Universal Approximation Theorem
The universal approximation theorem states that a sufficiently wide single-hidden-layer feedforward network can approximate any continuous function on a compact set to arbitrary precision. It guarantees only the existence of representational capacity, not trainability.
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The Universal Approximation Theorem (UAT) states that a single-hidden-layer feedforward network with enough hidden units can approximate any continuous function on a compact set to arbitrary precision.
UAT only guarantees existence; it does not guarantee that the network can be trained by gradient descent to the optimal solution, nor that the number of hidden units and the amount of data required are feasible in practice.
Treating UAT as proof that "deep networks are superior to shallow networks" is a common misconception.
All Facts (3)
The Universal Approximation Theorem (UAT) states that a single-hidden-layer feedforward network with enough hidden units can approximate any continuous function on a compact set to arbitrary precision.
50%UnverifiedUAT only guarantees existence; it does not guarantee that the network can be trained by gradient descent to the optimal solution, nor that the number of hidden units and the amount of data required are feasible in practice.
50%UnverifiedTreating UAT as proof that "deep networks are superior to shallow networks" is a common misconception.
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