Tai-Danae Bradley: Modeling Language with Tensor Networks

MIT Category Theory Seminar
2019/10/17
©Spifong
Title: Modeling Language with Tensor Networks
Abstract: Natural language has both a compositional and a statistical structure. These structures emerge when expressions in language combine to form longer expressions, and where the validity of an expression is captured by the statistics in the language. One model for this is a monoidal functor from a category of grammar to an appropriate semantics category. Another modeling choice is to let statistics serve as a proxy for grammar, taking inspiration from quantum probability theory. This talk features the latter. I’ll share an elementary passage from classical probability to quantum probability and use it to describe a tensor network model for language.

[@streampunksheep]

Modelling a language is such a daunting task.

[@farissaadat4437]

A nice reappearance of Tai-Danae on youtube. Great stuff as always.

[@grahamjoss4643]

Very clearly presented

[@tomholroyd7519]

RM3 is a symmetric monoidal closed category and a 3-valued logic that appears as a quotient of Z2 using "x and not x is true". The result is F4, which, through the Bellman's rule a^3 = 1 creates an isomorphism between "both true and false" and "neither true nor false". It is useful because for quantum you can say Both but as a scientists you can say I Don't Know

[@andrewcarr3703]

Wow, that was a fascinating lecture. Great work and thank you for posting.

[@NoNTr1v1aL]

I loved your episodes on PBS!

[@StephenPaulKing]

"Language as a quantum many body problem." Brilliant!

[@smtsjhr]

hehe that look @18:59 ! when you know they know you know . . .

[@pairadeau]

So interesting. Thanks.

[@WayOfTheCode]

It makes lot of sense that this is actually what happens in the brain. Seeing that babies learn the wider language with very narrow hearing of the given language.

[@evankim4096]

The AFK camera moments for extended periods of time really messed up the flow of the talk...

[@WayOfTheCode]

Wow math3ma is here, I have been studying her dissertation past few days.

[@lyrimetacurl0]

I wonder how sensory inputs or neural processes are connected to words.

[@nathanielvirgo]

I didn't really understand the thing about what the off-diagonal elements of the partial trace mean in terms of the joint distribution. Did anyone understand it well enough to state it more formally? It seems quite fundamental, I'd really like to understand it.

[@nathanielvirgo]

Aha! Equation 5 in the paper tells me what I wanted to know, and the rest of that section of the paper is really interesting!

[@ndmath]

At 21:14, which condition should be satisfied? I can't see it.

[@galenseilis5971]

Does this generalize to distributions over 3 or more measurable sets?

[@kongchan437]

I teresting...so if given a body of text "i drove my Ferrari to supermarket to buy 10 fresh apples but delayed on my way by 2 firetrucks ..." then i can most likely say there are 2 very likely objects with red color and somewhat likely but less likely 11 more other objects with red color..