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Dualistic geometry of the manifold of higher-order neurons

✍ Scribed by Shun-ichi Amari

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
940 KB
Volume
4
Category
Article
ISSN
0893-6080

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✦ Synopsis

A

.w of nerlral networks. in particular rite set of all rhe nellrotzs of higher-order. f~mtl.s a geortlerrical manifold. Specifically, the .set.s N,(k = 1, 2.

.) of the krh order t1euron.s constitute a hierarchy of manifolds N,, > N,, , > '.' > N, , where n is rhe number of'itlputs. A natural geometry is inrroduceri to NL and characteristics of higher-order neurons are studied therefrom. A Rietnannian metric is defined itI N, and a dual pair of a,ffine contlecrions are introduced in these manifolds. A higher-order neuron realizes a transfortnatiotl from vector itlpuCs to a scalar ourpur. Given a rramfortnation.

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