Nonparametric Neural Networks

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.