{"id":"https://openalex.org/W4415827751","doi":"https://doi.org/10.1088/2632-2153/ae1acd","title":"Range-aware graph positional encoding via high-order pretraining: theory and practice","display_name":"Range-aware graph positional encoding via high-order pretraining: theory and practice","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415827751","doi":"https://doi.org/10.1088/2632-2153/ae1acd"},"language":"en","primary_location":{"id":"doi:10.1088/2632-2153/ae1acd","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/ae1acd","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1088/2632-2153/ae1acd","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107595323","display_name":"Viet Anh Nguyen","orcid":"https://orcid.org/0000-0001-7736-2470"},"institutions":[{"id":"https://openalex.org/I109689652","display_name":"FPT University","ror":"https://ror.org/03esj4g97","country_code":"VN","type":"education","lineage":["https://openalex.org/I109689652"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Viet Anh Nguyen","raw_affiliation_strings":["FPT Software AI Center, FPT Corporation, No. 10, Pham Van Bach street, Hanoi, Hanoi, 10000, VIET NAM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FPT Software AI Center, FPT Corporation, No. 10, Pham Van Bach street, Hanoi, Hanoi, 10000, VIET NAM","institution_ids":["https://openalex.org/I109689652"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029125317","display_name":"Nhat Khang Ngo","orcid":"https://orcid.org/0009-0004-8762-9457"},"institutions":[{"id":"https://openalex.org/I109689652","display_name":"FPT University","ror":"https://ror.org/03esj4g97","country_code":"VN","type":"education","lineage":["https://openalex.org/I109689652"]},{"id":"https://openalex.org/I97750245","display_name":"Software (Spain)","ror":"https://ror.org/02ethns06","country_code":"ES","type":"company","lineage":["https://openalex.org/I4210087817","https://openalex.org/I97750245"]}],"countries":["ES","VN"],"is_corresponding":true,"raw_author_name":"Nhat Khang Ngo","raw_affiliation_strings":["FPT Software AI Center, FPT Corporation, No. 10, Pham Van Bach street, Hanoi, 10000, VIET NAM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"FPT Software AI Center, FPT Corporation, No. 10, Pham Van Bach street, Hanoi, 10000, VIET NAM","institution_ids":["https://openalex.org/I109689652","https://openalex.org/I97750245"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073178563","display_name":"Truong Son Hy","orcid":"https://orcid.org/0000-0002-5092-3757"},"institutions":[{"id":"https://openalex.org/I32389192","display_name":"University of Alabama at Birmingham","ror":"https://ror.org/008s83205","country_code":"US","type":"education","lineage":["https://openalex.org/I32389192"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Truong-Son Hy","raw_affiliation_strings":["Department of Computer Science, The University of Alabama at Birmingham, Birmingham, Birmingham, Alabama, 35294-2172, UNITED STATES"],"raw_orcid":"https://orcid.org/0000-0002-5092-3757","affiliations":[{"raw_affiliation_string":"Department of Computer Science, The University of Alabama at Birmingham, Birmingham, Birmingham, Alabama, 35294-2172, UNITED STATES","institution_ids":["https://openalex.org/I32389192"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029125317","https://openalex.org/A5073178563","https://openalex.org/A5107595323"],"corresponding_institution_ids":["https://openalex.org/I109689652","https://openalex.org/I32389192","https://openalex.org/I97750245"],"apc_list":{"value":1600,"currency":"GBP","value_usd":1962},"apc_paid":{"value":1600,"currency":"GBP","value_usd":1962},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15615362,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"4","first_page":"045043","last_page":"045043"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9469000101089478,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.9469000101089478,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.027300000190734863,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12292","display_name":"Graph Theory and Algorithms","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/autoencoder","display_name":"Autoencoder","score":0.6277999877929688},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6226000189781189},{"id":"https://openalex.org/keywords/encoder","display_name":"Encoder","score":0.4740000069141388},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.4205000102519989},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.3882000148296356},{"id":"https://openalex.org/keywords/mixed-graph","display_name":"Mixed graph","score":0.3343999981880188},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.31040000915527344}],"concepts":[{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.6277999877929688},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6226000189781189},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6053000092506409},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.592199981212616},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.4740000069141388},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37139999866485596},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3628999888896942},{"id":"https://openalex.org/C53052385","wikidata":"https://www.wikidata.org/wiki/Q17104046","display_name":"Mixed