Non-euclidean vector product for neural networks

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buir.contributor.authorÇetin, A. Enis
buir.contributor.orcidÇetin, A. Enis|0000-0002-3449-1958
dc.citation.epage6866en_US
dc.citation.spage6863en_US
dc.contributor.authorAfrasiyabi, A.en_US
dc.contributor.authorBadawi, Diaaen_US
dc.contributor.authorNasır, B.en_US
dc.contributor.authorYıldız, O.en_US
dc.contributor.authorYarman- Vural, F. T.en_US
dc.contributor.authorÇetin, A. Enisen_US
dc.date.accessioned2019-02-21T16:04:22Z
dc.date.available2019-02-21T16:04:22Z
dc.date.issued2018-04en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe present a non-Euclidean vector product for artificial neural networks. The vector product operator does not require any multiplications while providing correlation information between two vectors. Ordinary neurons require inner product of two vectors. We propose a class of neural networks with the universal approximation property over the space of Lebesgue integrable functions based on the proposed non-Euclidean vector product. In this new network, the 'product' of two real numbers is defined as the sum of their absolute values, with the sign determined by the sign of the product of the numbers. This 'product' is used to construct a vector product in RN. The vector product induces the l1 norm. The additive neural network successfully solves the XOR problem. Experiments on MNIST and CIFAR datasets show that the classification performance of the proposed additive neural network is comparable to the corresponding multi-layer perceptron and convolutional neural networks.
dc.description.sponsorshipA. Enis Çetin and Diaa Badawi’s work was funded by an NSF grant with grant number 1739396
dc.identifier.doi10.1109/ICASSP.2018.8461709
dc.identifier.issn1520-6149
dc.identifier.urihttp://hdl.handle.net/11693/50181
dc.language.isoEnglish
dc.publisherIEEE
dc.relation.isversionofhttps://doi.org/10.1109/ICASSP.2018.8461709
dc.relation.projectNational Science Foundation, NSF: 1739396
dc.source.titleICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedingsen_US
dc.subjectAdditive neural networksen_US
dc.subjectMultiplication-free operatoren_US
dc.subjectNon-Euclidean operatoren_US
dc.titleNon-euclidean vector product for neural networksen_US
dc.typeConference Paperen_US
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