New lower bounds on nonlinearity and a class of highly nonlinear functions

1997 ◽  
pp. 147-158
Author(s):  
Xian-Mo Zhang ◽  
Yuliang Zheng
Keyword(s):  
Lower Bounds ◽  
Nonlinear Functions ◽  
Highly Nonlinear

scholarly journals Kriging/RBF-Hybrid Response Surface Methodology for Highly Nonlinear Functions

2012 ◽  
Vol 6 (3) ◽  
pp. 81-96 ◽  
Author(s):  
Nobuo NAMURA ◽  
Koji SHIMOYAMA ◽  
Shinkyu JEONG ◽  
Shigeru OBAYASHI
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Nonlinear Functions ◽  
Highly Nonlinear

scholarly journals Selective and invariant features of neural response surfaces measured with principal curvature

2019 ◽  
Author(s):  
James R. Golden ◽  
Kedarnath P. Vilankar ◽  
David J. Field
Keyword(s):  
Cortical Neurons ◽  
Network Models ◽  
Neural Response ◽  
Response Surfaces ◽  
Principal Curvatures ◽  
Nonlinear Functions ◽  
Nonlinear Responses ◽  
Highly Nonlinear ◽  
Feature Selectivity ◽  
Visual Cortical

AbstractThe responses of most visual cortical neurons are highly nonlinear functions of image stimuli. With the sparse coding network, a recurrent model of V1 computation, we apply techniques from differential geometry to these nonlinear responses and classify them as forms of selectivity or invariance. The selectivity and invariance of responses of individual neurons are quantified by measuring the principal curvatures of neural response surfaces in high-dimensional image space. An extended two-layer version of the network model that captures some properties of higher visual cortical areas is also characterized using this approach. We argue that this geometric view allows for the quantification of feature selectivity and invariance in network models in a way that provides insight into the computations necessary for object recognition.

Highly nonlinear functions

2013 ◽  
Vol 74 (3) ◽  
pp. 665-672
Author(s):  
Kai-Uwe Schmidt
Keyword(s):  
Nonlinear Functions ◽  
Highly Nonlinear
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