Distributed optimization with faulty nodes: robust aggregation in hyperbolic space
The increasing deployment of distributed machine learning models necessitates robust optimization methods that can tolerate adversarial or faulty nodes. In this work, we propose a robust gradient aggregation method for distributed stochastic gradient descent that leverages hyperbolic geometry. Speci...
Saved in:
| Published in: | Neural computing & applications Vol. 37; no. 26; pp. 21563 - 21605 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
London
Springer London
01.09.2025
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0941-0643, 1433-3058 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | The increasing deployment of distributed machine learning models necessitates robust optimization methods that can tolerate adversarial or faulty nodes. In this work, we propose a robust gradient aggregation method for distributed stochastic gradient descent that leverages hyperbolic geometry. Specifically, local gradients computed at individual nodes are embedded into hyperbolic space using the Poincaré ball model, and their geometric median is computed as a robust aggregate. This aggregated gradient is then mapped back to Euclidean space for the gradient update. We also show that existing robust gradient aggregation methods like Krum can be improved using hyperbolic space. Compared to existing robust aggregation methods, our hyperbolic approach offers improved separation of outlier updates. We provide theoretical convergence guarantees and validate our method on benchmark datasets as well as on a traffic forecasting task, demonstrating its efficacy in mitigating Byzantine failures in distributed federated learning environments. |
|---|---|
| AbstractList | The increasing deployment of distributed machine learning models necessitates robust optimization methods that can tolerate adversarial or faulty nodes. In this work, we propose a robust gradient aggregation method for distributed stochastic gradient descent that leverages hyperbolic geometry. Specifically, local gradients computed at individual nodes are embedded into hyperbolic space using the Poincaré ball model, and their geometric median is computed as a robust aggregate. This aggregated gradient is then mapped back to Euclidean space for the gradient update. We also show that existing robust gradient aggregation methods like Krum can be improved using hyperbolic space. Compared to existing robust aggregation methods, our hyperbolic approach offers improved separation of outlier updates. We provide theoretical convergence guarantees and validate our method on benchmark datasets as well as on a traffic forecasting task, demonstrating its efficacy in mitigating Byzantine failures in distributed federated learning environments. |
| Author | Vittamsetti, Vijay Monic Ghosh, Subhas Kumar |
| Author_xml | – sequence: 1 givenname: Subhas Kumar orcidid: 0000-0003-1522-7067 surname: Ghosh fullname: Ghosh, Subhas Kumar email: subhas.ghosh@westpac.com.au organization: Westpac Institutional Bank – sequence: 2 givenname: Vijay Monic surname: Vittamsetti fullname: Vittamsetti, Vijay Monic organization: Westpac Institutional Bank |
| BookMark | eNp9kEtLxDAUhYOM4MzoH3AVcF29aR5N3cn4hAFBdB2SNulkmGlq0iLjr7dawZ2ruzjfORe-BZq1obUInRO4JADFVQLgOckg5xkhrOAZHKE5YZRmFLicoTmUbIwFoydokdIWAJiQfI5ebn3qozdDb2scut7v_afufWjxh-832Olh1x9wG2qbrnEMZkg91k0TbTNRvsWbQ2ejCTtf4dTpyp6iY6d3yZ793iV6u797XT1m6-eHp9XNOquILCAT1mopSE2cLqXNC1MWxFFhKDFSGFNyWrK6dGUuDZTGVZV1zDHJhMkpZ2DpEl1Mu10M74NNvdqGIbbjS0VzxpkUkBcjlU9UFUNK0TrVRb_X8aAIqG93anKnRnfqx52CsUSnUhrhtrHxb_qf1hfjz3Q8 |
