{"id":"https://openalex.org/W4399439301","doi":"https://doi.org/10.1007/s10462-024-10741-2","title":"Rotation invariance and equivariance in 3D deep learning: a survey","display_name":"Rotation invariance and equivariance in 3D deep learning: a survey","publication_year":2024,"publication_date":"2024-06-07","ids":{"openalex":"https://openalex.org/W4399439301","doi":"https://doi.org/10.1007/s10462-024-10741-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10462-024-10741-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10462-024-10741-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10462-024-10741-2.pdf","source":{"id":"https://openalex.org/S122814990","display_name":"Artificial Intelligence Review","issn_l":"0269-2821","issn":["0269-2821","1573-7462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Review","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10462-024-10741-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061265936","display_name":"Jiajun Fei","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiajun Fei","raw_affiliation_strings":["State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Institute for Artificial Intelligence at Tsinghua University (THUAI), Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Institute for Artificial Intelligence at Tsinghua University (THUAI), Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102011846","display_name":"Zhidong Deng","orcid":"https://orcid.org/0000-0001-9970-1023"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhidong Deng","raw_affiliation_strings":["State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Institute for Artificial Intelligence at Tsinghua University (THUAI), Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Intelligent Technology and Systems, Department of Computer Science and Technology, Institute for Artificial Intelligence at Tsinghua University (THUAI), Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing, 100084, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5102011846"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":2.8612,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.91859717,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"57","issue":"7","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9954000115394592,"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"}},"topics":[{"id":"https://openalex.org/T14339","display_name":"Image Processing and 3D Reconstruction","score":0.9954000115394592,"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"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9894999861717224,"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/equivariant-map","display_name":"Equivariant map","score":0.9375268220901489},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.7168248891830444},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.682898223400116},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.6675133109092712},{"id":"https://openalex.org/keywords/subcategory","display_name":"Subcategory","score":0.6289713382720947},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5719547867774963},{"id":"https://openalex.org/keywords/rotational-invariance","display_name":"Rotational invariance","score":0.5176094770431519},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4615730047225952},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.43900784850120544},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39232683181762695},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3468417525291443},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32444334030151367},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3226678967475891},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25179266929626465},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13268357515335083}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.9375268220901489},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.7168248891830444},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.682898223400116},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6675133109092712},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.6289713382720947},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5719547867774963},{"id":"https://openalex.org/C33098168","wikidata":"https://www.wikidata.org/wiki/Q108537107","display_name":"Rotational