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  • Re: Another beautiful day doing math that has no real world application

    From Mild Shock@21:1/5 to Mild Shock on Thu Mar 20 20:24:01 2025
    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


    --- SoupGate-Win32 v1.05
    * Origin: fsxNet Usenet Gateway (21:1/5)
  • From sobriquet@21:1/5 to All on Fri Mar 21 01:34:27 2025
    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.

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