Neural networks learn to magnify areas near decision boundaries

01/26/2023

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by   Jacob A. Zavatone-Veth, et al.

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We study how training molds the Riemannian geometry induced by neural network feature maps. At infinite width, neural networks with random parameters induce highly symmetric metrics on input space. Feature learning in networks trained to perform classification tasks magnifies local areas along decision boundaries. These changes are consistent with previously proposed geometric approaches for hand-tuning of kernel methods to improve generalization.