Re: Another beautiful day doing math that has no real world applications (Re: Prolog totally missed the AI Boom)

Op 20/03/2025 om 20:24 schreef Mild Shock:

Hi,
 No joke, I wonder whether category can
express the sharing in such a function
block diagram:
       +----+   +----+   +----+
      |    |-->| g1 |-->|    |
      |    |   +----+   |    |
x -->| f  |            | h  |--> y
      |    |   +----+   |    |
      |    |-->| g2 |-->|    |
      +----+   +----+   +----+
 With common subexpessions, i.e. computing
f only once, I can write the forward pass as follows:
 p, q = f(x)
y = h(g1(p), g2(q))
 But what common expressios has the
gradient? How would I express the
 subexpression things "category logic" style,
which has as a main operation composition?
 How comes a gradient out with such composition?
 Bye
 Mild Shock schrieb:

Hi,
>
I guess:
>
 > category theory is to set theory
 >
 > what
 >
 > autograd is to calculus
>
LoL
>
Bye
>
See also:
>
Another beautiful day doing math that has no real world applications
https://x.com/MathMatize/status/1902708970306891901
>
sobriquet schrieb:

>
Set theory relates to logic as category theory relates to... ?
>
https://www.youtube.com/watch?v=1KUhLHlgG2Q

>

 

I dunno.. I think it's likely AI will soon be able to elaborate on such questions. Once it is able to come up with concepts from scratch to develop a conceptual framework completely independently from all knowledge accumulated by humans over many generations.