{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1390295802047924992.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.5687/iscie.36.17"}},{"identifier":{"@type":"URI","@value":"https://www.jstage.jst.go.jp/article/iscie/36/1/36_17/_pdf"}}],"resourceType":"学術雑誌論文(journal article)","dc:title":[{"@language":"en","@value":"Stability Analysis of Continuous-Time Recurrent Neural Networks by IQC with Copositive Multipliers"},{"@language":"ja","@value":"積分二次制約と共正値マルチプライアを用いた連続時間再帰型ニューラルネットワークの安定性解析"}],"dc:language":"ja","description":[{"type":"abstract","notation":[{"@language":"en","@value":"<p>This paper addresses the stability analysis problem of recurrent neural networks (RNNs) with activation functions being rectified linear units (ReLUs). In particular, we focus on the linear nonegative properties of the input-output signals of ReLUs. To capture these linear properties within the framework of integral quadratic constraint (IQC), we introduce a copositive multiplier constructed from a copositive matrix. This enables us to capture the linear input-output properties of ReLUs in quadratic form. By using the copositive multipliers in additon to existing multipliers, we can reduce the conservatism of the IQC-based stability analysis for RNNs. We also show that the proposed IQC-based stability condition with copositive multipliers can be viewed as an extension of a recently proposed scaled small-gain stability condition based on the <i>L</i><sub>2+ </sub>induced norm.</p>"}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1410295802047924995","@type":"Researcher","foaf:name":[{"@language":"en","@value":"Takao Ryota"},{"@language":"ja","@value":"高尾 亮太"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"九州大学 大学院 システム情報科学研究院"},{"@language":"en","@value":"Graduate School of Information Science and Electrical Engineering, Kyushu University"}]},{"@id":"https://cir.nii.ac.jp/crid/1410295802047924992","@type":"Researcher","foaf:name":[{"@language":"en","@value":"Fujii Tatsuki"},{"@language":"ja","@value":"藤井 達希"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"九州大学 大学院 システム情報科学研究院"},{"@language":"en","@value":"Graduate School of Information Science and Electrical Engineering, Kyushu University"}]},{"@id":"https://cir.nii.ac.jp/crid/1420845751143878784","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"80346080"},{"@type":"NRID","@value":"1000080346080"},{"@type":"CINII_AUTHOR_ID","@value":"DA17473528"},{"@type":"URI","@value":"https://ci.nii.ac.jp/author/DA17473528#entity"},{"@type":"URI","@value":"https://viaf.org/viaf/NII%7CDA17473528"},{"@type":"NRID","@value":"9000243899892"},{"@type":"NRID","@value":"9000404645265"},{"@type":"NRID","@value":"9000024286181"},{"@type":"NRID","@value":"9000411825087"},{"@type":"NRID","@value":"9000024261899"},{"@type":"NRID","@value":"9000024103996"},{"@type":"NRID","@value":"9000023116838"},{"@type":"NRID","@value":"9000279889185"},{"@type":"NRID","@value":"9000403960195"},{"@type":"NRID","@value":"9000391813706"},{"@type":"NRID","@value":"9000024873950"},{"@type":"NRID","@value":"9000403960186"},{"@type":"NRID","@value":"9000258683699"},{"@type":"NRID","@value":"9000279889191"},{"@type":"NRID","@value":"9000001058535"},{"@type":"NRID","@value":"9000391988958"},{"@type":"NRID","@value":"9000254772277"},{"@type":"NRID","@value":"9000023034473"},{"@type":"NRID","@value":"9000415418892"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read0192962"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/yebihara"}],"foaf:name":[{"@language":"en","@value":"Ebihara Yoshio"},{"@language":"ja","@value":"蛯原 義雄"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"九州大学 大学院 システム情報科学研究院"},{"@language":"en","@value":"Graduate School of Information Science and Electrical Engineering, Kyushu University"}]},{"@id":"https://cir.nii.ac.jp/crid/1410295802047924994","@type":"Researcher","foaf:name":[{"@language":"en","@value":"Motooka Hayato"},{"@language":"ja","@value":"本岡 駿人"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"九州大学 大学院 システム情報科学研究院"},{"@language":"en","@value":"Graduate School of Information Science and Electrical Engineering, Kyushu University"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"13425668"},{"@type":"LISSN","@value":"13425668"},{"@type":"EISSN","@value":"2185811X"}],"prism:publicationName":[{"@language":"en","@value":"Transactions