| Cites_doi | 10.1109/JIOT.2020.2991401 10.1109/JIOT.2024.3454064 10.1109/COMST.2018.2844341 10.24432/C53G6X 10.1109/ACCESS.2025.3530297 10.1109/TITS.2024.3493199 10.1109/JIOT.2022.3161050 10.1145/357172.357176 10.1093/comjnl/bxae141 10.1109/ACCESS.2021.3067331 10.1145/3377454 10.1109/JIOT.2018.2867333 10.1017/9781009701853.003 10.1109/CVPR.2008.4587747 10.1145/322186.322188 10.1109/TITS.2022.3157056 10.1038/s41598-024-82759-z 10.1109/TSP.2022.3153135 10.1109/ICSSIT53264.2022.9716331 10.1109/TIA.2024.3430229 10.1109/IJCNN55064.2022.9892326 10.1109/TITS.2024.3510913 10.3390/ijgi10070485 10.1016/j.array.2022.100158 10.1145/3298981 10.1016/0196-6774(82)90004-9 10.1109/ACCESS.2025.3540955 10.1109/JIOT.2024.3462302 10.1109/TNNLS.2020.2978386 10.5555/3304222.3304273 10.1109/TITS.2019.2935152 10.1145/3154503 10.1007/978-94-009-5438-0_20 10.1007/s10479-008-0352-z 10.1145/3701740 10.1145/3447548.3467275 10.1109/TRO.2022.3178296 10.1137/080743706 10.1016/j.jestch.2018.09.003 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025. |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s00521-025-11475-0 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1433-3058 |
| EndPage | 21605 |
| ExternalDocumentID | 10_1007_s00521_025_11475_0 |
| GroupedDBID | -Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 123 1N0 1SB 2.D 203 28- 29N 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 53G 5QI 5VS 67Z 6NX 8FE 8FG 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AAPKM AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBRH ABBXA ABDBE ABDBF ABDZT ABECU ABFSG ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACSTC ACUHS ACZOJ ADHHG ADHIR ADHKG ADIMF ADKFA ADKNI ADKPE ADMLS ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFEXP AFGCZ AFHIU AFKRA AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGQPQ AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. B0M BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EAD EAP EBLON EBS ECS EDO EIOEI EJD EMI EMK EPL ESBYG EST ESX F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P2P P62 P9O PF0 PHGZM PHGZT PQGLB PT4 PT5 PUEGO QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ~8M ~EX AAYXX AFFHD CITATION |
| ID | FETCH-LOGICAL-c1870-6eea861d1fa98e27b971f36b31b86bb95394d9f928b09bfccef4f4846b23540e3 |
| IEDL.DBID | RSV |
| ISSN | 0941-0643 |
| IngestDate | Wed Nov 05 15:30:52 EST 2025 Sat Nov 29 07:32:48 EST 2025 Tue Sep 02 01:13:34 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 26 |
| Keywords | Distributed optimization algorithm Federated learning Stochastic gradient descent Robust aggregation rule Byzantine resilience Hyperbolic space |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c1870-6eea861d1fa98e27b971f36b31b86bb95394d9f928b09bfccef4f4846b23540e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-1522-7067 |
| PQID | 3245486027 |
| PQPubID | 2043988 |
| PageCount | 43 |
| ParticipantIDs | proquest_journals_3245486027 crossref_primary_10_1007_s00521_025_11475_0 springer_journals_10_1007_s00521_025_11475_0 |
| PublicationCentury | 2000 |
| PublicationDate | 20250900 2025-09-00 20250901 |
| PublicationDateYYYYMMDD | 2025-09-01 |
| PublicationDate_xml | – month: 9 year: 2025 text: 20250900 |
| PublicationDecade | 2020 |
| PublicationPlace | London |
| PublicationPlace_xml | – name: London – name: Heidelberg |
