Applied Category Theory at NIST (Part 1)

I think it’s really cool how applied category theory is catching on. My former student Blake Pollard is working at the National Institute of Standards and Technology on applications of category theory to electrical engineering. He’s working with Spencer Breiner… and now Breiner is helping run a workshop on this stuff:

• Applied Category Theory: Bridging Theory & Practice, March 15–16, 2018, NIST, Gaithersburg, Maryland, USA. Organized by Spencer Breiner and Eswaran Subrahmanian.

It’s by invitation only, but I can’t resist mentioning its existence. Here’s the idea:

What: The Information Technology Laboratory at NIST is pleased to announce a workshop on Applied Category Theory to be held at NIST’s Gaithersburg, Maryland campus on March 15 & 16, 2018. The meeting will focus on practical avenues for introducing methods from category theory into real-world applications, with an emphasis on examples rather than theorems.

Who: The workshop aims to bring together two distinct groups. First, category theorists interested in pursuing applications outside of the usual mathematical fields. Second, domain experts and research managers from industry, government, science and engineering who have in mind potential domain applications for categorical methods.

Intended Outcomes: A proposed landscape of potential CT applications and the infrastructure needed to realize them, together with a 5-10 year roadmap for developing the field of applied category theory. This should include perspectives from industry, academia and government as well as major milestones, potential funding sources, avenues for technology transfer and necessary improvements in tool support and methodology. Exploratory collaborations between category theorists and domain experts. We will ask that each group come prepared to meet the other side. Mathematicians should be prepared with concrete examples that demonstrate practical applications of CT in an intuitive way. Domain experts should bring to the table specific problems to which they can devote time and/or funding as well as some reasons about why they think CT might be relevant to this application.

Invited Speakers:
John Baez (University of California at Riverside) and John Foley (Metron Scientific Solutions).
Bob Coecke (University of Oxford).
Dusko Pavlovic (University of Hawaii).

Some other likely participants include Chris Boner (Metron), Arquimedes Canedo (Siemens at Princeton), Stephane Dugowson (Supméca), William Edmonson (North Carolina A&T), Brendan Fong (MIT), Mark Fuge (University of Maryland), Jack Gray (Penumbra), Helle Hansen (Delft), Jelle Herold (Statebox), Marisa Hughes (Johns Hopkins), Steve Huntsman (BAE Systems), Patrick Johnson (Dassault Systèmes), Al Jones (NIST), Cliff Joslyn (Pacific Northwest National Laboratory), Richard Malek (NSF), Tom Mifflin (Metron), Ira Monarch (Carnegie Mellon), John Paschkewitz (DARPA), Evan Patterson (Stanford), Blake Pollard (NIST), Emilie Purvine (Pacific Northwest National Laboratory), Mark Raugas (Pacific Northwest National Laboratory), Bill Regli (University of Maryland), Michael Robinson (American U.) Alberto Speranzon (Honeywell Aerospace), David Spivak (MIT), Eswaran Subrahmanian (Carnegie Mellon), Jamie Vicary (Birmingham and Oxford), and Ryan Wisnesky (Categorical Informatics).

A bunch of us will stay on into the weekend and talk some more. I hope we make a lot of progress—and I plan to let you know how it goes!

I’ll be giving a joint talk with John Foley about our work using operads to design networks. This work is part of the Complex Adaptive System Composition and Design Environment project being done by Metron Scientific Solutions and managed by John Paschkewitz at DARPA.

28 Responses to Applied Category Theory at NIST (Part 1)

1. Jed Harris says:

What is the movie showing?

• John Baez says:

Click on it! There is some connection to category theory, if you read enough.

2. John,

A friend of mine who works at NIST in the area of information modelling and information standards (specifically the IEC Common Information Model) may wish to audit some of these sessions; you say “invitation only”, but I cannot think that you do not want an audience…?

Thanks,
FW

• John Baez says:

I’m not running this conference; Spencer Breiner is. But since your friend is at NIST, they can easily contact him and see what the deal is. For all I know, all workshops at NIST might be open to everyone who works there. That’s how it works at some places.

3. Keith Harbaugh says:

Hope Michael Johnson of Macquarie is invited. He’s done quite a lot to apply cat theory to applications, with experience with real businesses. I’m impressed by these attempts. Also, Bob Rosebrugh has collaborated on some of that.

• John Baez says:

I’m friends with Michael and I think he’s great. I don’t think he’s coming, alas. I just found a better list of likely attendees, and I’ll use that to update the short list I had on this blog article.

4. In March, I’ll be talking at Spencer Breiner‘s workshop on Applied Category Theory at the National Institute of Standards and Technology. I’ll be giving a joint talk with John Foley about our work using operads to design networks. This work is part of the Complex Adaptive System Composition and Design Environment project being done by Metron Scientific Solutions and managed by John Paschkewitz at DARPA.

• Complex Adaptive Systems: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6.

But we’ve done a lot more, and my blog articles are having trouble keeping up with the details! So I’d like to sketch out the big picture as it stands today.

5. John Baez says:

The workshop has started! First Bob Coecke spoke on “From quantum foundations to cognitions” via pictures. Some of the newer work of his is discussed here:

• Cory Griffith and Jade Master, Linguistics using category theory, The n-Category Café, 6 Februrary 2018.

• Tai-Danae Bradley and Brad Theilman, Cognition, convexity and category theory, The n-Category Café, 10 March 2018.

6. John Baez says:

Now William Regli, the former DARPA director who hired John Paschkewitz, is talking about different DARPA activities that involve category theory. The first, it seems, was CASCADE — the project I’m working on, on systems of systems design. The second is called SIMPLEX, on representing data in different ways. The third is called TRADES, on designs in manufacturing, e.g. on additive manufacturing. They started using SysML, and it failed — some levels of abstraction weren’t covered by the model: you need to translate between very abstract specifications of a machine and others where you describe things voxel by voxel. So, interoperability is important, and now they’re starting to think about category theory.