of the Institute of Systems, Control and Information Engineers"},{"@language":"ja","@value":"システム制御情報学会論文誌"},{"@language":"en","@value":"Transactions of ISCIE"},{"@language":"en","@value":"Trans. ISCIE"},{"@language":"en","@value":"Transactions of the Institute of Systems, Control and Information Engineers"},{"@language":"ja","@value":"システム制御情報学会論文誌"}],"dc:publisher":[{"@language":"en","@value":"THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE)"},{"@language":"ja","@value":"一般社団法人 システム制御情報学会"}],"prism:publicationDate":"2023-01-15","prism:volume":"36","prism:number":"1","prism:startingPage":"17","prism:endingPage":"25"},"reviewed":"false","url":[{"@id":"https://www.jstage.jst.go.jp/article/iscie/36/1/36_17/_pdf"}],"availableAt":"2023-01-15","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=recurrent%20neural%20networks","dc:title":"recurrent neural networks"},{"@id":"https://cir.nii.ac.jp/all?q=rectified%20linear%20units","dc:title":"rectified linear units"},{"@id":"https://cir.nii.ac.jp/all?q=stability%20analysis","dc:title":"stability analysis"},{"@id":"https://cir.nii.ac.jp/all?q=integral%20quadratic%20constraints","dc:title":"integral quadratic constraints"},{"@id":"https://cir.nii.ac.jp/all?q=copositive%20multipliers","dc:title":"copositive multipliers"}],"project":[{"@id":"https://cir.nii.ac.jp/crid/1040285300696494208","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"20H04145"},{"@type":"JGN","@value":"JP20H04145"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20H04145/"}],"notation":[{"@language":"ja","@value":"悪条件錐線形計画問題の理論とアルゴリズム"},{"@language":"en","@value":"Theory and algorithms for ill-conditioned conic linear programming"}]},{"@id":"https://cir.nii.ac.jp/crid/1040581301854597120","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"23K20949"},{"@type":"JGN","@value":"JP23K20949"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23K20949/"}],"notation":[{"@language":"ja","@value":"錐計画に基づく再帰型ニューラルネットワークの安定性解析と最適設計"},{"@language":"en","@value":"Stability Analysis and Optimal Synthesis of Recurrent Neural Networks by Conic Programming"}]}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360011143576663424","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"System analysis via integral quadratic constraints"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013168760319616","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.svg\"><mml:msub><mml:mi>l</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> induced norm analysis of discrete-time LTI systems for nonnegative input signals and its application to stability analysis of recurrent neural networks"}]},{"@id":"https://cir.nii.ac.jp/crid/1360016866369593984","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Absolute stability analysis of discrete time feedback interconnections"}]},{"@id":"https://cir.nii.ac.jp/crid/1360292619527674368","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Completely Positive Matrices"}]},{"@id":"https://cir.nii.ac.jp/crid/1360294646281860480","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks"}]},{"@id":"https://cir.nii.ac.jp/crid/1360579818612555392","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Stability Conditions for Systems with Monotone and Slope-Restricted Nonlinearities"}]},{"@id":"https://cir.nii.ac.jp/crid/1360857597946456832","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Stability analysis of discrete-time recurrent neural networks"}]},{"@id":"https://cir.nii.ac.jp/crid/1390866591962855040","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Construction and Input-to-output Characteristics Evaluation of Compressed Model of Recurrent Neural Networks for Their Stability Analysis"},{"@language":"ja","@value":"再帰型ニューラルネットワークの安定性判別のための圧縮モデルの構築と入出力特性の評価"},{"@language":"ja-Kana","@value":"サイキガタ ニューラルネットワーク ノ アンテイセイ ハンベツ ノ タメ ノ アッシュク モデル ノ コウチク ト ニュウシュツリョク トクセイ ノ ヒョウカ"}]}],"dataSourceIdentifier":[{"@type":"JALC","@value":"oai:japanlinkcenter.org:2010565613"},{"@type":"CROSSREF","@value":"10.5687/iscie.36.17"},{"@type":"KAKEN","@value":"PRODUCT-25243179"},{"@type":"KAKEN","@value":"PRODUCT-25233573"},{"@type":"OPENAIRE","@value":"doi_________::e6278d83c3763de6702e5b387f295d8a"},{"@type":"CROSSREF","@value":"10.9746/sicetr.61.104_references_DOI_TFvj14KvLXsgwVDXVZFeXFtpNjd"}]}