| PublicationTitle | Neural computing & applications |
| PublicationTitleAbbrev | Neural Comput & Applic |
| PublicationYear | 2025 |
| Publisher | Springer London Springer Nature B.V |
| Publisher_xml | – name: Springer London – name: Springer Nature B.V |
| References | 11475_CR28 K Pillutla (11475_CR22) 2022; 70 11475_CR29 11475_CR26 H Rafi (11475_CR8) 2025; 12 11475_CR27 Q Yang (11475_CR3) 2019; 10 J Bai (11475_CR41) 2021; 10 B Akdemir (11475_CR10) 2025; 13 T Landman (11475_CR9) 2025; 13 11475_CR36 W Jian (11475_CR6) 2024; 26 M Mohammadi (11475_CR30) 2018; 20 11475_CR17 11475_CR59 D Dolev (11475_CR20) 1982; 3 J Bian (11475_CR31) 2022; 9 Z Wu (11475_CR35) 2021; 32 JW Cannon (11475_CR52) 1997; 31 11475_CR60 X Yuan (11475_CR33) 2023; 24 11475_CR61 L Lamport (11475_CR18) 1982; 4 J Verbraeken (11475_CR44) 2020; 53 L Bottou (11475_CR42) 1999 R Peter (11475_CR49) 1985; 8 R Xin (11475_CR4) 2025; 57 11475_CR24 11475_CR25 11475_CR23 11475_CR1 11475_CR21 Y Chen (11475_CR48) 2017; 1 11475_CR2 Y Wang (11475_CR7) 2025; 61 J Li (11475_CR16) 2022; 38 E Weiszfeld (11475_CR54) 2009; 167 NN Srinidhi (11475_CR14) 2019; 22 GH Hardy (11475_CR56) 1934 L Zhao (11475_CR39) 2020; 21 11475_CR50 M Pease (11475_CR19) 1980; 27 11475_CR57 11475_CR58 11475_CR11 11475_CR55 11475_CR53 11475_CR51 Y Liu (11475_CR32) 2020; 7 Q Guo (11475_CR40) 2025; 15 Q Liu (11475_CR5) 2024; 26 D Mosk-Aoyama (11475_CR47) 2010; 20 11475_CR37 I Zhou (11475_CR13) 2022; 14 11475_CR38 AL Diedrichs (11475_CR12) 2018; 5 Y Wang (11475_CR34) 2024; 11 SMAA Abir (11475_CR15) 2021; 9 11475_CR46 11475_CR45 11475_CR43 |
| References_xml | – volume: 7 start-page: 7751 issue: 8 year: 2020 ident: 11475_CR32 publication-title: IEEE Internet Things J doi: 10.1109/JIOT.2020.2991401 – volume: 11 start-page: 40656 issue: 24 year: 2024 ident: 11475_CR34 publication-title: IEEE Internet Things J doi: 10.1109/JIOT.2024.3454064 – volume: 20 start-page: 2923 issue: 4 year: 2018 ident: 11475_CR30 publication-title: IEEE Commun Surv Tutor doi: 10.1109/COMST.2018.2844341 – ident: 11475_CR60 doi: 10.24432/C53G6X – volume: 13 start-page: 14317 year: 2025 ident: 11475_CR10 publication-title: IEEE Access doi: 10.1109/ACCESS.2025.3530297 – volume: 26 start-page: 2227 issue: 2 year: 2024 ident: 11475_CR6 publication-title: Trans Intell Transport Sys doi: 10.1109/TITS.2024.3493199 – volume: 9 start-page: 8364 issue: 11 year: 2022 ident: 11475_CR31 publication-title: IEEE Internet Things J doi: 10.1109/JIOT.2022.3161050 – ident: 11475_CR50 – ident: 11475_CR58 – volume: 4 start-page: 382 issue: 3 year: 1982 ident: 11475_CR18 publication-title: ACM Trans Program Lang Syst doi: 10.1145/357172.357176 – ident: 11475_CR11 doi: 10.1093/comjnl/bxae141 – volume: 9 start-page: 50961 year: 2021 ident: 11475_CR15 publication-title: IEEE Access doi: 10.1109/ACCESS.2021.3067331 – ident: 11475_CR29 – volume: 53 start-page: 1 issue: 2 year: 2020 ident: 11475_CR44 publication-title: ACM Comput Surv doi: 10.1145/3377454 – ident: 11475_CR21 – volume: 5 start-page: 4589 issue: 6 year: 2018 ident: 11475_CR12 publication-title: IEEE Internet Things J doi: 10.1109/JIOT.2018.2867333 – ident: 11475_CR25 – volume-title: Inequalities year: 1934 ident: 11475_CR56 – volume: 31 start-page: 59 year: 1997 ident: 11475_CR52 publication-title: Flavors Geometry doi: 10.1017/9781009701853.003 – ident: 11475_CR55 doi: 10.1109/CVPR.2008.4587747 – volume: 27 start-page: 228 issue: 2 year: 1980 ident: 11475_CR19 publication-title: J ACM