[HN Gopher] A Little Calculus ___________________________________________________________________ A Little Calculus Author : __rito__ Score : 41 points Date : 2023-05-03 09:47 UTC (1 days ago) (HTM) web link (papl.cs.brown.edu) (TXT) w3m dump (papl.cs.brown.edu) | [deleted] | haskellandchill wrote: | Wish they covered co-induction. I've read the paper linked in the | definition but still don't have a very strong intuition for it. | excalibur wrote: | A little bit of calculus in my life | | A little trigonometry by my side | | A little Fibonacci's all I need | | A little inequality's what I see | | A little bit of lambda in the sun | | A little bit binary all night long | | A little probability, here I am | | A little [?]2 makes me your man | sampo wrote: | > We'll implement _numerical_ differentiation, though in | principle we could also implement _symbolic_ differentiation | | I'd like to argue, that when it comes to computers and | differentiation, _automatic_ differentiation is the most useful, | most important in practice. But often only _symbolic_ and | _numerical_ differentiation are mentioned. | version_five wrote: | AD is important for training neural networks, or sgd (et al) | generally. But that's still only one field. Numerical | differentiation is still important e.g. for differential | equation solvers. I don't think you can say AD is the most | important or useful - maybe for understanding pop culture. | reikonomusha wrote: | I think this is because automatic differentiation is a | manifestation of just one rule of differentiation: the chain | rule. With numerical differentiation, you only need to be able | to evaluate the function at hand. With automatic | differentiation, you need to "seed" your program with the | differentials of all existing functions. | | What's nice about a discussion of symbolic differentiation is | that we can prove a few rules rigorously, and then use those | rules to purely mechanically differentiate algebraic | expressions we encountered up to trigonometry. | | You're right though, in practice, for complex functions | expressed as programs, automatic differentiation is superior. ___________________________________________________________________ (page generated 2023-05-04 23:00 UTC)