%Aigaion2 BibTeX export from Idiap Publications %Saturday 21 December 2024 06:18:05 PM @ARTICLE{Mayo98a1, author = {Mayoraz, Eddy}, projects = {Idiap}, title = {On the Complexity of Recognizing Regions Computable by Two-Layered Perceptrons}, journal = {Annals Mathematics and Artificial Intelligence}, year = {1999}, crossref = {mayo98a}, abstract = {This work is concerned with the computational complexity of the recognition of $ÞPtwo$, the class of regions of the Euclidian space that can be classified exactly by a two-layered perceptron. Some subclasses of $ÞPtwo$ of particular interest are also studied, such as the class of iterated differences of polyhedra, or the class of regions $V$ that can be classified by a two-layered perceptron with as only hidden units the ones associated to $(d-1)$-dimensional facets of $V$. In this paper, we show that the recognition problem for $ÞPtwo$ as well as most other subclasses considered here is \NPH\ in the most general case. We then identify special cases that admit polynomial time algorithms.}, pdf = {https://publications.idiap.ch/attachments/reports/1998/rr98-03.pdf}, postscript = {ftp://ftp.idiap.ch/pub/reports/1998/rr98-03.ps.gz}, ipdinar={1998}, ipdmembership={learning}, } crossreferenced publications: @TECHREPORT{Mayo98a, author = {Mayoraz, Eddy}, projects = {Idiap}, title = {On the Complexity of Recognizing Regions Computable by Two-Layered Perceptrons}, type = {Idiap-RR}, number = {Idiap-RR-03-1998}, year = {1998}, institution = {IDIAP}, abstract = {This work is concerned with the computational complexity of the recognition of $ÞPtwo$, the class of regions of the Euclidian space that can be classified exactly by a two-layered perceptron. Some subclasses of $ÞPtwo$ of particular interest are also studied, such as the class of iterated differences of polyhedra, or the class of regions $V$ that can be classified by a two-layered perceptron with as only hidden units the ones associated to $(d-1)$-dimensional facets of $V$. In this paper, we show that the recognition problem for $ÞPtwo$ as well as most other subclasses considered here is \NPH\ in the most general case. We then identify special cases that admit polynomial time algorithms.}, pdf = {https://publications.idiap.ch/attachments/reports/1998/rr98-03.pdf}, postscript = {ftp://ftp.idiap.ch/pub/reports/1998/rr98-03.ps.gz}, ipdmembership={learning}, }