2017/05/25 by Lorien X. Hayden, Hayden, Lorien X., Alexander A. Alemi +6
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #AI in cancer detection #Cell Image Analysis Techniques #Computer Vision and Pattern Recognition (cs.CV) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Computer and information sciences #FOS: Physical sciences #Generative Adversarial Networks and Image Synthesis #cond-mat.dis-nn #cs.CV
paper · pdf · doi:10.48550/arxiv.1705.10589
arxiv created 2017/05/25 · openalex publication_date 2017/05/25 · arxiv updated 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.