and semantics of higher order computation. |
| Impact | - Talks at international conferences FSCD 2022 and CSL 2023. - Invited talk at the Workshop on Differentiable Programming (Paris, 2022). - Papers accepted for publications at international conferences FSCD and CSL. - Book in preparation on the subject of diagrammatic methods for higher order programming, published by Cambridge University Press |
| Start Year | 2020 |
| Description | APR seminar (LIP6 at Sorbonne University) |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I gave a talk (online) entitled "A diagrammatic axiomatisation of finite-state automata" to the LIP6 at Sorbonne University. My presentation sparked questions and discussions with several members of the group afterwards. |
| Year(s) Of Engagement Activity | 2020 |
| Description | Blog post "String diagrams for the lambda-calculus" |
| Form Of Engagement Activity | Engagement focused website, blog or social media channel |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I wrote a blog post explaining a research topic to a wider audience. This sparked several questions and further discussions with other researchers and students in the field. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://piedeleu.com/posts/diagrammatic-lambda-calculus/ |
| Description | Cosynus seminar (LIX laboratory, École Polytechnique) |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I gave a talk (online) entitled "A diagrammatic axiomatisation of finite-state automata" to the Cosynus team of the LIX Laboratoire of the École Polytechnique, presenting joint work with Fabio Zanasi. The talk sparked questions and further discussions with several members of the group afterwards. |
| Year(s) Of Engagement Activity | 2021 |
| Description | FoSSaCS conference talk |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | I gave a talk at the 24th International Conference on Foundations of Software Science and Computation Structures (online), to present the paper "A String Diagrammatic Axiomatisation of Finite-State Automata" (see associated publication). The talk sparked questions and discussions with several audience members afterwards. |
| Year(s) Of Engagement Activity | 2021 |
| URL | https://etaps.org/2021/fossacs/fossacs-programme |
| Description | Invited Keynote Speaker at the 14th International Conference on Mathematics of Program Construction (MPC 2022), Tbilisi, Georgia. |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Invited Keynote Speaker at the 14th International Conference on Mathematics of Program Construction (MPC 2022), Tbilisi, Georgia. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Invited Speaker at the 3rd Italian Category Theory Workshop (ItaCa III), Pisa, Italy |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Invited Speaker at the 3rd Italian Category Theory Workshop (ItaCa III), Pisa, Italy |
| Year(s) Of Engagement Activity | 2022 |
| Description | Invited Speaker at the International Workshop 'Differentiable Programming', Paris, France |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Other audiences |
| Results and Impact | Invited Speaker at the International Workshop 'Differentiable Programming', Paris, France. About 50 attendants. |
| Year(s) Of Engagement Activity | 2022 |