Learning with Known Operators reduces Maximum Training Error Bounds.

Clicks: 338
ID: 5015
2019
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Abstract
We describe an approach for incorporating prior knowledge into machine learning algorithms. We aim at applications in physics and signal processing in which we know that certain operations must be embedded into the algorithm. Any operation that allows computation of a gradient or sub-gradient towards its inputs is suited for our framework. We derive a maximal error bound for deep nets that demonstrates that inclusion of prior knowledge results in its reduction. Furthermore, we also show experimentally that known operators reduce the number of free parameters. We apply this approach to various tasks ranging from CT image reconstruction over vessel segmentation to the derivation of previously unknown imaging algorithms. As such the concept is widely applicable for many researchers in physics, imaging, and signal processing. We assume that our analysis will support further investigation of known operators in other fields of physics, imaging, and signal processing.
Reference Key
maier2019learningnature Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Maier, Andreas K;Syben, Christopher;Stimpel, Bernhard;Würfl, Tobias;Hoffmann, Mathis;Schebesch, Frank;Fu, Weilin;Mill, Leonid;Kling, Lasse;Christiansen, Silke;
Journal nature machine intelligence
Year 2019
DOI
10.1038/s42256-019-0077-5
URL
Keywords Keywords not found

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