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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The expressiveness of deep neural network (DNN) is a perspective tounderstandthe surprising performance of DNN. The number of linear regions, i.e.pieces thata piece-wise-linear function represented by a DNN, is generally usedto measurethe expressiveness. And the upper bound of regions number partitionedby a rec-tifier network, instead of the number itself, is a more practicalmeasurement ofexpressiveness of a rectifier DNN. In this work, we propose a newand tighter up-per bound of regions number. Inspired by the proof of this upperbound and theframework of matrix computation in Hinz & Van de Geer (2019), wepropose ageneral computational approach to compute a tight upper bound ofregions numberfor theoretically any network structures (e.g. DNN with all kindof skip connec-tions and residual structures). Our experiments show our upperbound is tighterthan existing ones, and explain why skip connections andresidual structures canimprove network performance.

A General Computational Framework to Measure the Expressiveness of Complex Networks Using a Tighter Upper Bound of Linear Regions