{"id":"https://openalex.org/W7134091360","doi":"https://doi.org/10.48550/arxiv.2603.05343","title":"Preserving Continuous Symmetry in Discrete Spaces: Geometric-Aware Quantization for SO(3)-Equivariant GNNs","display_name":"Preserving Continuous Symmetry in Discrete Spaces: Geometric-Aware Quantization for SO(3)-Equivariant GNNs","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W7134091360","doi":"https://doi.org/10.48550/arxiv.2603.05343"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.05343","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128256186","display_name":"Haoyu Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Haoyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101280195","display_name":"Ping Xue","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xue, Ping","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128225437","display_name":"Hao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Hao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128220795","display_name":"Tianfan Fu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fu, Tianfan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20302223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.5932000279426575,"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"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.5932000279426575,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.2329999953508377,"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/T12292","display_name":"Graph Theory and Algorithms","score":0.02800000086426735,"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":0.7085000276565552},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.6425999999046326},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5453000068664551},{"id":"https://openalex.org/keywords/vector-quantization","display_name":"Vector quantization","score":0.513700008392334},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.3986999988555908},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.39809998869895935}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.7085000276565552},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.6425999999046326},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5453000068664551},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5300999879837036},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.516700029373169},{"id":"https://openalex.org/C199833920","wikidata":"https://www.wikidata.org/wiki/Q612536","display_name":"Vector quantization","level":2,"score":0.513700008392334},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.3986999988555908},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.39809998869895935},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.38109999895095825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3601999878883362},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.335999995470047},{"id":"https://openalex.org/C2781220375","wikidata":"https://www.wikidata.org/wiki/Q814208","display_name":"Flocking (texture)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C2778242569","wikidata":"https://www.wikidata.org/wiki/Q1996344","display_name":"Continuous symmetry","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C2776394503","wikidata":"https://www.wikidata.org/wiki/Q5282063","display_name":"Discrete symmetry","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2736999988555908},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2549999952316284}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.05343","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.05343","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.05343","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.05343","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.5476016402244568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Equivariant":[0],"Graph":[1],"Neural":[2],"Networks":[3],"(GNNs)":[4],"are":[5],"essential":[6],"for":[7,182],"physically":[8],"consistent":[9],"molecular":[10,179],"simulations":[11,181],"but":[12],"suffer":[13],"from":[14,95],"high":[15],"computational":[16],"costs":[17],"and":[18,45,66,110,117,172],"memory":[19,174],"bottlenecks,":[20],"especially":[21],"with":[22,113],"high-order":[23],"representations.":[24],"While":[25],"low-bit":[26,128],"quantization":[27,115],"offers":[28],"a":[29,59,85,103,119],"solution,":[30],"applying":[31],"it":[32],"naively":[33],"to":[34,42,98,124,161],"rotation-sensitive":[35],"features":[36,112],"destroys":[37],"the":[38,132,141],"SO(3)-equivariant":[39],"structure,":[40],"leading":[41],"significant":[43],"errors":[44],"violations":[46],"of":[47,143],"conservation":[48],"laws.":[49],"To":[50],"address":[51],"this":[52,55],"issue,":[53],"in":[54,75,127],"work,":[56],"we":[57],"propose":[58],"Geometric-Aware":[60],"Quantization":[61,88],"(GAQ)":[62],"framework":[63],"that":[64,91,107,136],"compresses":[65],"accelerates":[67],"equivariant":[68,96],"models":[69,139],"while":[70,151],"rigorously":[71],"preserving":[72],"continuous":[73],"symmetry":[74],"discrete":[76],"spaces.":[77],"Our":[78],"approach":[79],"introduces":[80],"three":[81],"key":[82],"contributions:":[83],"(1)":[84],"Magnitude-Direction":[86],"Decoupled":[87],"(MDDQ)":[89],"scheme":[90],"separates":[92],"invariant":[93],"lengths":[94],"orientations":[97],"maintain":[99],"geometric":[100],"fidelity;":[101],"(2)":[102],"symmetry-aware":[104],"training":[105],"strategy":[106],"treats":[108],"scalar":[109],"vector":[111],"distinct":[114],"schedules;":[116],"(3)":[118],"robust":[120],"attention":[121],"normalization":[122],"mechanism":[123],"stabilize":[125],"gradients":[126],"regimes.":[129],"Experiments":[130],"on":[131],"rMD17":[133],"benchmark":[134],"demonstrate":[135],"our":[137],"W4A8":[138],"match":[140],"accuracy":[142],"FP32":[144],"baselines":[145],"(9.31":[146],"meV":[147],"vs.":[148],"23.20":[149],"meV)":[150],"reducing":[152],"Local":[153],"Equivariance":[154],"Error":[155],"(LEE)":[156],"by":[157],"over":[158],"30x":[159],"compared":[160],"naive":[162],"quantization.":[163],"On":[164],"consumer":[165],"hardware,":[166],"GAQ":[167],"achieves":[168],"2.39x":[169],"inference":[170],"speedup":[171],"4x":[173],"reduction,":[175],"enabling":[176],"stable,":[177],"energy-conserving":[178],"dynamics":[180],"nanosecond":[183],"timescales.":[184]},"counts_by_year":[],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2026-03-07T00:00:00"}