The n-Category Café

Good hunting. I hear a startup is hiring in #2 but I’m sure you’ve heard too.

Re #6, the work of Paul Thagard seems profoundly relevant (see, e.g., Conceptual Revolutions, and admits a sheafy description along the lines of arXiv:2401.16713). That paper requires (and will get) updating: we didn’t know about Thagard’s work until after writing, but that work is remarkably prescient though also outdated (e.g., graphs versus simplicial gizmos, MAX-CUT versus MAX-SAT, no LLMs to produce weights, etc.).

Again, good hunting and keep your chin up.

I’m so sorry it’s come to this! I’ve spread the word on Mastodon. You were a bit ahead of your time with your interest in category theory and machine learning. But now I think these ideas may become important, especially if people take several different approaches, since some won’t work but others could. There’s Symbolica and Quantinuum, but I bet others will emerge.

From the article on Symbolica:

Symbolica recently co-authored a paper with Google DeepMind on “categorical deep learning,” which mathematically demonstrated how its approach could supersede previous work on geometric deep learning to build structurally-aware models.

Symbolica’s focus on rigor and interpretability may also find receptive audiences among enterprise adopters of AI, particularly in heavily regulated industries, and in governmental agencies grappling with how to responsibly deploy and oversee increasingly powerful AI systems. If Symbolica can successfully navigate the chasm between theoretical breakthroughs and real-world applications, it could capture a significant slice of an enterprise AI market expected to top $270 billion by 2032.

At a philosophical level, Symbolica’s efforts to move beyond pattern-matching to genuine machine reasoning, if successful, would mark a major milestone on the road to artificial general intelligence—the still-speculative notion of AI systems that can match the fluid intelligence of the human mind.

From the material on Quantinuum:

At Quantinuum we have been working on this issue for some time –– and we began way before AI systems such as generative LLM’s became fashionable. In our AI team based out of Oxford, we have been focused on the development of frameworks for “compositional models” of artificial intelligence. Our intentions and aims are to build artificial intelligence that is interpretable and accountable. We do this in part by using a type of math called “category theory” that has been used in everything from classical computer programming to neuroscience.

Category theory has proven to be a sort of “Rosetta stone”, as John Baez put it, for understanding our universe in an expansive sense — category theory is helpful for things as seemingly disparate as physics and cognition. In a very general sense, categories represent things and ways to go between things, or in other words, a general science of systems and processes. Using this basic framework to understand cognition, we can build new artificial intelligences that are more useful to us –– and we can build them on quantum computers, which promise remarkable computing power.

Our AI team, led by Dr Stephen Clark, Head of AI at Quantinuum, has published a new paper applying these concepts to image recognition. They used their compositional quantum framework for cognition and AI to demonstrate how concepts like shape, color, size, and position can be learned by machines –– including quantum computers.

“In the current environment with accountability and transparency being talked about in artificial intelligence, we have a body of research that really matters, and which will fundamentally affect the next generation of AI systems. This will happen sooner than many anticipate” said Ilyas Khan, Quantinuum’s founder.

I am upset by what has happened at Kent.

I remember the post 17 years ago when you got your permanent position there.

Thanks all for the sympathy and suggestions!

Not a bad time to leave – they’re reducing all remaining staff’s research time considerably.

In searching for background on the Kent job cuts I got confused by headlines such as BBC:University of Kent proposes cuts to courses and jobs which appears to reflect UK/US language differences.

I read this as Kent was just axing some classes. In the US “course” can mean a 1 semester sequence of class meetings often called a “class” or extended to a sequence of such classes such as a “course in database administration”. In the UK it appears that “course” means an academic department (or maybe all the classes a student takes from that department.)

Anyway it sucks that Kent is ridding itself of several departments so that it can “support growth in key areas such as business, psychology and biosciences.”

At the Washington Post, Gary Smith has proposed a solution to the financial problems of universities, which might work well at Kent:

I will use Pomona College, where I have taught for decades, as a specific example of how easily my proposal might be implemented. In 1990, Pomona had 1,487 students, 180 tenured and tenure-track professors, and 56 administrators — deans, associate deans, assistant deans and the like, not counting clerical staff, cleaners and so on. As of 2022, the most recent year for which I have data, the number of students had increased 17 percent, to 1,740, while the number of professors had fallen to 175. The number of administrators had increased to 310, an average of 7.93 new administrators per year. Even for a college as rich as Pomona, this insatiable demand for administrators will eventually cause a budget squeeze. Happily, there is a simple solution.

Pomona’s professor-administrator ratio has plummeted from 3.21 to 0.56. A linear extrapolation of this trend gives a professor-administrator ratio of zero within this decade. This trend can be accelerated by not replacing retiring or departing professors and by offering generous incentives for voluntary departures. To maintain its current 9.94 student-faculty ratio, the college need only admit fewer students each year as the size of its faculty withers away. A notable side effect would be a boost in Pomona’s U.S. News & World Report rankings as its admissions rate approaches zero.

And just like that, the college would be rid of two nuisances at once. Administrators could do what administrators do — hold meetings, codify rules, debate policy, give and attend workshops, and organize social events — without having to deal with whiny students and grumpy professors.

Very sorry to hear about this. (Thanks for John Baez for the heads up on Mastodon.) It was a great pleasure to welcome you to Jena for your colloquium talk on Feb 1, 2007. Hope something turns up, but I realise that it won’t be easy.