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by dimatura 340 days ago
I'm not sure I quite understand what you're aiming at with these questions, but there are certainly techniques in ML based on thinking of functions as vectors. The first one that comes to mind is Anyboost [1], which views boosting as doing "gradient descent" in function space - where each "gradient step" is not a typical vector (as you'd see e.g in neural nets) but a function, corresponding in practice to a base classifier. Another that is very popular are gaussian processes - one way to think about them is as modeling functions as samples from an infinite-dimensional gaussian (at least some of them).

[1] https://proceedings.neurips.cc/paper_files/paper/1999/file/9...