doi: 10.1145/322186.322188 – volume: 24 start-page: 8738 issue: 8 year: 2023 ident: 11475_CR33 publication-title: IEEE Trans Intell Transp Syst doi: 10.1109/TITS.2022.3157056 – ident: 11475_CR53 – volume: 15 start-page: 953 issue: 1 year: 2025 ident: 11475_CR40 publication-title: Sci Rep doi: 10.1038/s41598-024-82759-z – volume: 70 start-page: 1142 year: 2022 ident: 11475_CR22 publication-title: IEEE Trans Signal Process doi: 10.1109/TSP.2022.3153135 – ident: 11475_CR17 doi: 10.1109/ICSSIT53264.2022.9716331 – ident: 11475_CR57 – volume: 61 start-page: 1352 issue: 1 year: 2025 ident: 11475_CR7 publication-title: IEEE Trans Ind Appl doi: 10.1109/TIA.2024.3430229 – ident: 11475_CR2 – ident: 11475_CR36 doi: 10.1109/IJCNN55064.2022.9892326 – volume: 26 start-page: 2777 issue: 2 year: 2024 ident: 11475_CR5 publication-title: Trans Intell Transport Sys doi: 10.1109/TITS.2024.3510913 – volume: 10 start-page: 485 issue: 7 year: 2021 ident: 11475_CR41 publication-title: ISPRS Int J Geo Inf doi: 10.3390/ijgi10070485 – ident: 11475_CR26 – ident: 11475_CR43 – volume: 14 year: 2022 ident: 11475_CR13 publication-title: Array doi: 10.1016/j.array.2022.100158 – ident: 11475_CR23 – volume: 10 start-page: 1 issue: 2 year: 2019 ident: 11475_CR3 publication-title: ACM Trans Intell Syst Technol doi: 10.1145/3298981 – ident: 11475_CR46 – start-page: 9 volume-title: On-line learning and stochastic approximations year: 1999 ident: 11475_CR42 – volume: 3 start-page: 14 issue: 1 year: 1982 ident: 11475_CR20 publication-title: J Algorithms doi: 10.1016/0196-6774(82)90004-9 – volume: 13 start-page: 30377 year: 2025 ident: 11475_CR9 publication-title: IEEE Access doi: 10.1109/ACCESS.2025.3540955 – ident: 11475_CR61 – volume: 12 start-page: 1688 issue: 2 year: 2025 ident: 11475_CR8 publication-title: IEEE Internet Things J doi: 10.1109/JIOT.2024.3462302 – ident: 11475_CR27 – volume: 32 start-page: 4 issue: 1 year: 2021 ident: 11475_CR35 publication-title: IEEE Trans Neural Netw Learn Syst doi: 10.1109/TNNLS.2020.2978386 – ident: 11475_CR38 doi: 10.5555/3304222.3304273 – volume: 21 start-page: 3848 issue: 9 year: 2020 ident: 11475_CR39 publication-title: IEEE Trans Intell Transp Syst doi: 10.1109/TITS.2019.2935152 – volume: 1 start-page: 1 issue: 2 year: 2017 ident: 11475_CR48 publication-title: Proc ACM Meas Anal Comput Syst doi: 10.1145/3154503 – ident: 11475_CR1 – volume: 8 start-page: 283 year: 1985 ident: 11475_CR49 publication-title: Math Stat Appl doi: 10.1007/978-94-009-5438-0_20 – volume: 167 start-page: 7 issue: 1 year: 2009 ident: 11475_CR54 publication-title: Ann Oper Res doi: 10.1007/s10479-008-0352-z – volume: 57 start-page: 1 issue: 5 year: 2025 ident: 11475_CR4 publication-title: ACM Comput Surv doi: 10.1145/3701740 – ident: 11475_CR51 – ident: 11475_CR59 – ident: 11475_CR37 doi: 10.1145/3447548.3467275 – volume: 38 start-page: 3550 issue: 6 year: 2022 ident: 11475_CR16 publication-title: IEEE Trans Rob doi: 10.1109/TRO.2022.3178296 – ident: 11475_CR28 – volume: 20 start-page: 3260 issue: 6 year: 2010 ident: 11475_CR47 publication-title: SIAM J Optim doi: 10.1137/080743706 – ident: 11475_CR45 – volume: 22 start-page: 1 issue: 1 year: 2019 ident: 11475_CR14 publication-title: Eng Sci Technol Int J doi: 10.1016/j.jestch.2018.09.003 – ident: 11475_CR24 |
| SSID | ssj0004685 |
| Score | 2.3903365 |
| Snippet | The increasing deployment of distributed machine learning models necessitates robust optimization methods that can tolerate adversarial or faulty nodes. In... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| StartPage | 21563 |
