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Comment by sitkack | Hacker News Reader

I find this stuff fascinating, at least in the application of differential calculus to things I thought non-continuous, differential grammars, differential regex, etc.

It seems like operating in the discrete domain was fine for small problems where problems could be brute forced, but if we want to get into an analytical regime for larger problems, differentiation is akin to recursion/induction in that it allows us to make tractable smaller problems. Is that roughly correct?

How would you recommend an undergrad bootstrap themselves on this subject? Are there patterns we can apply to transform discrete problems into differentiable problems?

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I think it’s too early to say what differential lambda calculus or linear logic is “good for” in a practical sense. However, I don’t tend to think of it as being about breaking problems into smaller pieces.

I think it is more about error propagation: you can’t estimate which inputs to an algorithm contribute more to the final error, without some notion of derivative of an algorithm with respect to its inputs (even if those inputs are discrete, so that making infinitesimal variations does not obviously make sense).

Linear Logic is amazing-ly useful, http://homepages.inf.ed.ac.uk/wadler/topics/linear-logic.htm...

Rust [0] wouldn't exist without it.

Oddly enough, I think the next discontinuity in programming language design will be in making it easier to construct anytime [1], incremental [2] and succinct [3] programs. There is a tyranny of poor tolerancing that we currently have a very hard time from escaping.

Is it that differentiable programs can be made sloppy in a way that a non-differentiable one can't? Have you looked at the research of using DNN for physics simulations? [4]

[0] https://www.rust-lang.org/en-US/

[1] https://en.wikipedia.org/wiki/Anytime_algorithm

[2] https://en.wikipedia.org/wiki/Incremental_computing

[3] https://en.wikipedia.org/wiki/Succinct_data_structure

[4] https://www.youtube.com/watch?v=iOWamCtnwTc

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