Variational Inference for Infinitely Deep Neural Networks
This work addresses the challenge of automatically determining model complexity in neural networks for machine learning practitioners, though it is incremental as it builds on existing infinite-depth models.
The authors tackled the problem of modeling data with adaptive complexity by introducing an infinitely deep probabilistic neural network (UDN) and developed a variational inference algorithm to approximate its posterior, showing that it adapts depth to dataset complexity and outperforms standard and other infinite-depth networks.
We introduce the unbounded depth neural network (UDN), an infinitely deep probabilistic model that adapts its complexity to the training data. The UDN contains an infinite sequence of hidden layers and places an unbounded prior on a truncation L, the layer from which it produces its data. Given a dataset of observations, the posterior UDN provides a conditional distribution of both the parameters of the infinite neural network and its truncation. We develop a novel variational inference algorithm to approximate this posterior, optimizing a distribution of the neural network weights and of the truncation depth L, and without any upper limit on L. To this end, the variational family has a special structure: it models neural network weights of arbitrary depth, and it dynamically creates or removes free variational parameters as its distribution of the truncation is optimized. (Unlike heuristic approaches to model search, it is solely through gradient-based optimization that this algorithm explores the space of truncations.) We study the UDN on real and synthetic data. We find that the UDN adapts its posterior depth to the dataset complexity; it outperforms standard neural networks of similar computational complexity; and it outperforms other approaches to infinite-depth neural networks.