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

We study the capacity of \emph{sign} perceptrons neural networks (SPNN) andparticularly focus on 1-hidden layer \emph{treelike committee machine} (TCM)architectures. Similarly to what happens in the case of a single perceptronneuron, it turns out that, in a statistical sense, the capacity of acorresponding multilayered network architecture consisting of multiple\emph{sign} perceptrons also undergoes the so-called phase transition (PT)phenomenon. This means: (i) for certain range of system parameters (size ofdata, number of neurons), the network can be properly trained to accuratelymemorize \emph{all} elements of the input dataset; and (ii) outside the regionsuch a training does not exist. Clearly, determining the corresponding phasetransition curve that separates these regions is an extraordinary task andamong the most fundamental questions related to the performance of any network.Utilizing powerful mathematical engine called Random Duality Theory (RDT), weestablish a generic framework for determining the upper bounds on the 1-hiddenlayer TCM SPNN capacity. Moreover, we do so for \emph{any} given (odd) numberof neurons. We further show that the obtained results \emph{exactly} match thereplica symmetry predictions of \cite{EKTVZ92,BHS92}, thereby proving that thestatistical physics based results are not only nice estimates but alsomathematically rigorous bounds as well. Moreover, for $d\leq 5$, we obtain thecapacity values that improve on the best known rigorous ones of\cite{MitchDurb89}, thereby establishing a first, mathematically rigorous,progress in well over 30 years.

Capacity of the treelike sign perceptrons neural networks with one hidden layer -- RDT based upper bounds