no code implementations • 11 Dec 2020 • Nelia Charalambous, Zhiqin Lu, Julie Rowlett
We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary.
Spectral Theory Analysis of PDEs Differential Geometry
no code implementations • 11 Dec 2020 • Zhiqin Lu, Julie Rowlett
We prove that the presence or absence of corners is spectrally determined in the following sense: any simply connected domain with piecewise smooth Lipschitz boundary cannot be isospectral to any connected domain, of any genus, which has smooth boundary.
Spectral Theory Mathematical Physics Analysis of PDEs Differential Geometry Mathematical Physics 35P99 (primary), 35K05 (secondary)
no code implementations • 10 Dec 2020 • Zhiqin Lu, Julie Rowlett
Following the introduction, the main techniques used in inverse isospectral problems are collected and discussed.
Spectral Theory Analysis of PDEs Differential Geometry primary 58C40, secondary 35P99
no code implementations • 22 Dec 2017 • Pierre Baldi, Peter Sadowski, Zhiqin Lu
Specifically, random backpropagation and its variations can be performed with the same non-linear neurons used in the main input-output forward channel, and the connections in the learning channel can be adapted using the same algorithm used in the forward channel, removing the need for any specialized hardware in the learning channel.
no code implementations • 8 Dec 2016 • Pierre Baldi, Peter Sadowski, Zhiqin Lu
It is remarkable both because of its effectiveness, in spite of using random matrices to communicate error information, and because it completely removes the taxing requirement of maintaining symmetric weights in a physical neural system.
no code implementations • 20 Aug 2011 • Pierre Baldi, Zhiqin Lu
The general framework described here is useful to classify autoencoders and identify general common properties that ought to be investigated for each class, illuminating some of the connections between information theory, unsupervised learning, clustering, Hebbian learning, and autoencoders.