Variational bounds on the diffusive and hydrodynamic permeabilities of randomly perforated sheets

1983 ◽  
pp. 370-390 ◽  
Author(s):  
George H. Malone ◽  
Suk Youn Suh ◽  
Stephen Prager
Keyword(s):  
Variational Bounds ◽  
Perforated Sheets

scholarly journals Damage Evaluation for Perforated Sheets under Biaxial Deformation.

2002 ◽  
Vol 68 (667) ◽  
pp. 428-433 ◽  
Author(s):  
Shigeru NAGAKI ◽  
Katsutoshi SUMIYOSHI ◽  
Katsuyuki ABE
Keyword(s):  
Damage Evaluation ◽  
Biaxial Deformation ◽  
Perforated Sheets

Lower and upper variational bounds in calculations of Coulomb and nuclear systems

2000 ◽  
Vol 63 (3) ◽  
pp. 353-364
Author(s):  
A. G. Donchev ◽  
N. N. Kolesnikov ◽  
V. I. Tarasov
Keyword(s):  
Variational Bounds ◽  
Nuclear Systems

Unified formulae of variational bounds for multiphase anisotropic elastic composites

2008 ◽  
Vol 79 (3) ◽  
pp. 189-204
Author(s):  
H. Brito-Santana ◽  
R. Rodríguez-Ramos ◽  
R. Guinovart-Díaz ◽  
J. Bravo-Castillero ◽  
F. J. Sabina ◽  
...  
Keyword(s):  
Variational Bounds ◽  
Anisotropic Elastic ◽  
Elastic Composites

Deflection of perforated sheets in explosion welding

1989 ◽  
Vol 3 (4) ◽  
pp. 286-288
Author(s):  
A I Kheifets ◽  
O A Denyachenko ◽  
S P Timchenko ◽  
L I Sedykh
Keyword(s):  
Explosion Welding ◽  
Perforated Sheets

scholarly journals A Comparison of Variational Bounds for the Information Bottleneck Functional

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1229 ◽  
Author(s):  
Bernhard C. Geiger ◽  
Ian S. Fischer
Keyword(s):  
Cost Function ◽  
Short Note ◽  
General Setting ◽  
Conditional Entropy ◽  
Variational Bounds ◽  
Information Bottleneck ◽  
Feasible Sets ◽  
Shed Light ◽  
Relevant Cost ◽  
General Setup

In this short note, we relate the variational bounds proposed in Alemi et al. (2017) and Fischer (2020) for the information bottleneck (IB) and the conditional entropy bottleneck (CEB) functional, respectively. Although the two functionals were shown to be equivalent, it was empirically observed that optimizing bounds on the CEB functional achieves better generalization performance and adversarial robustness than optimizing those on the IB functional. This work tries to shed light on this issue by showing that, in the most general setting, no ordering can be established between these variational bounds, while such an ordering can be enforced by restricting the feasible sets over which the optimizations take place. The absence of such an ordering in the general setup suggests that the variational bound on the CEB functional is either more amenable to optimization or a relevant cost function for optimization in its own regard, i.e., without justification from the IB or CEB functionals.

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