Today on the blog I’ve started a new mini-series called “Language, Statistics, & Category Theory” to describe some ideas my collaborators and I share in a recent paper on mathematical structure in language. Part 1 is now live! math3ma.com/blog/language-… We open with the idea that language is algebraic: you can “multiply”words together (concatenation) to get new expressions:

red × firetruck = red firetruck

I’ve mentioned this idea previously in a "promo video" I made for my PhD thesis last year:

I’m happy to share a new paper with @MStoudenmire and John Terilla: arxiv.org/abs/1910.07425 We share a tensor network generative model, a deterministic training algo & estimate generalization error, all with the clarity of linear algebra. Now on the blog! math3ma.com/blog/modeling-… @MStoudenmire I’ll explain some of the ideas here, sticking to a "lite" version. (Check out the paper for the full version!)

If you’ve been following the posts on Math3ma for the past 6-or-so months, you’ll be delighted to know the content is all related. But more on that later…

Every probability distribution can be viewed as a quantum state & vice versa. There's a nice mathematical dictionary between the two worlds! So, what *is* a quantum state? And what's the dictionary? "A First Look at Quantum Probability, Part 2" is here! math3ma.com/blog/a-first-l… I’ll share a few of the ideas here, picking up where we left off in Part 1:

https://twitter.com/math3ma/status/1151950130280574976

Hello friends! I’m excited to share with you the start of a mini-series on quantum probability theory. It's a *first* look at the subject, so the only prerequisites are linear algebra and basic probability. Part 1 is now on Math3ma! math3ma.com/blog/a-first-l… Part 1 motivates the mini-series by reflecting on a thought from the world of (classical) probability theory:

*Marginal probability doesn’t have memory.*

What do I mean?