Title: Nonparametric Neural Networks,
Abstract: Automatically determining the optimal size of a neural network for a given
task without prior information currently requires an expensive global search
and training many networks from scratch. In this paper, we address the problem
of automatically finding a good network size during a single training cycle. We
introduce *nonparametric neural networks*, a non-probabilistic framework for
conducting optimization over all possible network sizes and prove its soundness
when network growth is limited via an L_p penalty. We train networks under this
framework by continuously adding new units while eliminating redundant units
via an L_2 penalty. We employ a novel optimization algorithm, which we term
*adaptive radial-angular gradient descent* or *AdaRad*, and obtain promising
results.