Correction to Lower Bounds on VC-Dimension of Smoothly Parameterized Function Classes1
The earlier article gives lower bounds on the VC-dimension of various smoothly parameterized function classes. The results were proved by showing a relationship between the uniqueness of decision boundaries and the VC-dimension of smoothly parameterized function classes. The proof is incorrect; there is no such relationship under the conditions stated in the article. For the case of neural networks with tanh activation functions, we give an alternative proof of a lower bound for the VC-dimension proportional to the number of parameters, which holds even when the magnitude of the parameters is restricted to be arbitrarily small.