{"id":"https://openalex.org/W7160945995","doi":"https://doi.org/10.48550/arxiv.2605.08659","title":"Pushing Biomolecular Utility-Diversity Frontiers with Supergroup Relative Policy Optimization","display_name":"Pushing Biomolecular Utility-Diversity Frontiers with Supergroup Relative Policy Optimization","publication_year":2026,"publication_date":"2026-05-09","ids":{"openalex":"https://openalex.org/W7160945995","doi":"https://doi.org/10.48550/arxiv.2605.08659"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.08659","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.08659","pdf_url":"https://arxiv.org/pdf/2605.08659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2605.08659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125543372","display_name":"Xinwu Ye","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ye, Xinwu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135928584","display_name":"He Cao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cao, He","raw_affiliation_strings":["International Digital Economy Academy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Digital Economy Academy","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135983782","display_name":"Hao Li","orcid":"https://orcid.org/0000-0002-4234-7753","observed_orcids":["https://orcid.org/0000-0002-4234-7753"]},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Hao","raw_affiliation_strings":["Peking University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Peking University","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134289263","display_name":"Bin Feng","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Feng, Bin","raw_affiliation_strings":["International Digital Economy Academy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Digital Economy Academy","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135996135","display_name":"Zijing Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zijing","raw_affiliation_strings":["International Digital Economy Academy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Digital Economy Academy","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135926846","display_name":"Xiangru Tang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tang, Xiangru","raw_affiliation_strings":["Yale University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100345753","display_name":"Yu Li","orcid":"https://orcid.org/0000-0002-3664-6722","observed_orcids":["https://orcid.org/0000-0002-3664-6722","https://orcid.org/0000-0003-1865-8276","https://orcid.org/0009-0001-4705-049X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yu","raw_affiliation_strings":["International Digital Economy Academy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"International Digital Economy Academy","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135938242","display_name":"Shenghua Gao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Gao, Shenghua","raw_affiliation_strings":["The University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9585000276565552,"subfield":{"id":"https://openalex.org/subfields/3002","display_name":"Drug Discovery"},"field":{"id":"https://openalex.org/fields/30","display_name":"Pharmacology, Toxicology and Pharmaceutics"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10211","display_name":"Computational Drug Discovery Methods","score":0.9585000276565552,"subfield":{"id":"https://openalex.org/subfields/3002","display_name":"Drug Discovery"},"field":{"id":"https://openalex.org/fields/30","display_name":"Pharmacology, Toxicology and Pharmaceutics"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10462","display_name":"Reinforcement Learning in Robotics","score":0.006399999838322401,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.003599999938160181,"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/sample-diversity","display_name":"sample diversity","score":0.597000002861023},{"id":"https://openalex.org/keywords/protein-design","display_name":"protein design","score":0.7649999856948853},{"id":"https://openalex.org/keywords/diffusion-models","display_name":"diffusion models","score":0.4909999966621399},{"id":"https://openalex.org/keywords/group-relative-policy-optimization","display_name":"Group Relative Policy Optimization","score":0.5519999861717224},{"id":"https://openalex.org/keywords/reward-function-design","display_name":"reward function design","score":0.3930000066757202},{"id":"https://openalex.org/keywords/pareto-front","display_name":"Pareto front","score":0.6690000295639038}],"concepts":[{"id":"https://openalex.org/C2781316041","wikidata":"https://www.wikidata.org/wiki/Q1230584","display_name":"Diversity (politics)","level":2,"score":0.6930999755859375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5795000195503235},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.45159998536109924},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.45100000500679016},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.37720000743865967},{"id":"https://openalex.org/C64957494","wikidata":"https://www.wikidata.org/wiki/Q7643409","display_name":"Supergroup","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.34279999136924744},{"id":"https://openalex.org/C81977670","wikidata":"https://www.wikidata.org/wiki/Q585259","display_name":"Genetic diversity","level":3,"score":0.3352000117301941},{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31439998745918274},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.3077000081539154},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.29280000925064087},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C2778571376","wikidata":"https://www.wikidata.org/wiki/Q1355821","display_name":"Frontier","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2662999927997589},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.08659","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.08659","pdf_url":"https://arxiv.org/pdf/2605.08659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2605.08659","doi":"https://doi.org/10.48550/arxiv.2605.08659","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.08659","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2605.08659","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.08659","pdf_url":"https://arxiv.org/pdf/2605.08659","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7160945995.pdf","grobid_xml":"https://content.openalex.org/works/W7160945995.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W2896042778","https://openalex.org/W4387390253","https://openalex.org/W4391631327","https://openalex.org/W4400702561","https://openalex.org/W4402855424","https://openalex.org/W4403885717","https://openalex.org/W4404261766","https://openalex.org/W4404312025","https://openalex.org/W4406319145","https://openalex.org/W4414360322","https://openalex.org/W4414990164","https://openalex.org/W4415164199","https://openalex.org/W4416097246","https://openalex.org/W4417307776","https://openalex.org/W7154313303"],"related_works":["https://openalex.org/W4414360322","https://openalex.org/W4285428834","https://openalex.org/W7220973442","https://openalex.org/W7116065322","https://openalex.org/W2947037594","https://openalex.org/W7161712099","https://openalex.org/W7140295023","https://openalex.org/W2941957086","https://openalex.org/W7164473087","https://openalex.org/W4400860798"],"abstract_inverted_index":{"Biomolecular":[0],"generators":[1],"are":[2],"often":[3],"adapted":[4],"with":[5,87,106,131,171],"reward":[6,76],"feedback":[7],"to":[8,77,158],"improve":[9],"task-specific":[10],"utility,":[11],"but":[12],"pushing":[13],"utility":[14,98],"alone":[15],"can":[16],"concentrate":[17],"generation":[18],"on":[19,113],"a":[20,33,43,59,95],"narrow":[21],"family":[22],"of":[23,61],"candidates.":[24],"Maintaining":[25],"diversity":[26,31,66,75,82,101,167],"is":[27,32,184],"difficult":[28],"because":[29],"sample":[30],"set-level":[34,52,166],"property.":[35],"We":[36,110],"introduce":[37],"Supergroup":[38],"Relative":[39],"Policy":[40],"Optimization":[41],"(SGRPO),":[42],"flexible":[44],"GRPO-style":[45,108],"framework":[46],"that":[47,164],"directly":[48],"constructs":[49],"rewards":[50,168],"from":[51,94],"diversity.":[53],"For":[54],"each":[55],"condition,":[56,70],"SGRPO":[57,93,112,145],"samples":[58],"supergroup":[60],"candidate":[62],"sets,":[63],"compares":[64],"their":[65],"under":[67],"the":[68,73,147,153],"same":[69],"and":[71,103,124,134,138,151,174],"redistributes":[72],"group":[74],"individual":[78],"rollouts":[79],"through":[80],"leave-one-out":[81],"contributions":[83],"before":[84],"combining":[85],"it":[86,130],"rollout-level":[88],"utility.":[89],"This":[90],"design":[91],"decouples":[92],"particular":[96],"generator,":[97],"reward,":[99],"or":[100],"metric,":[102],"allows":[104],"instantiation":[105],"different":[107],"approaches.":[109],"evaluate":[111],"three":[114],"main":[115],"settings:":[116],"de":[117,125],"novo":[118,126],"small-molecule":[119,122],"design,":[120,123,128],"pocket-based":[121],"protein":[127],"instantiating":[129],"both":[132],"GRPO":[133],"Coupled-GRPO":[135],"across":[136],"autoregressive":[137],"discrete":[139],"diffusion":[140],"generators.":[141],"Across":[142],"decoding":[143],"sweeps,":[144],"expands":[146],"utility-diversity":[148],"Pareto":[149],"frontier":[150],"achieves":[152],"best":[154],"frontier-level":[155],"metrics":[156],"relative":[157],"baselines.":[159],"Our":[160],"analyses":[161],"further":[162],"show":[163],"direct":[165],"remain":[169],"effective":[170],"small":[172],"groups":[173],"help":[175],"preserve":[176],"broader":[177],"generation-distribution":[178],"coverage":[179],"during":[180],"post-training.":[181],"The":[182],"code":[183],"available":[185],"at":[186],"https://github.com/IDEA-XL/SGRPO.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-05-13T00:00:00"}