{"id":"https://openalex.org/W7169535587","doi":"https://doi.org/10.48550/arxiv.2607.14108","title":"Eta Given Delta: Defining LLM Tool Efficiency With Marginal Tool Utility","display_name":"Eta Given Delta: Defining LLM Tool Efficiency With Marginal Tool Utility","publication_year":2026,"publication_date":"2026-05-07","ids":{"openalex":"https://openalex.org/W7169535587","doi":"https://doi.org/10.48550/arxiv.2607.14108"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.14108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14108","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.14108","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141077468","display_name":"Nyx Iskandar","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Iskandar, Nyx","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5141077468"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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/T10456","display_name":"Multi-Agent Systems and Negotiation","score":0.12800000607967377,"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/T10456","display_name":"Multi-Agent Systems and Negotiation","score":0.12800000607967377,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.08470000326633453,"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/T10653","display_name":"Robot Manipulation and Learning","score":0.0771000012755394,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7106000185012817},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.5788000226020813},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5705000162124634},{"id":"https://openalex.org/keywords/suite","display_name":"Suite","score":0.527899980545044},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.40400001406669617},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.3856000006198883}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7106000185012817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6401000022888184},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5788000226020813},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5705000162124634},{"id":"https://openalex.org/C79581498","wikidata":"https://www.wikidata.org/wiki/Q1367530","display_name":"Suite","level":2,"score":0.527899980545044},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.40400001406669617},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C2780898871","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Performance metric","level":2,"score":0.37389999628067017},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C2777466363","wikidata":"https://www.wikidata.org/wiki/Q17008971","display_name":"Design tool","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C13736549","wikidata":"https://www.wikidata.org/wiki/Q4489420","display_name":"Industrial engineering","level":1,"score":0.31700000166893005},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.30790001153945923},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2565000057220459},{"id":"https://openalex.org/C200601418","wikidata":"https://www.wikidata.org/wiki/Q2193887","display_name":"Reliability engineering","level":1,"score":0.2549000084400177},{"id":"https://openalex.org/C5941749","wikidata":"https://www.wikidata.org/wiki/Q19768","display_name":"Machine tool","level":2,"score":0.2524000108242035},{"id":"https://openalex.org/C51485801","wikidata":"https://www.wikidata.org/wiki/Q16966861","display_name":"Efficient frontier","level":3,"score":0.25130000710487366}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.14108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14108","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.14108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.14108","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1,130],"introduces":[2],"tool":[3,15,25,33,41,46,58,65,76,80,99,168],"efficiency,":[4],"a":[5,35,45,83,113,152],"new":[6,36],"quantitative":[7,37,125],"metric":[8,38,126],"to":[9,94,144,165],"evaluate":[10],"the":[11,57,72,124,145],"rate":[12],"of":[13,74,147],"useful":[14,48],"calls":[16],"in":[17,67,82,128,131],"an":[18],"LLM":[19,148],"agent":[20,159],"trajectory.":[21],"To":[22],"ensure":[23],"that":[24,97,140,170,174],"efficiency":[26,108,121],"is":[27,47,117,137],"well-defined,":[28],"we":[29,70],"also":[30],"introduce":[31],"marginal":[32,75],"utility,":[34],"defined":[39],"per":[40],"call":[42,81],"indicating":[43],"whether":[44,50],"or":[49],"it":[51],"can":[52],"be":[53],"safely":[54],"removed":[55],"from":[56,179],"suite":[59],"without":[60],"affecting":[61],"accuracy":[62,111],"while":[63],"increasing":[64],"efficiency;":[66],"this":[68,129,141],"paper,":[69],"determine":[71],"sign":[73],"utility":[77],"for":[78,154,172],"each":[79],"trajectory":[84,134],"using":[85,110],"LLM-as-a-Judge.":[86],"While":[87],"much":[88],"prior":[89],"work":[90,116,142],"has":[91],"been":[92],"done":[93],"develop":[95],"techniques":[96],"improve":[98],"use":[100],"by":[101],"LLMs":[102],"and":[103,158],"design":[104],"evaluation":[105,149],"methods":[106],"measuring":[107,120],"indirectly":[109],"as":[112,151],"proxy,":[114],"our":[115,138],"centered":[118],"on":[119],"directly":[122],"via":[123],"proposed":[127],"post":[132],"hoc":[133],"analyses.":[135],"It":[136],"intention":[139],"contributes":[143],"frontier":[146],"research":[150],"springboard":[153],"future":[155],"benchmark":[156],"designs":[157],"harness":[160],"engineering":[161],"(specifically":[162],"with":[163],"regards":[164],"creating":[166],"lean":[167],"suites)":[169],"optimize":[171],"metrics":[173],"complement":[175],"but":[176],"are":[177],"distinct":[178],"accuracy.":[180]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-18T00:00:00"}