invariance","level":2,"score":0.5176094770431519},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4615730047225952},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.43900784850120544},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39232683181762695},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3468417525291443},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32444334030151367},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3226678967475891},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25179266929626465},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13268357515335083},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10462-024-10741-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10462-024-10741-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10462-024-10741-2.pdf","source":{"id":"https://openalex.org/S122814990","display_name":"Artificial Intelligence Review","issn_l":"0269-2821","issn":["0269-2821","1573-7462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Review","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10462-024-10741-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10462-024-10741-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10462-024-10741-2.pdf","source":{"id":"https://openalex.org/S122814990","display_name":"Artificial Intelligence Review","issn_l":"0269-2821","issn":["0269-2821","1573-7462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Artificial Intelligence Review","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5541826327","display_name":null,"funder_award_id":"62176134","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399439301.pdf"},"referenced_works_count":269,"referenced_works":["https://openalex.org/W2966661","https://openalex.org/W130099911","https://openalex.org/W569478347","https://openalex.org/W1030883578","https://openalex.org/W1590776313","https://openalex.org/W1629010235","https://openalex.org/W1641498739","https://openalex.org/W1644641054","https://openalex.org/W1920022804","https://openalex.org/W1923184257","https://openalex.org/W1928739709","https://openalex.org/W1954297438","https://openalex.org/W1966790179","https://openalex.org/W1974165720","https://openalex.org/W1985238052","https://openalex.org/W1985907520","https://openalex.org/W1989476314","https://openalex.org/W1995808589","https://openalex.org/W2009422376","https://openalex.org/W2058256495","https://openalex.org/W2075156252","https://openalex.org/W2076498053","https://openalex.org/W2080635178","https://openalex.org/W2084177652","https://openalex.org/W2093414253","https://openalex.org/W2097117768","https://openalex.org/W2101032778","https://openalex.org/W2104489082","https://openalex.org/W2130479394","https://openalex.org/W2130558599","https://openalex.org/W2150066425","https://openalex.org/W2153693853","https://openalex.org/W2156222070","https://openalex.org/W2160643963","https://openalex.org/W2160821342","https://openalex.org/W2161168419","https://openalex.org/W2194775991","https://openalex.org/W2211722331","https://openalex.org/W2335829695","https://openalex.org/W2411681238","https://openalex.org/W2460657278","https://openalex.org/W2461470610","https://openalex.org/W2519379752","https://openalex.org/W2553307952","https://openalex.org/W2558027072","https://openalex.org/W2560609797","https://openalex.org/W2566265240","https://openalex.org/W2585152223","https://openalex.org/W2586114507","https://openalex.org/W2594519801","https://openalex.org/W2595840341","https://openalex.org/W2597851033","https://openalex.org/W2602311553","https://openalex.org/W2605973302","https://openalex.org/W2612326916","https://openalex.org/W2766448241","https://openalex.org/W2768638516","https://openalex.org/W2778051509","https://openalex.org/W2783099639","https://openalex.org/W2788775653","https://openalex.org/W2795221267","https://openalex.org/W2796422723","https://openalex.org/W2796426482","https://openalex.org/W2797184202","https://openalex.org/W2798510813","https://openalex.org/W2798998662","https://openalex.org/W2888486794","https://openalex.org/W2889123596","https://openalex.org/W2889300857","https://openalex.org/W2893477965","https://openalex.org/W2894691497","https://openalex.org/W2898797193","https://openalex.org/W2898968651","https://openalex.org/W2902965877","https://openalex.org/W2920456178","https://openalex.org/W2921571372","https://openalex.org/W2931742923","https://openalex.org/W2937458416","https://openalex.org/W2948107928","https://openalex.org/W2948178948","https://openalex.org/W2948196881","https://openalex.org/W2949708697","https://openalex.org/W2952241957","https://openalex.org/W2953524386","https://openalex.org/W2961368225","https://openalex.org/W2962731536","https://openalex.org/W2962835968","https://openalex.org/W2962941647","https://openalex.org/