The computational intractability of training sigmoidal neural networks
We demonstrate that the problem of approximately interpolating a target function by a neural network is computationally intractable. In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node...
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| Veröffentlicht in: | IEEE transactions on information theory 1997-01, Vol.43 (1), p.167-173 |
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| container_title | IEEE transactions on information theory |
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| creator | Jones, L.K. |
| description | We demonstrate that the problem of approximately interpolating a target function by a neural network is computationally intractable. In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node is shown to be NP-hard and NP-complete if the internal nodes are in addition piecewise ratios of polynomials. This partially answers a question of Blum and Rivest (1992) concerning the NP-completeness of training a logistic sigmoidal 3-node network. An extension of the result is then given for networks with n monotone sigmoidal internal nodes and one convex output node. This indicates that many multivariate nonlinear regression problems may be computationally infeasible. |
| doi_str_mv | 10.1109/18.567673 |
| format | Article |
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In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node is shown to be NP-hard and NP-complete if the internal nodes are in addition piecewise ratios of polynomials. This partially answers a question of Blum and Rivest (1992) concerning the NP-completeness of training a logistic sigmoidal 3-node network. An extension of the result is then given for networks with n monotone sigmoidal internal nodes and one convex output node. 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In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node is shown to be NP-hard and NP-complete if the internal nodes are in addition piecewise ratios of polynomials. This partially answers a question of Blum and Rivest (1992) concerning the NP-completeness of training a logistic sigmoidal 3-node network. An extension of the result is then given for networks with n monotone sigmoidal internal nodes and one convex output node. 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(IEEE)</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>199701</creationdate><title>The computational intractability of training sigmoidal neural networks</title><author>Jones, L.K.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c304t-7e80ac6048267c970f93cdadd9624e2a18848cc742d8aa62ae7c0e991a8c59953</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Computer networks</topic><topic>Feedforward neural networks</topic><topic>Information technology</topic><topic>Interpolation</topic><topic>Logistics</topic><topic>Neural networks</topic><topic>Polynomials</topic><topic>Search problems</topic><topic>Vectors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Jones, L.K.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Jones, L.K.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The computational intractability of training sigmoidal neural networks</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>1997-01</date><risdate>1997</risdate><volume>43</volume><issue>1</issue><spage>167</spage><epage>173</epage><pages>167-173</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>We demonstrate that the problem of approximately interpolating a target function by a neural network is computationally intractable. In particular the interpolation training problem for a neural network with two monotone Lipschitzian sigmoidal internal activation functions and one linear output node is shown to be NP-hard and NP-complete if the internal nodes are in addition piecewise ratios of polynomials. This partially answers a question of Blum and Rivest (1992) concerning the NP-completeness of training a logistic sigmoidal 3-node network. An extension of the result is then given for networks with n monotone sigmoidal internal nodes and one convex output node. This indicates that many multivariate nonlinear regression problems may be computationally infeasible.</abstract><cop>New York</cop><pub>IEEE</pub><doi>10.1109/18.567673</doi><tpages>7</tpages></addata></record> |
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| ispartof | IEEE transactions on information theory, 1997-01, Vol.43 (1), p.167-173 |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Computer networks Feedforward neural networks Information technology Interpolation Logistics Neural networks Polynomials Search problems Vectors |
| title | The computational intractability of training sigmoidal neural networks |
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