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Differential and Algebraic Geometry of Multilayer Perceptrons

Shun-ichi AMARI, Tomoko OZEKI

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Summary :

Information geometry is applied to the manifold of neural networks called multilayer perceptrons. It is important to study a total family of networks as a geometrical manifold, because learning is represented by a trajectory in such a space. The manifold of perceptrons has a rich differential-geometrical structure represented by a Riemannian metric and singularities. An efficient learning method is proposed by using it. The parameter space of perceptrons includes a lot of algebraic singularities, which affect trajectories of learning. Such singularities are studied by using simple models. This poses an interesting problem of statistical inference and learning in hierarchical models including singularities.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.1 pp.31-38
Publication Date
2001/01/01
Publicized
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Type of Manuscript
Special Section INVITED PAPER (Special Section on the 10th Anniversary of the IEICE Transactions of Fundamentals: "Last Decade and 21st Century")
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