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Archetypal landscapes for deep neural networks. | LitMetric

Archetypal landscapes for deep neural networks.

Proc Natl Acad Sci U S A

Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.

Published: September 2020

AI Article Synopsis

Article Abstract

The predictive capabilities of deep neural networks (DNNs) continue to evolve to increasingly impressive levels. However, it is still unclear how training procedures for DNNs succeed in finding parameters that produce good results for such high-dimensional and nonconvex loss functions. In particular, we wish to understand why simple optimization schemes, such as stochastic gradient descent, do not end up trapped in local minima with high loss values that would not yield useful predictions. We explain the optimizability of DNNs by characterizing the local minima and transition states of the loss-function landscape (LFL) along with their connectivity. We show that the LFL of a DNN in the shallow network or data-abundant limit is funneled, and thus easy to optimize. Crucially, in the opposite low-data/deep limit, although the number of minima increases, the landscape is characterized by many minima with similar loss values separated by low barriers. This organization is different from the hierarchical landscapes of structural glass formers and explains why minimization procedures commonly employed by the machine-learning community can navigate the LFL successfully and reach low-lying solutions.

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Source
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7486703PMC
http://dx.doi.org/10.1073/pnas.1919995117DOI Listing

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