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

In this paper we explore a connection between deep networks and learning inreproducing kernel Krein space. Our approach is based on the concept ofpush-forward - that is, taking a fixed non-linear transform on a linearprojection and converting it to a linear projection on the output of a fixednon-linear transform, pushing the weights forward through the non-linearity.Applying this repeatedly from the input to the output of a deep network, theweights can be progressively "pushed" to the output layer, resulting in a flatnetwork that has the form of a fixed non-linear map (whose form is determinedby the structure of the deep network) followed by a linear projectiondetermined by the weight matrices - that is, we take a deep network and convertit to an equivalent (indefinite) kernel machine. We then investigate theimplications of this transformation for capacity control and uniformconvergence, and provide a Rademacher complexity bound on the deep network interms of Rademacher complexity in reproducing kernel Krein space. Finally, weanalyse the sparsity properties of the flat representation, showing that theflat weights are (effectively) Lp-"norm" regularised with 0<p<1 (bridgeregression).

From deep to Shallow: Equivalent Forms of Deep Networks in Reproducing Kernel Krein Space and Indefinite Support Vector Machines