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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

- Online ISSN

- DOI

- 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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Shun-ichi AMARI, Tomoko OZEKI, "Differential and Algebraic Geometry of Multilayer Perceptrons" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 1, pp. 31-38, January 2001, doi: .

Abstract: 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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_1_31/_p

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@ARTICLE{e84-a_1_31,

author={Shun-ichi AMARI, Tomoko OZEKI, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Differential and Algebraic Geometry of Multilayer Perceptrons},

year={2001},

volume={E84-A},

number={1},

pages={31-38},

abstract={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.},

keywords={},

doi={},

ISSN={},

month={January},}

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TY - JOUR

TI - Differential and Algebraic Geometry of Multilayer Perceptrons

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 31

EP - 38

AU - Shun-ichi AMARI

AU - Tomoko OZEKI

PY - 2001

DO -

JO - IEICE TRANSACTIONS on Fundamentals

SN -

VL - E84-A

IS - 1

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - January 2001

AB - 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.

ER -