Convolution Is Fancy Multiplication
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Convolution Is Fancy Multiplication
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Re: Convolution Is Fancy Multiplication
#2I think that calling it outer product makes more sense https://arxiv.org/pdf/1905.01289v1.pdf.
Re: Convolution Is Fancy Multiplication
#3As someone who's forgotten almost all college calculus, this was incredibly well written and understandable!
Re: Convolution Is Fancy Multiplication
#4"look it's just autocorrelation but upside down and backwards" is ... closer to true than it really ought to be.
Re: Convolution Is Fancy Multiplication
#5"look it's just autocorrelation but upside down and backwards" is ... closer to true than it really ought to be.
They are adjoints. http://www.reproducibility.org/RSF/book/gee/ajt/paper_html/i...
I have written something on adjoints, they are literally everywhere https://github.com/adamnemecek/adjoint
Re: Convolution Is Fancy Multiplication
#6That's because convolution literally is a type of product on the space of integrable functions: https://en.wikipedia.org/wiki/Convolution#Algebraic_properti...
Re: Convolution Is Fancy Multiplication
#7That's because convolution literally is a type of product on the space of integrable functions: https://en.wikipedia.org/wiki/Convolution#Algebraic_properti...
Ah, that explains it perfectly!
Re: Convolution Is Fancy Multiplication
#8Convolution is digit-based multiplication, so why not start with that?
100101 * 23 = 2302323. If you defer the carry over to the end, the digit-based steps we do is convolution. That said, giving lots of examples like those in the article is useful.
Next up looking at multiplying two polynomials in a single variable.
Edit: changed digit-wise to digit-based to make it clear that I'm not asking to multiply corresponding digits.
Re: Convolution Is Fancy Multiplication
#9That's because convolution literally is a type of product on the space of integrable functions: https://en.wikipedia.org/wiki/Convolution#Algebraic_properti...
Ah, that explains it perfectly!
I'm not sure if this is a sarcastic reply or not, but, it kinda does. Fubini's theorem is a hell of a drug.
Re: Convolution Is Fancy Multiplication
#10The first example is explained a bit too quickly, so it’s not that intuitive. It seems this hospital has one patient the first day, two on the second, three on the third, and so on. I guess that’s a “schedule” but it seems more like a history of what happened?
It’s not a “list of patients” either, which had me thinking they were patient ids. A better phrase would be a “list of patient counts”.