Jeffrey's prior sampling of deep sigmoidal networks
This work provides insights into the geometry of neural network representations, which is incremental for understanding model reduction in machine learning.
The paper investigates the low-dimensional structure learned by Deep Belief Networks and Stacked Denoising Autoencoders, finding that the model manifold is a slightly elongated hyperball with reconstructed data mostly on its boundaries.
Neural networks have been shown to have a remarkable ability to uncover low dimensional structure in data: the space of possible reconstructed images form a reduced model manifold in image space. We explore this idea directly by analyzing the manifold learned by Deep Belief Networks and Stacked Denoising Autoencoders using Monte Carlo sampling. The model manifold forms an only slightly elongated hyperball with actual reconstructed data appearing predominantly on the boundaries of the manifold. In connection with the results we present, we discuss problems of sampling high-dimensional manifolds as well as recent work [M. Transtrum, G. Hart, and P. Qiu, Submitted (2014)] discussing the relation between high dimensional geometry and model reduction.