Questions tagged [universal-approximation-theorems]

For questions related to the (different) universal approximation theorems (UATs), for example, in the context of feed-forward neural networks.

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How can neural networks approximate any continuous function but have $\mathcal{VC}$ dimension only proportional to their number of parameters?

Neural networks typically have $\mathcal{VC}$ dimension that is proportional to their number of parameters and inputs. For example, see the papers Vapnik-Chervonenkis dimension of recurrent neural ...
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0answers
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Are No Free Lunch theorem and Universal Approximation theorem contradictory in the context of neural networks?

To my understanding NFL states that, we cannot have an hypothesis (let's assume it is an approximator like NN in this case) class that can't achieve certain accuracy parameters $\leq \epsilon$ with ...
3
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Which machine learning models are universal function approximators?

The universal approximation theorem states that a feed-forward neural network with a single hidden layer containing a finite number of neurons can approximate any continuous function (provided some ...
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3answers
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Is there a mathematical proof that shows that certain parameters work “better” than others for a certain task?

The machine learning community often only provides empirical results, but I am also interested in theoretical results and proofs. Specifically, is there a mathematical proof that shows that certain ...