W2963231572","https://openalex.org/W2963281829","https://openalex.org/W2963509914","https://openalex.org/W2963527880","https://openalex.org/W2963530975","https://openalex.org/W2963706542","https://openalex.org/W2963727135","https://openalex.org/W2963892972","https://openalex.org/W2964014140","https://openalex.org/W2964134613","https://openalex.org/W2965945745","https://openalex.org/W2967896598","https://openalex.org/W2969993800","https://openalex.org/W2971090287","https://openalex.org/W2975950300","https://openalex.org/W2978088842","https://openalex.org/W2978329087","https://openalex.org/W2979750740","https://openalex.org/W2979888373","https://openalex.org/W2981440248","https://openalex.org/W2981487534","https://openalex.org/W2981856165","https://openalex.org/W2981995220","https://openalex.org/W2982319484","https://openalex.org/W2982589786","https://openalex.org/W2982658732","https://openalex.org/W2986519585","https://openalex.org/W2990869131","https://openalex.org/W2991284067","https://openalex.org/W2995505408","https://openalex.org/W2997216793","https://openalex.org/W2998658430","https://openalex.org/W3003709258","https://openalex.org/W3004414671","https://openalex.org/W3006051909","https://openalex.org/W3012015905","https://openalex.org/W3012143260","https://openalex.org/W3026070007","https://openalex.org/W3033671339","https://openalex.org/W3034266912","https://openalex.org/W3034675048","https://openalex.org/W3034707001","https://openalex.org/W3034806393","https://openalex.org/W3035506734","https://openalex.org/W3035541121","https://openalex.org/W3035547893","https://openalex.org/W3035574168","https://openalex.org/W3036842464","https://openalex.org/W3045965269","https://openalex.org/W3080366021","https://openalex.org/W3082681509","https://openalex.org/W3091046813","https://openalex.org/W3091337047","https://openalex.org/W3097293074","https://openalex.org/W3102669005","https://openalex.org/W3104644561","https://openalex.org/W3106739598","https://openalex.org/W3106762210","https://openalex.org/W3107886455","https://openalex.org/W3118409809","https://openalex.org/W3120377000","https://openalex.org/W3122683654","https://openalex.org/W3123008382","https://openalex.org/W3126732353","https://openalex.org/W3126857668","https://openalex.org/W3127013332","https://openalex.org/W3128692417","https://openalex.org/W3129380256","https://openalex.org/W3130266661","https://openalex.org/W3131379059","https://openalex.org/W3131660994","https://openalex.org/W3138156140","https://openalex.org/W3138367801","https://openalex.org/W3158545781","https://openalex.org/W3161865928","https://openalex.org/W3162959074","https://openalex.org/W3163187545","https://openalex.org/W3164401570","https://openalex.org/W3167283626","https://openalex.org/W3167684723","https://openalex.org/W3168037706","https://openalex.org/W3168713672","https://openalex.org/W3171712086","https://openalex.org/W3172200891","https://openalex.org/W3174339691","https://openalex.org/W3176054420","https://openalex.org/W3176751833","https://openalex.org/W3177826989","https://openalex.org/W3179677995","https://openalex.org/W3183520159","https://openalex.org/W3197129748","https://openalex.org/W3198471943","https://openalex.org/W3201055005","https://openalex.org/W3201680641","https://openalex.org/W3203118522","https://openalex.org/W3203310607","https://openalex.org/W3203597819","https://openalex.org/W3210518039","https://openalex.org/W3211126885","https://openalex.org/W3211345561","https://openalex.org/W3212697465","https://openalex.org/W3215790636","https://openalex.org/W3217151331","https://openalex.org/W4205205600","https://openalex.org/W4206453737","https://openalex.org/W4211040010","https://openalex.org/W4212962167","https://openalex.org/W4213288279","https://openalex.org/W4213341656","https://openalex.org/W4220677593","https://openalex.org/W4220784957","https://openalex.org/W4220908436","https://openalex.org/W4220938680","https://openalex.org/W4221146126","https://openalex.org/W4221146657","https://openalex.org/W4225405705","https://openalex.org/W4226327324","https://openalex.org/W4226391773","https://openalex.org/W4226405412","https://openalex.org/W4280630571","https://openalex.org/W4282934516","https://openalex.org/W4283727985","https://openalex.org/W4285102336","https://openalex.org/W4286893572","https://openalex.org/W4287555635","https://openalex.org/W4288349627","https://openalex.org/W4292738040","https://openalex.org/W4293680926","https://openalex.org/W4297779807","https://openalex.org/W4300717179","https://openalex.org/W4304092564","https://openalex.org/W4307416138","https://