[HN Gopher] A Little Calculus
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       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.
        
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