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If there is a pattern in data, such as it fitting on a curve, and you approximate that curve, then that should generalize to unseen data. What's surprising about that? A single polynominal regression wouldn't be able to do it, because some curves cannot be expressed as a polynominal, but superposition of multiple polynominals is apparently good enough.


> then that should generalize to unseen data.

It's not guaranteed at all. Overcomplicated models will "overfit" the training data and generalize very poorly.

> some curves cannot be expressed as a polynominal

You can approximate any (continuous and blah blah) curve arbitrarily well with Taylor expansions.

In fact, polynomials are one of the the most common examples to demonstrate overfitting. See figure 2 on wikipedia (https://en.wikipedia.org/wiki/Overfitting)


If that worked, people would use it, but it doesn't, so they don't.




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