@julesh
Applied Compositional Thinking
Relays (1)
- wss://relay.ditto.pub – read & write
Recent Notes
More than 6 years after noticing it I have *finally* understood the Bayesian chain rule (*) intuitively
If you have conditional distributions P(y | x) and P(z | y), the Bayesian chain rule really just says
P(x | z) = ∫dy P(y | z) P(x | y)
Only if you expand P(z | y) using Bayes' law you get the term P(y), which is the pushforward of the prior. It's exactly like writing the differential chain rule in Leibniz notation,
dz/dx = dy/dx dz/dy
which similarly notationally suppresses the pushforward compared to the Lagrange/Jacobi notation
(g.f)'(x) = f'(x) g'(f(x))
* https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.24
If you have conditional distributions P(y | x) and P(z | y), the Bayesian chain rule really just says
P(x | z) = ∫dy P(y | z) P(x | y)
Only if you expand P(z | y) using Bayes' law you get the term P(y), which is the pushforward of the prior. It's exactly like writing the differential chain rule in Leibniz notation,
dz/dx = dy/dx dz/dy
which similarly notationally suppresses the pushforward compared to the Lagrange/Jacobi notation
(g.f)'(x) = f'(x) g'(f(x))
* https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.24
Downside of LLM culture that I have not seen mentioned anywhere before: The best way to understand something is to explain it to someone else, and people don't ask people to explain things anymore
The paradox of the stone: "Could God create a stone so heavy that even he could not lift it?" was solved by Grothendieck by introducing an infinite tower of gods. The God of the n'th universe can only...
@nprofile1q... There is a better resolution using type-in-type: an omnipotent God can create a stone so heavy that they can't lift it, and then they can lift it
Animist as in *everything* has a categorical soul if you listen careful enough. Not just three things.
@nprofile1q... What is this heresy? Category theory is not superior to the Son or the Holy Ghost, but equal to them
@nprofile1q... I wonder if there's some model theoretic universality result that all finite (or not too big) commutative rings embed into one specific commutative ring that involves numbers, like the ring of rationals or something like that?
There are fascinating connections between the Riemann zeta function and music theory. I'll probably write a paper about this, but I can't resist talking about a little piece of the story. I will *...
@nprofile1q... I wonder what this looks like for rings that have very little to do with numbers, like boolean rings or rings of functions
I begrudgingly agree with everything Macron said. I for one welcome our new French centrist overlords
https://www.bbc.com/news/articles/ce8n1zdnpd3o
https://www.bbc.com/news/articles/ce8n1zdnpd3o
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@nprofile1q... I never made the connection before but something similar probably happened over the last few decades in fields that use applied calculus because of Wolfram Alpha and similar tools, and nobody seems to particularly mind
@nprofile1q... I'm preparing to move my stuff off Godaddy and OVH are my leading contender, do you still recommend them?
The hardest problem in computer science is naming things, therefore Nicolaas de Bruijn solved the hardest problem in computer science
nostr:nprofile1qy2hwumn8ghj7un9d3shjtnyd968gmewwp6kyqpq6hx49ptzmru6djkmefdzdtx8dep9jup92hf8sngjcxk2h9h7msysa03n8d it's just a string diagram in Para(SLens) or something right?
@nprofile1q... Well yes but everything is that, that doesn't distinguish what is special about transformers
It's weirdly difficult to find good sources that explain how transformers and attention actually work, considering how important they are. Everybody just seems to repeat a variant of this diagram from the original paper, as though it actually explains anything
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