graph","level":5,"score":0.3343999981880188},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3319999873638153},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.30970001220703125},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.2793999910354614},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.271699994802475},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C2987255567","wikidata":"https://www.wikidata.org/wiki/Q33002955","display_name":"Knowledge graph","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1088/2632-2153/ae1acd","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/ae1acd","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a764ed12ff2a4295a4dd3b7f83df26b3","is_oa":true,"landing_page_url":"https://doaj.org/article/a764ed12ff2a4295a4dd3b7f83df26b3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Machine Learning: Science and Technology, Vol 6, Iss 4, p 045043 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1088/2632-2153/ae1acd","is_oa":true,"landing_page_url":"https://doi.org/10.1088/2632-2153/ae1acd","pdf_url":null,"source":{"id":"https://openalex.org/S4210200687","display_name":"Machine Learning Science and Technology","issn_l":"2632-2153","issn":["2632-2153"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320083","host_organization_name":"IOP Publishing","host_organization_lineage":["https://openalex.org/P4310320083","https://openalex.org/P4310311669"],"host_organization_lineage_names":["IOP Publishing","Institute of Physics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Machine Learning: Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1179283095","https://openalex.org/W2158787690","https://openalex.org/W2165698076","https://openalex.org/W2594183968","https://openalex.org/W2788919350","https://openalex.org/W2949592116","https://openalex.org/W2966357564","https://openalex.org/W2968734407","https://openalex.org/W2971401012","https://openalex.org/W3035664258","https://openalex.org/W3210824699","https://openalex.org/W4384662896"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Unsupervised":[1],"pre-training":[2,59],"on":[3,61,65,138,267],"vast":[4],"amounts":[5],"of":[6,77,92,243,248,271],"graph":[7,33,80,140,159,163],"data":[8,16],"is":[9,17,143,185,254,285],"critical":[10],"in":[11],"real-world":[12],"applications":[13],"wherein":[14],"labeled":[15],"limited,":[18],"such":[19],"as":[20],"molecule":[21],"properties":[22],"prediction":[23,269],"or":[24],"materials":[25],"science.":[26],"Existing":[27],"approaches":[28],"pre-train":[29],"models":[30],"for":[31,156,170,177],"specific":[32],"domains,":[34,151],"neglecting":[35],"the":[36,78,90,139,154,174,178,241,246,255,260],"inherent":[37],"connections":[38],"within":[39],"networks.":[40],"This":[41],"limits":[42],"their":[43,67,129],"ability":[44],"to":[45,48,73,124,147,180,279],"transfer":[46],"knowledge":[47],"various":[49,150],"supervised":[50],"tasks.":[51],"In":[52],"this":[53],"work,":[54],"we":[55],"propose":[56],"a":[57,113],"novel":[58],"strategy":[60],"graphs":[62],"that":[63,169],"focuses":[64],"modeling":[66],"multi-resolution":[68,130],"structural":[69],"information,":[70],"allowing":[71],"us":[72],"capture":[74],"global":[75],"information":[76,184],"whole":[79],"while":[81],"preserving":[82],"local":[83],"structures":[84],"around":[85],"its":[86,276],"nodes.":[87],"We":[88,166,263],"extend":[89],"work":[91],"Graph":[93],"Wave":[94],"let":[95],"P":[96,118],"ositional":[97],"E":[98,120],"ncoding":[99],"(WavePE)":[100],"from":[101,128,149],"Ngo":[102],"et":[103],"al":[104],"(2023":[105],"J.":[106],"Chem.":[107],"Phys.":[108],"159":[109],"034109)":[110],"by":[111,259],"pretraining":[112],"H":[114],"igh-":[115],"O":[116],"rder":[117],"ermutation-":[119],"quivariant":[121],"Autoencoder":[122],"(HOPE-WavePE)":[123],"reconstruct":[125],"node":[126],"connectivities":[127],"wavelet":[131],"signals.":[132],"Since":[133],"our":[134],"approach":[135],"relies":[136],"solely":[137],"structure,":[141],"it":[142],"domain-agnostic":[144],"and":[145,162,245,252,274],"adaptable":[146],"datasets":[148],"therefore":[152],"paving":[153],"way":[155],"developing":[157],"general":[158],"structure":[160],"encoders":[161],"foundation":[164],"models.":[165],"theoretically":[167],"demonstrate":[168],"k":[171],"given":[172],"resolutions,":[173],"width":[175],"required":[176],"autoencoder":[179],"learn":[181],"arbitrarily":[182],"long-range":[183],"<mml:math":[186,231],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[187,232],"overflow=\"scroll\">":[188,233],"<mml:mrow>":[189,191,195,197,205,209,217,220,234],"<mml:mi>O</mml:mi>":[190],"<mml:mo>(</mml:mo>":[192],"<mml:msup>":[193,203,215],"<mml:mi>n</mml:mi>":[194,235],"<mml:mn>1</mml:mn>":[196,206,208,219],"<mml:mo>/</mml:mo>":[198,210,221],"</mml:mrow>":[199,201,211,213,222,224,227,228,238],"<mml:mi>k</mml:mi>":[200,212,223],"</mml:msup>":[202,214,225],"<mml:mi>r</mml:mi>":[204,237],"<mml:mo>+</mml:mo>":[207],"<mml:mi>\u03f5</mml:mi>":[216],"<mml:mo>\u2212</mml:mo>":[218],"<mml:mo>)</mml:mo>":[226],"</mml:math>":[229,239],"where":[230],"<mml:mo>,</mml:mo>":[236],"denote":[240],"number":[242],"nodes":[244],"rank":[247],"normalized":[249],"Laplacian,":[250],"respectively,":[251],"\u03b5":[253],"error":[256],"tolerance":[257],"defined":[258],"Frobenius":[261],"norm.":[262],"also":[264],"evaluate":[265],"HOPE-WavePE":[266],"graph-level":[268],"tasks":[270],"different":[272],"areas":[273],"show":[275],"superiority":[277],"compared":[278],"other":[280],"methods.":[281],"Our":[282],"source":[283],"code":[284],"publicly":[286],"available":[287],"at":[288],"https://github.com/HySonLab/WaveletPE":[289],".":[290]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-11-03T00:00:00"}