openalex.org/W4308235894","https://openalex.org/W4308448663","https://openalex.org/W4309163186","https://openalex.org/W4310895557","https://openalex.org/W4312251507","https://openalex.org/W4312700461","https://openalex.org/W4312723820","https://openalex.org/W4312799694","https://openalex.org/W4312985712","https://openalex.org/W4312997492","https://openalex.org/W4313067950","https://openalex.org/W4313172691","https://openalex.org/W4318827596","https://openalex.org/W4319300068","https://openalex.org/W4319300083","https://openalex.org/W4319301058","https://openalex.org/W4320736692","https://openalex.org/W4321020868","https://openalex.org/W4321471548","https://openalex.org/W4321512572","https://openalex.org/W4323315532","https://openalex.org/W4328007191","https://openalex.org/W4372259749","https://openalex.org/W4379806306","https://openalex.org/W4380372879","https://openalex.org/W4381739927","https://openalex.org/W4382239989","https://openalex.org/W4382407310","https://openalex.org/W4382450863","https://openalex.org/W4383097449","https://openalex.org/W4383109286","https://openalex.org/W4384648121","https://openalex.org/W4385800972","https://openalex.org/W4385805005","https://openalex.org/W4385805115","https://openalex.org/W4385975620","https://openalex.org/W4386065549","https://openalex.org/W4386065804","https://openalex.org/W4386076224","https://openalex.org/W4386076348","https://openalex.org/W4386076363","https://openalex.org/W4390873193","https://openalex.org/W4390874674","https://openalex.org/W4399563688","https://openalex.org/W6600474023","https://openalex.org/W6601180101","https://openalex.org/W6611670707","https://openalex.org/W6633481509","https://openalex.org/W6814982423"],"related_works":["https://openalex.org/W2069360731","https://openalex.org/W2798549588","https://openalex.org/W1975341022","https://openalex.org/W1995820642","https://openalex.org/W3210901769","https://openalex.org/W4226313719","https://openalex.org/W2384722316","https://openalex.org/W1871605645","https://openalex.org/W186912772","https://openalex.org/W4399439301"],"abstract_inverted_index":{"Abstract":[0],"Deep":[1],"neural":[2],"networks":[3],"(DNNs)":[4],"in":[5,21,128,201],"3D":[6,23,25,181],"scenes":[7,28],"show":[8],"a":[9,37,87,148,168],"strong":[10,82],"capability":[11],"of":[12,71,130,150,171,180],"extracting":[13],"high-level":[14],"semantic":[15,182],"features":[16],"and":[17,27,39,48,60,74,81,99,120,134,155,161,174,184,192,199],"significantly":[18],"promote":[19],"research":[20,194],"the":[22,68],"field.":[24],"shapes":[26],"often":[29],"exhibit":[30],"complicated":[31],"transformation":[32],"symmetries,":[33],"where":[34],"rotation":[35,46,72,97,117,121],"is":[36,146],"challenging":[38],"necessary":[40],"subject.":[41],"To":[42],"this":[43,55],"end,":[44],"many":[45],"invariant":[47,98,118],"equivariant":[49,100,122,136],"methods":[50,111,152],"have":[51],"been":[52],"proposed.":[53],"In":[54,140],"survey,":[56],"we":[57,66,85,166,187],"systematically":[58],"organize":[59],"comprehensively":[61],"overview":[62,170],"all":[63],"methods.":[64],"First,":[65],"rewrite":[67],"previous":[69],"definition":[70],"invariance":[73],"equivariance":[75],"by":[76],"classifying":[77],"them":[78],"into":[79,112],"weak":[80,96],"categories.":[83],"Second,":[84],"provide":[86,188],"unified":[88],"theoretical":[89],"framework":[90],"to":[91],"analyze":[92],"these":[93],"methods,":[94],"especially":[95],"ones":[101,119],"that":[102],"are":[103,125,153,163],"seldom":[104],"analyzed":[105],"theoretically.":[106],"We":[107],"then":[108],"divide":[109],"existing":[110],"two":[113,177],"main":[114],"categories,":[115],"i.e.,":[116],"ones,":[123],"which":[124],"further":[126],"subclassified":[127],"terms":[129],"manipulating":[131],"input":[132],"ways":[133],"basic":[135],"block":[137],"structures,":[138],"respectively.":[139],"each":[141],"subcategory,":[142],"their":[143,159],"common":[144],"essence":[145],"highlighted,":[147],"couple":[149],"representative":[151],"analyzed,":[154],"insightful":[156],"comments":[157],"on":[158,197],"pros":[160],"cons":[162],"given.":[164],"Furthermore,":[165],"deliver":[167],"general":[169],"relevant":[172],"applications":[173],"datasets":[175],"for":[176],"popular":[178],"tasks":[179],"understanding":[183],"molecule-related.":[185],"Finally,":[186],"several":[189],"open":[190],"problems":[191],"future":[193],"directions":[195],"based":[196],"challenges":[198],"difficulties":[200],"ongoing":[202],"research.":[203]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":11}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}