| SubjectTerms | Accuracy Artificial Intelligence Communication Computation Computational Biology/Bioinformatics Computational Science and Engineering Computer Science Data Mining and Knowledge Discovery Euclidean geometry Euclidean space Federated learning Hyperbolic coordinates Image Processing and Computer Vision Machine learning Network management systems Nodes Optimization Optimization algorithms Original Article Privacy Probability and Statistics in Computer Science Robustness Sensors Traffic flow |
| Title | Distributed optimization with faulty nodes: robust aggregation in hyperbolic space |
| URI | https://link.springer.com/article/10.1007/s00521-025-11475-0 https://www.proquest.com/docview/3245486027 |
| Volume | 37 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: Springer Journals customDbUrl: eissn: 1433-3058 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004685 issn: 0941-0643 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV05T8MwFLYQMLBQTlEoyAMbRMrhODYbAiqmCnGpW-SzVIIEJS0S_55nN2kBwQBzrKfo-V3f8zsQOk6TlChwNYFhAgCKEDoAKbGBYlYlJrQxkdYvm8gGAzYc8pumKaxuq93bJ0lvqefNbi6DCdA3TgOI4bM0AKC-krppMw6j3z1-6ob0izgBt7iaHpI0rTI_0_jqjhYx5rdnUe9t-p3__ecGWm-iS3w-E4dNtGSKLdRpNzfgRpG30e2lm5frVl0ZjUuwGi9NOyZ2eVlsxfR58o6LUpv6DFelnNYTLEYAzUezU-MCPwGAraSbKozBKCmzgx76V_cX10GzXSFQEShpQI0RjEY6soIzE2eSZ5FNqEwiyaiUPE040dzymMmQS6uUscQSCFdk7HJFJtlFy0VZmD2Es1BTTQkVRCYAEKmAMCQ0WkitBWE266KTlsn562yIRj4fl-zZlQO7cs-uPOyiXnsPeaNQdQ5xX-r3ZQGx05bvi8-_U9v_2_EDtBa7q_NVZD20PKmm5hCtqrfJuK6OvKB9AEqnzdE |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEA5SBb1Yn1itmoM3Dewj-_ImaqlYi2iV3pZkk9SC7sruVvDfO0l3WxU96HlDWCaZme9LMvMhdOS5Hk0g1RAZMiAojAkCu0SRJFSJKy3lUK6M2ETQ74fDYXRbFYUV9Wv3-krSROpZsZs-wQTq63gEMHzgESDqi1TL7GiOfv_4qRrSCHECb9Fveqhblcr8PMfXdDTHmN-uRU226TT_959raLVCl_hsuh3W0YJMN1CzVm7AlSNvorsL3S9XS11JgTOIGi9VOSbW57JYsclz-Y7TTMjiFOcZnxQlZiOg5qPpqHGKn4DA5lx3FcYQlBK5hR46l4PzLqnUFUhig5MSX0oW-rawFYtC6QQ8Cmzl-ty1eehzHnluREWkIifkVsRVkkhFFQW4wh19ViTdbdRIs1TuIBxYwhc-9RnlLhBEnwEMsaRgXAhGQxW00HFt5Ph12kQjnrVLNuaKwVyxMVdstVC7Xoe4cqgiBtznGb0smOyktvv88--z7f5t-CFa7g5uenHvqn-9h1YcvYzmRVkbNcp8IvfRUvJWjov8wGy6D_oV0LU |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEF5ERbxYn1itugdvGprH5uVNrEVRSqkPegu72d1a0KQkqeC_d3aTtFX0IJ6zDGEeO_PNzgOhU9dxSQyuxhABBYBCKTdAS6QRBzJ2hCltwqReNuH3esFwGPYXuvh1tXv9JFn2NKgpTUnRnnDZnjW-qWwmwGDbNSCe910DQPsKASSjiroGD88LnZF6KSdgGFXfQ5yqbeZnGl9d0zze_PZEqj1Pt_H_f95EG1XUiS9LNdlCSyLZRo16owOuDHwHDTpqjq5agSU4TuE2eavaNLHK12JJp6_FB05SLvILnKVsmheYjgCyj8pT4wS_ALDNmJo2jOGyisUueupeP17dGNXWBSO2wHgNTwgaeBa3JA0DYfss9C3peMyxWOAxFrpOSHgoQztgZshkHAtJJIEwhtkqhyScPbScpInYR9g3ucc94lHCHACOHoXwxBScMs4pCaTfRGc1w6NJOVwjmo1R1uyKgF2RZldkNlGrlklUGVoeQTzo6j1aQOy8lsH88-_UDv52_ASt9Tvd6P62d3eI1m0lRV1o1kLLRTYVR2g1fi_GeXas9e8TrI_ZmQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Distributed+optimization+with+faulty+nodes%3A+robust+aggregation+in+hyperbolic+space&rft.jtitle=Neural+computing+%26+applications&rft.au=Ghosh%2C+Subhas+Kumar&rft.au=Vittamsetti%2C+Vijay+Monic&rft.date=2025-09-01&rft.pub=Springer+Nature+B.V&rft.issn=0941-0643&rft.eissn=1433-3058&rft.volume=37&rft.issue=26&rft.spage=21563&rft.epage=21605&rft_id=info:doi/10.1007%2Fs00521-025-11475-0&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0941-0643&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0941-0643&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0941-0643&client=summon |