4 ms·
Carrying Is a 2-Cocycle [pdf]
- 082349872349872 4y agocf https://news.ycombinator.com/item?id=34884628 https://news.ycombinator.com/item?id=34884628
- boxfire 4y agoWish I saw this write-up in like 2009. The terminology in Cohomology was pretty opaque to me until I (much later) learned the concepts via a backwards mapping from learning deeper applications of algebraic geometry. I would have learned that much easier if I understood this easier.
- 0xcafefood 4y agoCould you link to whatever source (paper, book, etc) you read connecting deep learning to algebraic geometry? Sounds interesting.
- red_trumpet 4y agoI don't think "learning deeper applications of algebraic geometry" has anything to do with "deep learning" in a machine learning context. My best guess is that OP had a course about rather abstract homological algebra, which he only grokked after learning about applications in algebraic geometry, which were "deeper" in some sense.
- boxfire 4y agoShe and yes this is right.
- boxfire 4y agoDo check this discussion the other day: https://news.ycombinator.com/item?id=34816184#34826067 https://news.ycombinator.com/item?id=34816184#34826067
- raphlinus 4y agoCarry is also a monoid. Consider addition of two binary numbers. If the two digits are zero, then the output carry is zero no matter the input carry. If the two digits are one, then the output carry is one no matter the input carry. And if one is a zero and the other a one, then the output carry is the input carry. Call these values 0, 1, and X respectively. Now consider a binary operator combining two such values. It is associative and has X as an identity element, thus is a monoid: \ 0 1 X +------ 0 | 0 0 0 1 | 1 1 1 X | 0 1 X Now you can express the carry output of bit i as the inclusive scan (prefix sum) of these values from 0 to i. Because it's a monoid, you can implement it efficiently in parallel. There's a nontrivial literature in digital electronics exploiting this basic fact. Of course, to me everything is a monoid (including rendering vector graphics paths), so it should come as no surprise that I see things this way.