• ” They started using SysML, and it failed “

Perhaps predictable. SysML is a square-peg in a round-hole type of tool for everything but the narrow application area it’s designed for.

7. John Baez says:

Now Evan Patterson is talking about ways of analyzing computer code and figuring out what it really means… by using a functor from a ‘code category’ to a ‘concept category’. See his paper with some coauthors on Dataflow representation of data analyses: toward a platform for collaborative data science.

8. John Baez says:

Now Stéphane Dugowson is talking about ‘interactivity’, using a functorial approach to dynamics.

9. John Baez says:

Now Brendan Fong is talking about “Data structures for network languages”. He explained decorated cospan categories and advertised his brand-new free book:

• Brendan Fong and David Spivak, Seven Sketches in Compositionality: An Invitation to Applied Category Theory.

10. John Baez says:

Now Dusko Pavlovic is talking about computer security. He pointed out that computer security companies are motivated to charge you $9.50 to keep someone else from robbing you of$10… not to sell you a tool that will keep working forever. He then gave a quick sketch of modern ‘security science’. A modern definition of a secure system is IND-CCA2. Dusko needs to teach this stuff to 2nd-year undergrads… but it tends to involve too much detail, so he’s decided to use string diagrams to simplify things, and he’s writing a textbook on this. You can see his course notes here:

• Dusko Pavlovic, Basic Concepts of Computer Science.

11. John Baez says:

Now Steve Huntsman of BAE systems is giving a talk “Towards an operad of goals”, thinking about autonomous systems of systems.

12. John Baez says:

Now Ryan Wisnewsky is talking about his work with Patrick Schultz and David Spivak on “Categorical databases”. Their company Categorical Informatics has developed a software tool called AQL, for Algebraic Query Language. It lets you set up databases using sketches; the sketch specifies a category, and an actual specific database is a functor from that category to $\mathrm{Set}$. Functional data migration can be done using Kan extensions and the like.

13. John Baez says:

With lunch over, now Michael Robinson spoke about “Sheaf methods for inference”. Here’s something to read:

• Michael Robinson, Tutorial on sheaves in data analytics.

Emilie Purvine picked up where Robinson left off, and then spoke about methods of converting many different datatypes into vectors in vector spaces.

14. John Baez says:

Then Cliff Joslyn spoke on “Seeking a categorical theory of systems through the category of hypergraphs.” He mentioned this old paper:

• Dörfler and Waller, A category-theoretical approach to hypergraphs, Archiv der Mathematik.

15. John Baez says:

Now Rémy Tuyéras is talking about category theory in genetics. He’s working with David Spivak at MIT. He wrote a paper on this:

16. John Baez says:

Now Helle Hansen is talking about applications of coalgebras to Markov decision processes: “Long-term values in MDPs, corecursively”. A paper:

• Frank M.V. Feys, Helle Hvid Hansen and Lawrence S. Moss, Long-term values in Markov decision processes, (co)algebraically, in Coalgebraic Methods in Computer Science (CMCS 2018).

A Markov decision process can be seen as a coalgebra of a certain functor. The classical theory of these, not using coalgebras, is well-developed:

• M. L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, John Wiley & Sons, 2014.

However, many of the standard concepts can be nicely phrased in terms of maps from a coalgebra of one functor to an algebra of another, a simple categorical concept I’d never considered.

17. John Baez says:

Now Alberto Sperazon of Honeywell will talk about “Localization and planning for autonomous systems via (co)homology computation”—some work he did with Rob Ghrist.

18. John Baez says:

Joshua Tan just announced a new journal on applied category theory:

It will start up this summer. The executive editors are Joshua Tan, Nina Otter, and Brendan Fong, and the board of advisors includes Bob Coecke, Steve Lack, Kathryn Hess and myself. It’s being funded by Ilyas Khan of Cambridge Quantum Computing.

19. John Baez says:

Now David Spivak is talking about his work using category theory to help design a safer national airspace system. He described the project earlier at my workshop:

But this time he’s emphasizing the role of a hypergraph category where wires with arrows indicate ‘signal passing’, and the edges don’t have arrows.

• John Baez says:

Now he’s emphasizing that any in any topos E, there’s a hypergraph category where the morphisms are relations: a relation $R : X \to Y$ is a map from $X \times Y$ to the subobject classifier $\Omega.$ This is most familiar when E = Set and the subobject classifier is the 2-element set {T,F}, but he wants to use a topos that incorporates time-dependence—and that is what he explained in detail in his talk at my workshop (see above).

20. Keith Harbaugh says:

My thought: Why on earth is this conference not being publicized? When I google NIST Applied Category Theory: Bridging Theory & Practice your blogs are about the only references. Sure seems like there should at least be the program announced on the web. John, can you say anything about why this information isn’t on the web?

• John Baez says:

This was a workshop, not a conference, so it wasn’t open to the public. In fact, participants needed a badge and ID just to get through security and enter the National Institute of Standard and Technology! They have a nuclear reactor there, and they’re very security-conscious. Perhaps for this reason, the organizers were not very interested in outreach. I’ve been trying to publicize it myself, since I feel part of the the point of any such gathering is to drum up enthusiasm and spread information.

The talks were videotaped, and the talk slides collected. The organizers said all this material would probably be made public at some point. If it is, I will tell the whole world about it.

21. Here are links to the slides and videos for most of the talks from “Applied Category Theory: Bridging Theory & Practice”. They give a pretty good picture of what went on. Spencer Breiner put them up here; what follows is just a copy of what’s on his site.

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