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Deep ReLU Networks Can Fail the Best Approximation Property for Continuous Target Functions
We construct a continuous function on $[-1,1]^2$ for which the infimum of the $L^2$-approximation error over the class of ReLU networks with two hidden layers and architecture $(2,2,1,1)$ is not attained. This counterexample shows that deep ReLU networks do not satisfy the best approximation propert
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