  Large neural network models have high predictive power but may suffer from
overfitting if the training set is not large enough. Therefore, it is desirable
to select an appropriate size for neural networks. The destructive approach,
which starts with a large architecture and then reduces the size using a
Lasso-type penalty, has been used extensively for this task. Despite its
popularity, there is no theoretical guarantee for this technique. Based on the
notion of minimal neural networks, we posit a rigorous mathematical framework
for studying the asymptotic theory of the destructive technique. We prove that
Adaptive group Lasso is consistent and can reconstruct the correct number of
hidden nodes of one-hidden-layer feedforward networks with high probability. To
the best of our knowledge, this is the first theoretical result establishing
for the destructive technique.
