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Artificial Intelligence (AI) Development

What are the most important results in computational learning theory?

What are the most important results in computational and statistical learning theory, which can potentially be relevant in practice (but this not a strict requirement)?

I am looking for answers that list one or more of these results (e.g. bounds on the number of required examples to learn a certain task with a small error or confidence). So, I am looking for answers with mathematical formulas, but, ideally, you should briefly and intuitively explain the bounds and formulas (and eventually link to paper or book that provides more details).

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