English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We analyze the connection between minimizers with good generalizingproperties and high local entropy regions of a threshold-linear classifier inGaussian mixtures with the mean squared error loss function. We show that thereexist configurations that achieve the Bayes-optimal generalization error, evenin the case of unbalanced clusters. We explore analytically the error-countingloss landscape in the vicinity of a Bayes-optimal solution, and show that thecloser we get to such configurations, the higher the local entropy, implyingthat the Bayes-optimal solution lays inside a wide flat region. We alsoconsider the algorithmically relevant case of targeting wide flat minima of the(differentiable) mean squared error loss. Our analytical and numerical resultsshow not only that in the balanced case the dependence on the norm of theweights is mild, but also, in the unbalanced case, that the performances can beimproved.

Wide flat minima and optimal generalization in classifying high-dimensional Gaussian mixtures