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

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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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