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I’d probably have titled this something including either the term “linear” or “functional analysis”. Because submitted here, we will first interpret “functions”
by opportune 3y ago
I’d probably have titled this something including either the term “linear” or “functional analysis”. Because submitted here, we will first interpret “functions” in the context of a function in computer programming, where the statement is more provocative and thus clickbaity.
The problem is many real world functions and problems are nonlinear. But they may have linear components. For example, a dog can be recognized by its outline and the texture of the fur, pattern of the face, etc within that outline. Deep neural nets solve this by composing vector operations, hence the universal approximation theorem and existence of NNs that can recognize dogs (though I could have picked a better example as dog recognition is not continuous I think).
In the context of computer programming, it is not really a helpful statement to say that functions are vectors. But because of the universal approximation theorem and its relatives you could say that “functions are (can be approximated as) compositions of vector operations”
- HeavyStorm 3y agoYep, went there to learn how to use vectors to replace methods...
- eigenket 3y agoFor some reason computer programmers took the mathematical definition of "functions", used it for their things which are emphatically not mathematical functions, and are now complaining that they get confused by people talking about the old math definition.
- xigoi 3y agoSame with “vector”.
- oasisaimlessly 3y agoNothing in this article assumed that the functions in question were linear and/or being approximated.
- fanpu 3y agoThe title is actually perfect, but requires some context, after which you might appreciate its tongue-in-cheek beauty: The author studied at CMU, where the proudly-paraded slogan for an introductory functional programming classes is "Functions are values", which has an almost cult-like status - appearing on their TA hoodies, laptop stickers, and so on. Other classes soon caught on, first with the imperative programming class declaring that "Functions are pointers", then the introductory discrete math class's "Functions are tuples", and even "Functions are relations" from the databases class. So viewed in this lens, passing up the opportunity to title it what it was would have been unthinkable.